U.S. patent application number 14/231090 was filed with the patent office on 2015-10-01 for evaluation of compressed sensing in uwb systems with nbi.
This patent application is currently assigned to King Fahd University of Petroleum and Minerals. The applicant listed for this patent is King Fahd University of Petroleum and Minerals. Invention is credited to Saleh Ahmed Alawsh, Ali Hussain Muqaibel.
Application Number | 20150280863 14/231090 |
Document ID | / |
Family ID | 54191839 |
Filed Date | 2015-10-01 |
United States Patent
Application |
20150280863 |
Kind Code |
A1 |
Muqaibel; Ali Hussain ; et
al. |
October 1, 2015 |
EVALUATION OF COMPRESSED SENSING IN UWB SYSTEMS WITH NBI
Abstract
A method of mitigating narrow band interference (NBI) in ultra
wide band (UWB) systems operating around 10 GHz mitigates multiuser
interference from IEEE 802.22 and WiMAX, wherein the multiuser
interference interferes with both trained and blind UWB systems,
with the trained UWB system using pilot symbol assisted modulation.
The method passes a received UWB signal through a band pass filter
(BPF), wherein the BPF is located at a UWB receiver and the UWB
signal is a Hanning modulated pulse centered at 4 GHz frequency.
The method further measures a plurality of test functions,
determines a number of active users, notch filters NBI signals,
based on the determined number of active users, passes the notch
filtered signal through a quadratic programming algorithm, to
perform joint decoding, estimates an arrival of a UWB payload, and
demodulates the UWB payload, based on the estimated arrival of the
UWB payload.
Inventors: |
Muqaibel; Ali Hussain;
(Dhahran, SA) ; Alawsh; Saleh Ahmed; (Dhahran,
SA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
King Fahd University of Petroleum and Minerals |
Dhahran |
|
SA |
|
|
Assignee: |
King Fahd University of Petroleum
and Minerals
Dhahran
SA
|
Family ID: |
54191839 |
Appl. No.: |
14/231090 |
Filed: |
March 31, 2014 |
Current U.S.
Class: |
375/350 |
Current CPC
Class: |
H04B 2001/1063 20130101;
H04B 1/1036 20130101; H04B 1/7101 20130101; H04B 2001/6908
20130101; H04J 11/00 20130101; H04J 11/0026 20130101; H04B
2001/70724 20130101; H04B 1/719 20130101; H04L 1/0048 20130101 |
International
Class: |
H04L 1/00 20060101
H04L001/00 |
Claims
1: A method of mitigating interference by narrow band interference
(NBI) signals in ultra wide band (UWB) systems, comprising:
mitigating multiuser interference from narrowband interferers
operating in a range of 2-11 GHz, wherein the multiuser
interference interferes with a trained UWB system that uses pilot
symbol assisted modulation; passing a received UWB signal through a
band pass filter (BPF), wherein the BPF is located at a UWB
receiver and the received UWB signal is a Hanning modulated pulse;
measuring a plurality of test functions to determine frequencies of
the NBI signals in the received UWB signal; determining a number of
active users; notch filtering the NBI signals, based on the
determined frequencies of the NBI signals and the determined number
of active users; passing the notch filtered signal through a
quadratic programming algorithm, wherein the quadratic programming
algorithm performs joint decoding; estimating an arrival of a UWB
payload; and demodulating the UWB payload, based on the estimated
arrival of the UWB payload.
2: The method of claim 1, wherein the plurality of test functions
are based on matching pursuit compressed sensing and generalized
likelihood ratio test detection.
3: The method of claim 1 further comprising deriving distributions
of pilot group training symbols, values of number of frames per
symbol, and interference threshold to reduce bit error rate when a
plurality of NBI signals interfere with one of the UWB systems,
wherein the one of the UWB systems uses the pilot group training
symbols for channel estimation.
4: The method of claim 1 further comprising detecting and
mitigating more than one NBI signals interfering with the UWB
signal in an UWB channel in a blind UWB system, wherein the blind
UWB system is not based on training sequences.
5: The method of claim 1 wherein the trained UWB system further
combines pilot symbol assisted modulation with direct sequence
spread spectrum and time hopping for signaling.
6: The method of claim 5 further comprising detecting and
mitigating more than one NBI signals interfering with an UWB signal
in an UWB channel in a blind UWB system, wherein the UWB channel
randomly varies from frame to frame, and wherein the UWB signal is
subject to band pass filtering and quadratic programming and
interior point algorithm operation.
7: The method of claim 1 further comprising mitigating the
interference from NBI signals on the UWB systems by deriving values
of NBI bandwidth.
8: The method of claim 1 further comprising mitigating the
interference from NBI signals on UWB pulses by deriving values of
bandwidth of the UWB pulses, type of modulated window, and baud
rate.
9: The method of claim 1 further comprising mitigating interference
from NBI signals on the UWB systems by deriving a burst size.
10: The method of claim 1 further comprising reducing bit error
rate in one of the UWB systems with NBIs, by increasing burst sizes
of sending information, wherein said one of the UWB systems is
based on equally spaced pulses.
11: A non-transitory computer readable medium having instructions
stored therein that when executed by one or more processors cause
the one or more processors to perform a method of mitigating
interference by narrow band interference (NBI) signals in ultra
wide band (UWB) systems, the method comprising: mitigating
multiuser interference from narrowband interferers operating in a
range of 2-11 GHz, wherein the multiuser interference interferes
with a trained UWB system that uses pilot symbol assisted
modulation; passing a received UWB signal through a band pass
filter (BPF), wherein the BPF is located at a UWB receiver and the
received UWB signal is a Hanning modulated pulse; measuring a
plurality of test functions to determine frequencies of the NBI
signals in the received UWB signal; determining a number of active
users; notch filtering the NBI signals, based on the determined
frequencies of the NBI signals and the determined number of active
users; passing the notch filtered signal through a quadratic
programming algorithm, wherein the quadratic programming algorithm
performs joint decoding; estimating an arrival of a UWB payload;
and demodulating the UWB payload, based on the estimated arrival of
the UWB payload.
12: The non-transitory computer-readable medium of claim 11,
wherein the plurality of test functions are based on matching
pursuit compressed sensing and generalized likelihood ratio test
detection.
13: The non-transitory computer-readable medium of claim 11 wherein
the method further comprises deriving distributions of pilot group
training symbols, values of number of frame per symbol, and
interference threshold to reduce bit error rate when a plurality of
NBI signals interfere with one of the UWB systems, wherein the one
of the UWB systems uses the pilot group training symbols for
channel estimation.
14: The non-transitory computer-readable medium of claim 11,
wherein the method further comprises detecting and mitigating more
than one NBI signals interfering with an UWB signal in an UWB
channel in a blind UWB system, wherein the blind UWB system is not
based on training sequences.
15: The non-transitory computer-readable medium of claim 11 wherein
the trained UWB system further combines pilot symbol assisted
modulation with direct sequence spread spectrum and time hopping
for signaling.
16: The non-transitory computer-readable medium of claim 15 wherein
the method further comprises detecting and mitigating more than one
NBI signals interfering with an UWB signal in an UWB channel in a
blind UWB system, wherein the UWB channel randomly varies from
frame to frame, and wherein the UWB signal is subject to band pass
filtering and quadratic programming and interior point algorithm
operation.
17: The non-transitory computer-readable medium of claim 11 wherein
the method further comprises mitigating the interference from NBI
signals on the UWB systems by deriving values of NBI's
bandwidth.
18: The non-transitory computer-readable medium of claim 11 wherein
the method further comprises mitigating the interference from NBI
signals on UWB pulses by deriving values of bandwidth of the UWB
pulses, type of modulated window, and baud rate.
19: The non-transitory computer-readable medium of claim 11,
wherein the method further comprises mitigating interference from
NBI signals on one of the UWB systems by deriving a burst size and
further reducing bit error rate in an UWB system with NBIs, by
increasing burst sizes of sending information, wherein said one of
the UWB systems is based on equally spaced pulses.
20: An apparatus configured to mitigating interference by narrow
band interference (NBI) signals in ultra wide band (UWB) systems,
comprising: a UWB receiver to mitigate multiuser interference from
narrowband interferers operating in a range of 2-11 GHz, wherein
the multiuser interference interferes with a trained UWB system
that uses pilot symbol assisted modulation; a band pass filter
(BPF) to filter a received Harming modulated UWB pulse; measuring
circuitry to measure a plurality of test functions to determine
frequencies of the NBI signals in the received Hanning modulated
UWB pulse and to determine a number of active users; a notch filter
to filter the NBI signals, based on the determined frequencies of
the NBI signals and the determined number of active users; a joint
decoder to perform quadratic programming on the notch filtered
signal; an estimator to estimate an arrival of a UWB payload; and a
demodulator to demodulate the UWB payload, based on the estimated
arrival of the UWB payload.
Description
BACKGROUND
[0001] 1. Field of the Invention
[0002] The present disclosure relates to a method of compressed
sensing in ultra wide band systems with narrow band
interference.
[0003] 2. Description of Related Art
[0004] The "background" description provided herein is for the
purpose of generally presenting the context of the disclosure. Work
of the presently named inventors, to the extent it is described in
this background section, as well as aspects of the description
which may not otherwise qualify as prior art at the time of filing,
are neither expressly or impliedly admitted as prior art against
the present invention.
[0005] Ultra Wide-Band (UWB) technology is a promising a cutting
edge technology in delivering high data rate for short range
wireless communication systems. It is suitable for applications
which need low power such as multi-hop wireless networks. Recently,
UWB technology became a good candidate for short-range indoor
high-resolution positioning systems. UWB signals have the ability
to trade bandwidth for a reduced transmission power. This can be
achieved by sending a very short pulse duration which means very
large bandwidth. UWB signals include not only carrier-less
base-band signals, such as Impulse Radio (IR) or non-sinusoidal
pulses, but also wide-bandwidth signals with carriers, such as
Multi-Band Orthogonal Frequency Division Multiplexing
(MB-OFDM).
[0006] UWB radios are expected to be the next generation of
transmission system that can support high data rate and
power-constrained applications such as wireless sensor and body
area networks. Because of their large bandwidth, two problems
arise, namely the high speed analog-to-digital-conversion (ADC)
required at the receiver side and the coexistence with other
narrowband systems that share the same part of the spectrum. The
two problems can be reduced using compressive sensing (CS).
Narrowband interference (NBI) sources can be licensed or unlicensed
signals with different center frequencies and different
bandwidths.
[0007] Because of their large bandwidth, UWB signals may encounter
some problems especially with high sampling rate required at the
receiver side. Reducing the complexity of UWB receiver is an
important issue. Moreover, coherence existence with other
narrowband systems is a major concern which needs to be addressed
through a proper mechanism. CS is a promising signal processing
solution which can reduce the sampling requirements as well as
avoid the interference with narrowband systems.
[0008] Narrowband Interference (NBI) signals may have two
scenarios. One of them is overlaying the UWB spectrum over a
licensed narrowband signal. The other is the intentional jamming
where someone share part of the UWB spectrum in order to disturb
the existence transmission. See T. H. Stitz, T. Ihalainen, M.
Renfors, "Mitigation of Narrowband Interference in Filter Bank
Based Multicarrier Systems," in IEEE Communications Society, Vol.
7, pp. 3241-3246, 2006, incorporated herein by reference in its
entirety. Because of the power constraint of UWB signals, the
mitigation of the NBI over UWB system is a challenging task.
Although, both narrowband and UWB systems may affect each other,
the interest is on mitigation of the NBI effect on UWB systems.
When the narrowband signals are very strong, they will interfere
with UWB signal and may degrade the system performance. See F.
Dowla F. Nekoogar, and A. Spiridon, "Interference Mitigation in
Transmitted-Reference Ultra-Wideband Receivers," in IEEE Antennas
and Propagation Society, Vol. 4, pp. 1307-1310, June, 2004; H.
Nikookar and R. Prasad, Introduction to Ultra Wideband for Wireless
Communications, Springer, 2009; and C. Wang, M. Ma, R. Ying, and Y.
Yang, "Narrowband Interference Mitigation in DSUWB Systems," in
IEEE Signal Processing, Vol. 17 pp. 429-432, 2010, each
incorporated herein by reference in their entirety.
SUMMARY
[0009] The foregoing paragraphs have been provided by way of
general introduction, and are not intended to limit the scope of
the following claims. The described embodiments, together with
further advantages, will be best understood by reference to the
following detailed description taken in conjunction with the
accompanying drawings.
[0010] One aspect of the disclosure includes a method of mitigating
narrow band interference (NBI) in ultra wide band (UWB) systems
operating around 10 GHz mitigates multiuser interference from IEEE
802.22 and WiMAX, wherein the multiuser interference interferes
with both trained and blind UWB systems, with the trained UWB
system using pilot symbol assisted modulation.
[0011] In another embodiment the method passes a received UWB
signal through a band pass filter (BPF), wherein the BPF is located
at a UWB receiver and the UWB signal is a Hanning modulated pulse
centered at 4 GHz frequency.
[0012] In another embodiment the method measures a plurality of
test functions, determines a number of active users, notch filters
NBI signals, based on the determined number of active users, passes
the notch filtered signal through a quadratic programming
algorithm, to perform joint decoding, estimates an arrival of a UWB
payload, and demodulates the UWB payload, based on the estimated
arrival of the UWB payload.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The disclosure will be better understood from reading the
description which follows and from examining the accompanying
figures. These are provided solely as non-limiting examples of
embodiments. In the drawings:
[0014] FIG. 1 shows the main topics of the present disclosure;
[0015] FIG. 2 shows a FCC spectral mask for UWB indoor
communication systems;
[0016] FIG. 3 shows time and frequency domains for the Gaussian,
first, and second derivative Gaussian pulses;
[0017] FIG. 4 shows FCC spectral mask for UWB indoor communication
systems with narrowband systems;
[0018] FIG. 5 shows an autocorrelation receiver (AcR);
[0019] FIG. 6 shows a system architecture of CS based-UWB
system;
[0020] FIG. 7 shows a block diagram of the proposed system
model;
[0021] FIG. 8 shows impulse response and the power delay profile of
CMI;
[0022] FIG. 9 shows matching pursuit for signal structure
estimation;
[0023] FIG. 10 shows block diagram for the I-UWB system;
[0024] FIG. 11 shows implemented I-UWB signaling scheme;
[0025] FIG. 12 shows I-UWB receiver with GLRT detector;
[0026] FIG. 13 shows distribution of pulses transmitted over
time--Frames and chips are synchronized for all users;
[0027] FIG. 14 shows flowchart for the main steps of the UWB system
with training;
[0028] FIG. 15 shows BER as a function of Np1 and Np2;
[0029] FIG. 16 shows BER as a function of Np1 and Np3;
[0030] FIG. 17 shows BER as a function of Np2 and Np3;
[0031] FIG. 18 shows BER with different frame number;
[0032] FIG. 19 shows BER as a function of the interference
threshold;
[0033] FIG. 20 shows system performance for different NBI;
[0034] FIG. 21 shows performance for licensed NBIs;
[0035] FIG. 22 shows system performance when 0, 2, 3, 5, 10, 15, 20
and 25 users are active;
[0036] FIG. 23 shows throughput of DS-TH coding for different
number of interfering users;
[0037] FIG. 24 shows signal paths taken by the UWB-IR and the NBI
signals;
[0038] FIG. 25 shows Hanning window in time and frequency
domain;
[0039] FIG. 26 shows Hanning modulated pulse and its power
spectrum;
[0040] FIG. 27 shows frame format for the bursty data
transmission;
[0041] FIG. 28 shows correlator receiver with digital notch
filter;
[0042] FIG. 29 shows time and frequency domain representations of
the BPF;
[0043] FIG. 30 shows frequency domain for different test functions
selected randomly;
[0044] FIG. 31 shows location of the k.sup.th nonzero samples;
[0045] FIG. 32 shows flow chart for the main steps of the blind
system;
[0046] FIG. 33 shows performance of a partial band interferer for
different burst size;
[0047] FIG. 34 shows performance for different UWB modulated pulses
jammed by a partial band interferer;
[0048] FIG. 35 shows performance of a partial band interferer with
different bandwidth;
[0049] FIG. 36 shows performance of 2 partial bands interferer with
different bandwidth;
[0050] FIG. 37 shows BER performance as a function of the NBI's
bandwidth;
[0051] FIG. 38 shows BER performance in the presence of licensed
NBIs;
[0052] FIG. 39 shows BER performance when changing the bandwidth of
the UWB modulated pulse;
[0053] FIG. 40 shows BER performance for one partial band
interferer with different baud rate; and
[0054] FIG. 41 shows a computer system upon which an embodiment of
the present invention may be implemented.
DETAILED DESCRIPTION
[0055] The description provided here is intended to enable any
person skilled in the art to understand, make and use this
invention. Various modifications to the disclosed embodiments will
be readily apparent to those skilled in the art, and the general
principals defined herein may be applied to these modified
embodiments and applications without departing from the scope of
this invention. In each of the embodiment, the various actions
could be performed by program instruction running on one or more
processors, by specialized circuitry or by a combination of both.
Moreover, the invention can additionally be considered to be
embodied, entirely or partially, within any form of computer
readable carrier containing instructions that will cause the
executing device to carry out the technique disclosed herein. The
present invention is thus, not intended to be limited to the
disclosed embodiments, rather it is be accorded the widest scope
consistent with the principles and features disclosed herein.
[0056] Details of functions and configurations well known to a
person skilled in this art are omitted to make the description of
the present invention clear. The same drawing reference numerals
will be understood to refer to the same elements throughout the
drawings.
[0057] The present disclosure utilizes CS as a mean to mitigate NBI
in UWB systems. The mitigation is studied in both trained and blind
systems. CS is used to detect and remove NBI effects as well as
reduce the sampling rate at the receiver side. The Bit Error Rate
(BER) performance in both systems is examined by applying different
NBIs, with different center frequencies and bandwidths.
[0058] In the present disclosure, both trained and blind systems
have been examined in mitigating the effect of the NBI in UWB
system using CS as well as reduce the speeds of the ADC.
[0059] In trained systems, three training pilot groups are
required. The system is first trained to estimate the NBI with no
UWB transmission, then the UWB signal space is estimated and
finally the channel impulse response is extracted. This research
optimizes UWB systems with CS to mitigate the effect of NBI through
efficient assignments of pilot symbols among the required training.
Extensive simulation is conducted to investigate the optimum
distribution of the pilot symbols that enhances the system's
bit-error-rate (BER) performance. Based on this investigation, a
better understanding of the effect of the NBI's characteristics on
UWB systems with CS is drawn. Furthermore, the impact of the number
and the type of the NBI sources is also evaluated. The impact of
multiple users on the system behavior is considered. It is shown
that the number of pilot symbols in the third group is directly
proportional to the performance; hence once the minimum number of
pilot symbols for first two groups is met, the extra symbols should
be assigned to get information about the channel.
[0060] In blind UWB systems, the present disclosure investigates
the problem in bursty application such as wireless sensor network.
The receiver does a joint decoding of the time of arrival and the
data bits using quadratic programing (QP). A correlator receiver
combined with digital notch filter is applied. The basis functions
in the correlators are designed to be highly frequency selective
through windowing technique. Hence only few measurements are
corrupted by the interferer. Here, the present disclosure studies
the performance of different licensed and unlicensed NBIs and the
present disclosure extends the mitigation technique to suppress the
effect of multiple NBIs. The present disclosure discusses the
system behavior under different NBI's and UWB signal bandwidths.
Furthermore, the present disclosure evaluates the effect of the
burst size, the type of the modulated window and the baud rate on
the performance. For a partial band jammer, slight enhancement is
achieved when doubling the bandwidth. In the dual-band jammer case,
the enhancement due to the mitigation against the jammers is
evident. For the considered scenarios, the present disclosure
demonstrates that the BER is a strong function of the NBI's
bandwidth while it is a weak function of the pulse shape. As the
UWB signal's bandwidth increases, the number of the notched
measurements lessens and the present disclosure preserves the
important information about the transmitted pulse.
[0061] Details are given in how to generate UWB pulses as well as
UWB systems pros and cons. The issue of spectrum sharing between
UWB systems and different narrowband systems is also discussed. The
present disclosure provides channel modeling and narrowband
interferers modeling. In addition, compressive sensing framework
and how it is utilized to reconstruct sparse signals are
illustrated with details. The IEEE802.11.4a UWB channel model is
discussed in the present disclosure and also different interferers
models are presented. Furthermore, the present disclosure discusses
mitigation problem in training UWB systems. Those systems use pilot
symbol assisted modulation combined with direct sequence spread
spectrum and time hopping for signaling. The mitigation process
focuses on the detection and elimination of the most significant
NBI components in the Discrete Cosine Transform (DCT) or Discrete
Fourier Transform (DFT) domain. The present disclosure studies the
mitigation of the narrowband interference in blind systems. The
center frequency of the interfering source and the bandwidth of UWB
signal as well as other factors play an important role in the
mitigation process. The present disclosure provides summary of
findings, and the recommendation for future.
[0062] Both trained and blind systems have been investigated for
mitigating the NBI in UWB system using compressive sensing. The NBI
sources were assumed to be licensed and unlicensed signals with
different center frequencies and different bandwidths. [0063] In
trained systems, three training pilot groups are required. The
present disclosure investigates the effect of each pilot group
symbols and obtains the distribution that optimizes the BER
performance. The present disclosure shows that the first and the
last pilot group symbols are very important. Communications can be
achieved without using the second group. Though, the performance
can be enhanced if the second pilot group symbols are used. It is
also shown that the third group is the most dominant one. Hence
extra symbols should be assigned to estimate the channel. [0064]
Moreover, the trained system performance is further examined in the
presence of multiuser interference when other users share the same
channel. Throughput of the system is evaluated in the presence of
multiuser interference in addition to the NBI. [0065] In blind UWB
systems, the present disclosure extends the mitigation technique in
A. Oka and L. Lampe, "Compressed Sensing Reception of Bursty UWB
Impulse Radio is Robust to Narrow-Band Interference," in IEEE
Global Telecommunications, December, 2009, incorporated herein by
reference in its entirety, to mitigate the effect of two NBIs. For
the considered SIR, the present disclosure concludes that the 2
partial bands NBI has less effect on the performance than the
partial band jammer since the power at the effecting bands are so
low compared with that of the partial band NBI.
[0066] The present disclosure examines the effect of the NBI's
bandwidth and the UWB signal's bandwidth on system performance.
Those parameters are related to the mitigation process. For the
considered scenarios, the present disclosure demonstrates that the
BER is a strong function of the NBI's bandwidth and of the UWB
signal's bandwidth. In addition, the present disclosure studies
different parameters that may affect the system performance such as
the burst size, the type of the modulated window and the baud rate.
The present disclosure shows that sending the information using
large burst size outperforms sending it using small burst size
since the probability of making an error in one bit decreases as
the burst size increases. The present disclosure also proves that
the BER is a weak function of the considered modulated window.
Additionally, the performance is highly affected when the NBI's
center frequency is shifted to the center frequency of the
transmitted pulse.
[0067] Compressive sensing is a promising signal processing
technique used to reduce the sampling rate at the receiver as well
as reduce the effect of the NBI on the UWB systems. As depicted in
FIG. 1, the present disclosure includes three main topics, UWB, NBI
and CS. The present disclosure provides the reader with technical
background related to UWB signals, NBI, and CS techniques.
[0068] UWB signals are usually defined as any signal that occupies
bandwidth greater than 500 MHz or has a fractional bandwidth,
B.sub.f, greater than 0.2. The fractional bandwidth is defined as
the ratio between the signal bandwidth (BW) and its center
frequency f.sub.c as given by:
B f = BW f c = f H - f L ( f H + f L ) / 2 ( 1 - 1 )
##EQU00001##
where f.sub.L is the lower band, and f.sub.H is the upper band in
the frequency spectrum at -10 dB points. The approved bands for
indoor and outdoor UWB communications have a Power Spectral Density
(PSD) lower than part 15 FCC limits which is -41.3 dB/MHz in the
range of 3.1-10.6 GHz, as shown in FIG. 2. See Y. D. Alemseged and
K. Witrisal, "Two Stage Narrowband Interference Mitigation for
Transmitted Reference UWB Systems," in IEEE International Symposium
on Personal, Indoor and Mobile Radio Communications, PIMRC, Athens,
Greek, September 2007; X. Li and K. Kwak, "NBI Suppression UWB
System Based on Novel Nonlinear Chirp Pulses," in IEEE
Communications and Information Technology, pp. 1167-1170 September,
2009; and G. Zhao, M. Jin, W. Fan, "A Low-complexity NBI
Suppression Algorithm in UWB Systems," in IEEE Communication
Technology, November, 2006, each incorporated herein by reference
in their entirety.
[0069] UWB signals have the ability to trade bandwidth for a
reduced transmission power. The idea is based on sending a very
short pulse duration which improves the immunity to multipath. The
bandwidth is very large and according to Shannon theorem the data
rate will also be large. UWB systems are proposed for many
applications such as wireless sensor networks with low cost and low
complexity. See A. Oka and L. Lampe, "A Compressed Sensing Receiver
for Bursty Communication with UWB Impulse Radio," in Intl. Conf. on
Ultra-Wideband, pp. 279-284, September 2009; M. Ovtcharov, V.
Poulkov, G. Iliev and Z. Nikolova, "Narrowband interference
suppression for IEEE UWB channels," The Fourth Intern. Conf. on
Digital Telecommunications (ICDT 2009), pp. 43-47, Colmar, France,
July 20-25, 2009; and P. Zhang, Z. Hu, R. Qiu, and B. Sadler, "A
compressed Sensing Based Ultra-Wideband Communication System," in
Proc. IEEE International Conference on Communications ICC, pp. 1-5,
2009, each incorporated herein by reference in their entirety. One
of the benefits of low-power spectral density is a low probability
of detection. Therefore UWB signals are suitable for military
applications. Another benefit is the long battery life/lighter
batteries for UWB devices.
[0070] Table 1 also depicts the corresponding Effective Isotropic
Radiated Power (EIRP), and the frequencies for the indoor and the
outdoor UWB systems.
TABLE-US-00001 TABLE 1 Emission limits for indoor and outdoor
systems in EIRP (H. Nikookar and R. Prasad, Introduction to Ultra
Wideband for Wireless Communications, Springer, 2009, incorporated
herein by reference) Emission limit for UWB Indoor Outdoor
Frequency (GHz) EIRP (dBm/MHz) EIRP (dBm/MHz) 0.96-1.61 -75.3 -75.3
1.61-1.9 -53.3 -63.3 1.9-3.1 -51.3 -61.3 3.1-10.6 -41.3 -41.3
[0071] The choice of the UWB waveforms depends on many factors. The
most common waveform is the Gaussian pulse and its higher
derivatives. The higher derivatives are more favorable because of
their low DC content. The time and the frequency domain for the
first, and the second derivatives Gaussian pulses are shown in FIG.
3. Orthogonal Hermite or modified Hermite pulses, Legandre pulses
and Prolate spheroidal functions are also among several proposed
UWB waveforms. The Gaussian pulse is expressed mathematically
as:
p ( t ) = 1 2 .pi..sigma. 2 - t 2 2 .sigma. 2 ( 1 - 2 )
##EQU00002##
[0072] The first and the second derivative of the Gaussian pulse
are
p ' ( t ) = p ( t ) t = - t .sigma. 2 2 .pi..sigma. 2 - t 2 2
.sigma. 2 ( 1 - 3 ) p '' ( t ) = 2 p ( t ) t 2 = 1 .sigma. 2 2
.pi..sigma. 2 [ t 2 .sigma. 2 - 1 ] - t 2 2 .sigma. 2 ( 1 - 4 )
##EQU00003##
[0073] The energy of such pulses extends over large bandwidth. FIG.
3 shows the Gaussian pulse in time and frequency domains where the
amplitudes are normalized. The corresponding first and second
derivative Gaussian pulses are also plotted in both domains. The
graph as well indicates that there are low DC components for the
Gaussian derivative pulses. Next, in the present disclosure the
second derivative Gaussian pulse is used unless otherwise is
specified.
[0074] There are many systems that share the UWB frequency
spectrum, see FIG. 4. Those systems can be categorized into two
types. Systems having fixed or assigned frequency range are called
licensed systems. Systems which don't have assigned frequency
spectrum are known as unlicensed systems. The licensed systems are
the most important interference sources for the UWB signals
including WiMAX, WLAN, and Bluetooth.
[0075] FIG. 4 illustrates many narrowband systems that share the
UWB spectrum including, GPS, Personal Communications Service (PCS),
the Industrial, Scientific, and Medical band (ISM), WLAN, and
intentional jammers. Bluetooth and IEEE802.11b WLAN are two
standards which use the 2.4 GHz (ISM) band.
[0076] According to the sampling theorem, the minimum required
sampling frequency for accurate detection is twice the maximum
frequency of the transmitted signal. When acquiring a high
frequency signal, a very high speed ADC is needed. Those ADCs are
difficult to design.
[0077] The problem becomes worse with channel distortion and
Inter-Symbol Interference (IS I) which appears when a high data
rate goes over a frequency selective channel in such case an
equalizer is employed. High data rate requirements will definitely
affect the receiver design i.e. more complex Digital Signal
Processing (DSP) components are required.
[0078] CS technique has been used to reduce the speed of ADC into a
sub-Nyquist rate in UWB systems which can be designed and
implemented. This could be achieved if the UWB signal is sparse
i.e. has few nonzero terms. See A. Gomaa and N. Al-Dhahir, "A
Compressive Sensing Approach to NBI Cancellation in Mobile OFDM
Systems," in IEEE Communications Society, December, 2010; A. Gomaa
and N. Al-Dhahir, "A Sparsity-Aware Approach for NBI Estimation in
MIMO-OFDM," in IEEE Transactions on Wireless Communications, Vol.
10, No. 6, pp. 1854-1862 June, 2011; Z. Wang, G. R. Arce, J. L.
Paredes, and B. M. Sadler, "Compressed Detection for Ultra-Wideband
Impulse Radio," in Proc. 8th IEEE Intl. Workshop SPA WC, June 2007;
Z. Wang, G. R. Arce, B. M. Sadler, J. L. Paredes, S. Hoyos, and Z.
Yu, "Compressed UWB Signal Detection with Narrowband Interference
Mitigation," in IEEE Int. Conf on UWB, Vol. 2 pp. 157-160,
September, 2008; P. Zhang and R. C. Qiu, "Wireless Tomography, Part
III: Compressed Sensing for Ultra-Wideband Signals," in IEEE
Waveform Diversity and Design, pp. 35-39, August 2010, each
incorporated herein by reference in their entirety. More details
about CS are provided in the present disclosure.
[0079] First the present disclosure describes problems related to
the mitigation of NBI in UWB systems and utilization of CS to UWB
systems. Also, the present disclosure addresses the problem of NBI
in UWB systems based on CS.
[0080] Since UWB systems have a wide bandwidth; they may coexist
with other licensed or unlicensed narrowband systems. Generally,
wideband systems like Direct Sequence (DS) systems are capable of
interference suppression. The degree of the suppression may not be
satisfactory when the spreading gain is limited and a very strong
NBI is presented. Wang et al., see C. Wang, M. Ma, R. Ying, and Y.
Yang, "Narrowband Interference Mitigation in DS-UWB Systems," in
IEEE Signal Processing, Vol. 17 pp. 429-432, 2010, incorporated
herein by reference in its entirety, proposed DS-UWB system as an
extension to the code aided interference suppression which uses the
linear minimum mean-square error algorithm for multiuser detection.
See H. V. Poor and X. Wang, "Code-aided Interference Suppression
for DS/CDMA Communications--Part I: Interference Suppression
Capability," in IEEE Trans. Commun., Vol. 45, No. 9, pp. 1101-1111,
September 1997, incorporated herein by reference in its entirety. A
considerable enhancement in the NBI suppression capability is
achieved by introducing a new type of spreading sequence method. In
case of very high data rate application, inter-chip interference is
present because of the non-sharply peak autocorrelation of the
sequence. Consequently an equalizer needs to be implemented which
increases the receiver complexity. For such application, the
equalizer needed was avoided with spreading sequence that has
sharply peak autocorrelation. See C. Wang, R. Ying, Y. Wei, and Y.
Yang, "Spreading Sequence Selection Scheme For NBI Suppression in
DS-UWB System," in IEEE Ultra wideband and Ultra short Impulse
Signals, pp. 186-188, September, 2010, incorporated herein by
reference in its entirety.
[0081] The performance of DS pulse amplitude modulation UWB system
with IEEE802.11a WLAN as NBI source was studied by see X. Li and K.
Kwak, "NBI Suppression UWB System Based on Novel Nonlinear Chirp
Pulses," in IEEE Communications and Information Technology, pp.
1167-1170 September, 2009; and G. Zhao, M. Jin, W. Fan, "A
Low-complexity NBI Suppression Algorithm in UWB Systems," in IEEE
Communication Technology, November, 2006, each incorporated herein
by reference in its entirety.
[0082] The negative impact of NBI can be reduced by proper pulse
shaping. In X. Li and K. Kwak, "NBI Suppression UWB System Based on
Novel Nonlinear Chirp Pulses," in IEEE Communications and
Information Technology, pp. 1167-1170 September, 2009, incorporate
herein by reference nonlinear chirp pulses were used to create UWB
pulses and decrease the NBI. The pulses are flexible in the design
and have low complexity.
[0083] Another method to reject the NBI is based on Singular Value
Decomposition (SVD). To reduce the complexity of SVD, the input
data is segmented to several groups, every group is rearranged in
special way where the matrix dimension is reduced. At the end, SVD
is applied on every matrix; consequently the complexity is reduced
without clearly penalizing the BER.
[0084] Data can be used to modulate a polarity of the "data" pulse
with respect to a "reference" pulse. In Auto-Correlation Receiver
(AcR) shown in FIG. 5, the received reference signal is delayed and
then correlated with the data signal. The amount of the delay in an
AcR is matched to the delay between reference and data pulse at the
transmitter. The overall system is usually referred to as
Transmitted-Reference (TR) AcR.
[0085] Although no channel estimation is required, the receiver
front-end is open to undesirable noisy signals. On the darker side
also, AcR suffers from ISI when the data rate is increased.
Compared with coherent receiver, it is robust against the multipath
propagation at low complexity. A data model; proposed by K.
Witrisal and Y. D. Alemseged, "Narrowband interference mitigation
for Differential UWB systems," in IEEE Asilomar Conference on
Signals, Systems, and Computers, Monterey, Calif., November 2005,
incorporated herein by reference in its entirety, was applied
effectively for detection and NBI alleviation by combining several
AcR channels linearly.
[0086] Narrowband interference suppression in F. Dowla F. Nekoogar,
and A. Spiridon, "Interference Mitigation in Transmitted-Reference
Ultra-Wideband Receivers," in IEEE Antennas and Propagation
Society, Vol. 4, pp. 1307-1310, June, 2004, incorporated herein by
reference is accomplished by a modified feedback loop mechanism. In
this approach, feedback delay can be controlled to extract
information from a number of previous transmitted pulses. The
Signal-to-Interference Ratio (SIR) was improved as the number of
involved pulses increased giving a cleaner pulse.
[0087] Dang and Van Der Veen, in Q. Dang and A. van der Veen,
"Narrowband Interference Mitigation for a Transmit-Reference
Ultra-Wideband Receiver," in 14th European Signal Processing
Conference, 2006, incorporated herein by reference investigated the
mitigation problem in high data rate application. See Q. Dang and
A. van der Veen, "Narrowband Interference Mitigation for a
Transmit-Reference Ultra-Wideband Receiver," in 14th European
Signal Processing Conference, 2006, incorporated herein by
reference in its entirety. By oversampling, the transmitted symbols
can be detected by gathering the energy of all the multipath
arrivals. At certain range of SIR, it is possible to mitigate the
NBI, though the model becomes invalid when the NBI is too strong.
In this case, the NBI needs to be filtered before entering the
AcR.
[0088] In Y. D. Alemseged and K. Witrisal, "Two Stage Narrowband
Interference Mitigation for Transmitted Reference UWB Systems," in
IEEE International Symposium on Personal, Indoor and Mobile Radio
Communications, PIMRC, Athens, Greek, September 2007, incorporated
herein by reference NBI mitigation is achieved through a system
made of two stages, namely: an adaptive NBI cancellation and a
linear combiner. The scheme uses a canceller circuit based on feed
forward approach. The interference is filtered out through tunable
analog Band-Pass Filter (BPF) and subtracted from the received
signal before the correlator. The output of the correlator is
feedback to the canceller which adjusts the canceller parameters
until minimal interference is observed. In case of too strong NBI
or a second interferer is presented, a linear combiner is used to
reject any leakage. The AcR uses a method based on SVD to identify
the spectral location of the NBI. In Y. D. Alemseged, H. Harada,
and K. Witrisal, "Detection and Identification of NBI for
Multichannel UWB Autocorrelation Receivers," in IEEE Wireless
Communications and Networking, May, 2009, incorporated herein by
reference a method of threshold comparator based on the SVD of a
reduced rank of the received data matrix is used for NBI detection.
See Y. D. Alemseged, H. Harada, and K. Witrisal, "Detection and
Identification of NBI for Multichannel UWB Autocorrelation
Receivers," in IEEE Wireless Communications and Networking, May,
2009, incorporated herein by reference in its entirety. Then an
approach analogous to DFT calculation is followed for the NBI
center frequency identification.
[0089] Filtering is also used by other researchers for NBI
cancellation. A technique based on multicarrier called
amplitude-phase adaptive sine-modulated/cosine-modulated filter
bank equalizer was applied by T. H. Stitz, T. Ihalainen, M.
Renfors, "Mitigation of Narrowband Interference in Filter Bank
Based Multicarrier Systems," in IEEE Communications Society, Vol.
7, pp. 3241-3246, 2006, incorporated herein by reference. It was
used to mitigate the distortion on an OFDM sub-channel by a NBI
located at an OFDM adjacent sub-channel. Ovtcharov et al., in M.
Ovtcharov, V. Poulkov, G. Iliev and Z. Nikolova, "Narrowband
interference suppression for IEEE UWB channels," The Fourth Intern.
Conf. on Digital Telecommunications (ICDT 2009), pp. 43-47, Colmar,
France, July 20-25, 2009, incorporated herein by reference proposed
a scheme using complex adaptive digital filtering. The filter
monitors the NBI's frequency regularly based on the least mean
square algorithm to adjust its frequency to match the center
frequency of the NBI. The approach can eliminate the NBI effects;
however the performance becomes worse for SIR greater than 0 dB
because the NBI filter introduces amplitude and phase
distortion.
[0090] Apart from filtering, the NBI problem is solved as well by
introducing a pulse that meets the Federal Communication Committee
(FCC) spectrum mask and has spectral nulls at frequencies of NBI in
the UWB spectrum. See Y. Wang, X. Dong, and I. J. Fair, "A method
for spectrum shaping and NBI suppression in UWB communications,"
Proc. In IEEE Int. Conf. Commun. (ICC '06), Istanbul, Turkey, June
2006; Z. Wang, G. R. Arce, B. M. Sadler, J. L. Paredes, and X. Ma,
"Compressed Detection for Pilot Assisted Ultra-Wideband Impulse
Radio," in Proc. IEEE Int. Conf. on Ultra-Wideband, Singapore,
September 2007; Y. Wang, X. Dong, I. J. Fair, "Spectrum Shaping and
NBI Suppression in UWB Communications," in IEEE transactions on
wireless communications, Vol. 6, issue 5, pp. 1944-1952, May 2007;
and G. Zhang, Y. Dai, X. Zhang, Y. Lv and L. Chen, "Design and
Implementation of UWB Pulse with Multiple Narrow-Band Interferences
Mitigation," in IEEE Consumer Electronics, Communications and
Networks, pp. 1154-1157, April 2011, each incorporated herein by
reference in their entirety. The transmitted pulse for this
approach is represented by a coded based Gaussian monocycle pulse
where the value of each code bit gives the weighting coefficient of
each monocycle pulse. The resulting pulse is the sum of weighted
and overlapping Gaussian monocycles. Thus the shape of the
resulting spectrum is determined by both the Fourier transform of
the basic Gaussian monocycle pulse and the spectrum of the intended
codeword. Even though, a set of multi-variables nonlinear equations
has to be solved to get the codeword. The approach can be applied
for different modulation techniques such as pulse position
modulation, and OFDM-UWB and IR UWB.
[0091] In G. Zhang, Y. Dai, X. Zhang, Y. Lv and L. Chen, "Design
and Implementation of UWB Pulse with Multiple Narrow-Band
Interferences Mitigation," in IEEE Consumer Electronics,
Communications and Networks, pp. 1154-1157, April 2011,
incorporated herein by reference the FCC mask was realized through
combining multiple Gaussian derivative pulses (1.sup.st-15.sup.th)
with proper scaling. The resulting pulse is added to a similar one
with a certain time delay. The final resultant pulse meets the FCC
PSD, bandwidth mask, and has multiple nulls to mitigate the NBI at
certain frequencies. The nulls can be controlled by changing the
time delay. The pulses designed in Y. Wang, X. Dong, and I. J.
Fair, "A method for spectrum shaping and NBI suppression in UWB
communications," Proc. in IEEE Int. Conf. Commun. (ICC '06),
Istanbul, Turkey, June 2006, incorporated herein by reference and
Z. Wang, G. R. Arce, J. L. Paredes, and B. M. Sadler, "Compressed
Detection for Ultra-Wideband Impulse Radio," in Proc. 8th IEEE
Intl. Workshop SPAWC, June 2007, incorporated herein by reference
are suitable only for single NBI whereas in G. Zhang, Y. Dai, X.
Zhang, Y. Lv and L. Chen, "Design and Implementation of UWB Pulse
with Multiple Narrow-Band Interferences Mitigation," in IEEE
Consumer Electronics, Communications and Networks, pp. 1154-1157,
April 2011, incorporated herein by reference they have the ability
to suppress multiple NBI with low implementation cost and low
power.
[0092] The NBI can be reduced by exploiting the UWB signals
immunity to the multipath effect based on interference Selection
Diversity (SD) in Single-Input-Multiple-Output (SIMO) system. In
contrast to the conventional SD, the receiver selects the weakest
signal and feeds it to the demodulator. Since UWB signal power over
all antennas is almost constant, while the interfering power varies
independently from one antenna to another when the multipath angle
spread is high, any increase in the received power is related to a
superior NBI power. See J. Ibrahim, R. M. Buehrer, "NBI Mitigation
for UWB Systems Using Multiple Antenna Selection Diversity," in
IEEE Transactions on Vehicular Technology, Vol. 56, No. 4, pp. 23
63-2374, July 2007, incorporated herein by reference in its
entirety. Better performance was realized through doubling the
number of receiving antennas. In addition, this approach does not
need fast ADC, synchronization and knowledge of the location or the
statistical characteristics of the NBI signal.
[0093] The present disclosure has discussed several methods to
solve the NBI problem. Given that the promised solution is the CS;
the present disclosure concentrates on the literature that exploits
CS for UWB systems.
[0094] Even when no interference is assumed, compressive sensing
techniques are used to reduce the sampling rate to sub-Nyquist rate
and hence results in low ADC requirements. Researchers on UWB
systems used CS in training systems, while others applied it for
blind system. See B. Jin, S. Zhang, J. Pan, and K. Lin,
"Sub-Nyquist sampling based narrowband interference mitigation in
UWB impulse radio," Electronics Letters, Vol. 48, no. 15, pp.
963-964, Jul. 19, 2012; and Z. Wang, G. R. Arce, B. M. Sadler, J.
L. Paredes, and X. Ma, "Compressed Detection for Pilot Assisted
Ultra-Wideband Impulse Radio," in Proc. IEEE Int. Conf. on
Ultra-Wideband, Singapore, September 2007, each incorporated herein
by reference in their entirety. For the case of impulse radio
(I-UWB), CS was applied by many researchers. See A. Oka and L.
Lampe, "Compressed Sensing Reception of Bursty UWB Impulse Radio is
Robust to Narrowband Interference," in IEEE GLOBECOM,
November-December 2009, incorporated herein by reference in its
entirety. Other researchers applied CS for UWB systems in bursty
applications such as wireless sensor networks. See B. Jin, S.
Zhang, J. Pan, and K. Lin, "Serial compressed sensing communication
system for UWB impulse radio in bursty applications," Electronics
Letters, Vol. 47, no. 6, pp. 412-414, Mar. 17, 2011, incorporated
herein by reference in its entirety.
[0095] A serial system structure; shown in FIG. 6; was proposed by
P. Zhang, Z. Hu, R. Qiu, and B. Sadler, "A compressed Sensing Based
Ultra-Wideband Communication System," in Proc. IEEE International
Conference on Communications ICC, pp. 1-5, 2009, incorporated
herein by reference. The system is suitable for I-UWB
communications, which is sparse in time domain. An UWB signal is
transmitted by supplying a sparse bit stream through an UWB pulse
generator and a pre-coding filter. After the channel, a low-rate
ADC samples the received signal which is then processed by a
recovery algorithm.
[0096] Based on the CS UWB Single-Input-Single-Output (SISO) system
in P. Zhang, Z. Hu, R. Qiu, and B. Sadler, "A compressed Sensing
Based Ultra-Wideband Communication System," in Proc. IEEE
International Conference on Communications ICC, pp. 1-5, 2009,
incorporated herein by reference a Multiple-Input-Multiple-Output
(MIMO) system was proposed by P. Zhang and R. C. Qiu, "Wireless
Tomography, Part III: Compressed Sensing for Ultra-Wideband
Signals," in IEEE Waveform Diversity and Design, pp. 35-39, August
2010, incorporated herein by reference. The method in P. Zhang and
R. C. Qiu, "Wireless Tomography, Part III: Compressed Sensing for
Ultra-Wideband Signals," in IEEE Waveform Diversity and Design, pp.
35-39, August 2010, incorporated herein by reference is different
from the method in P. Zhang, Z. Hu, R. Qiu, and B. Sadler, "A
compressed Sensing Based Ultra-Wideband Communication System," in
Proc. IEEE International Conference on Communications ICC, pp. 1-5,
2009, incorporated herein by reference in that the UWB channel was
modeled with pulse distortion. Though, the total samples/sec at the
receiver is almost the same, the sampling rate is reduced at each
receiver branch compared with P. Zhang, Z. Hu, R. Qiu, and B.
Sadler, "A compressed Sensing Based Ultra-Wideband Communication
System," in Proc. IEEE International Conference on Communications
ICC, pp. 1-5, 2009, incorporated herein by reference system.
[0097] A CS based Maximum Likelihood Sequence Estimation (MLSE)
correlator receiver was proposed in A. Oka and L. Lampe, "A
Compressed Sensing Receiver for Bursty Communication with UWB
Impulse Radio," in Intl. Conf on Ultra-Wideband, pp. 279-284,
September 2009, incorporated herein by reference. It consists of an
analog front-end which contains a bank of correlators with test
functions, low ADC, and DSP back-end based on a computationally
efficient Quadratic Program (QP) reconstruction. The number of
correlators is smaller than the required by Shannon-Nyquist
sampling theorem.
[0098] To support burst applications see B. Jin, S. Zhang, J. Pan,
and K. Lin, "Serial compressed sensing communication system for UWB
impulse radio in bursty applications," Electronics Letters, Vol.
47, no. 6, pp. 412-414, Mar. 17, 2011; and B. Jin, S. Zhang, J.
Pan, and K. Lin, "Sub-Nyquist sampling based narrowband
interference mitigation in UWB impulse radio," Electronics Letters,
Vol. 48, no. 15, pp. 963-964, Jul. 19, 2012, each incorporated
herein by reference suggested the use of a pre-coding filter
followed by UWB pulse generator.
[0099] Generalized Likelihood Ratio Test (GLRT) detector based on
compressive measurements, where the received signal was projected
onto a random digital basis, was derived by see Z. Wang, G. R.
Arce, J. L. Paredes, and B. M. Sadler, "Compressed Detection for
Ultra-Wideband Impulse Radio," in Proc. 8th IEEE Intl. Workshop
SPAWC, June 2007, incorporated herein by reference. CS was applied
for channel estimation. The complexity of the system was reduced by
taking advantage of the sparsity of the received signal. Two
compressive measurements were applied. The first one was based on
random basis as in Z. Wang, G. R. Arce, J. L. Paredes, and B. M.
Sadler, "Compressed Detection for Ultra-Wideband Impulse Radio," in
Proc. 8th IEEE Intl. Workshop SPAWC, June 2007, incorporated herein
by reference while the other was constructed based on the subspace
signal structure estimated by Matching Pursuit (MP) algorithm. For
training, pilot symbol assisted modulation was used to provide
information about the channel, and to estimate the signal
structure.
[0100] Applying CS technique, as mentioned, was mainly used to
reduce the sampling rate. Few researches have investigated the
possibility of NBI mitigation in UWB systems by utilizing CS.
Similar studies utilized CS in NBI mitigation for OFDM systems. An
algorithm based on CS technique was proposed in A. Gomaa and N.
Al-Dhahir, "A Compressive Sensing Approach to NBI Cancellation in
Mobile OFDM Systems," in IEEE Communications Society, December,
2010; and A. Gomaa and N. Al-Dhahir, "A Sparsity-Aware Approach for
NBI Estimation in MIMO-OFDM," in IEEE Transactions on Wireless
Communications, Vol. 10, No. 6, pp. 1854-1862 June, 2011, each
incorporated herein by reference to estimate and mitigate the NBI
signals undergoing fast and frequency-selective fading channels in
OFDM systems. Before channel estimation, NBI is estimated and
cancelled. Both references studied the case of asynchronous jamming
where the NBIs and the desired signals do not coincide (some
frequency offset).
[0101] Wang et al. in Z. Wang, G. R. Arce, B. M. Sadler, J. L.
Paredes, S. Hoyos, and Z. Yu, "Compressed UWB Signal Detection with
Narrowband Interference Mitigation," in IEEE Int. Conf. on UWB,
Vol. 2 pp. 157-160, September, 2008, incorporated herein by
reference extended the subspace detection method in Z. Wang, G. R.
Arce, B. M. Sadler, J. L. Paredes, and X. Ma, "Compressed Detection
for Pilot Assisted Ultra-Wideband Impulse Radio," in Proc. IEEE
Int. Conf. on Ultra-Wideband, Singapore, September 2007,
incorporated herein by reference to NBI mitigation in which the NBI
subspace is estimated from random measurements when the UWB signal
is absent. The coefficients of the NBI signal were estimated using
Basis Pursuit Denoising (BPDN) algorithm. Once the UWB symbols are
detected, both null subspace of the NBI and UWB subspace--estimated
by BPDN--are used to construct the compressive measurement matrix.
For signaling purpose, pilot symbol assisted modulation combined
with direct sequence spread spectrum coding and time-hopping
(DS-TH) coding was suggested. The pilot symbols were divided into
three groups in order to: estimate the NBI subspace; estimate the
UWB signal subspace; and provide information about the
channels.
[0102] Combining the correlator receiver with digital notch filter
was applied to NBI suppression when strong NBI was present from
licensed systems like WiMAX. The NBI affects only small part of the
CS measurements by setting the test functions to be highly
frequency selective at the correlators. During the QP
reconstruction, a `digital notch` was employed which discovers and
drops those affected measurements with only few numbers of
correlators. An approach in between see A. Oka and L. Lampe,
"Compressed Sensing Reception of Bursty UWB Impulse Radio is Robust
to Narrow-Band Interference," in IEEE Global Telecommunications,
December, 2009; and Z. Wang, G. R. Arce, B. M. Sadler, J. L.
Paredes, S. Hoyos, and Z. Yu, "Compressed UWB Signal Detection with
Narrowband Interference Mitigation," in IEEE Int. Conf. on UWB,
Vol. 2 pp. 157-160, September, 2008, each incorporated herein by
reference was also used for NBI elimination. The proposed system
used a training sequence in the first burst and did not transmit
any information. Then a method similar to that in Z. Wang, G. R.
Arce, B. M. Sadler, J. L. Paredes, S. Hoyos, and Z. Yu, "Compressed
UWB Signal Detection with Narrowband Interference Mitigation," in
IEEE Int. Conf. on UWB, Vol. 2 pp. 157-160, September, 2008,
incorporated herein by reference was used to detect the
coefficients of the NBI.
[0103] For CS based UWB systems, no additional hardware are
required to detect and mitigate the NBI subspace as well as no ISI
was assumed (low pulse rate). The NBI signals in are sparsely
characterized in the DCT. Though in A. Oka and L. Lampe,
"Compressed Sensing Reception of Bursty UWB Impulse Radio is Robust
to Narrow-Band Interference," in IEEE Global Telecommunications,
December, 2009, incorporated herein by reference the baud rate
might be close to the Nyquist rate with imperfect timing. The basis
functions are sinusoidal waveforms which are sparse in frequency
domain.
[0104] In light of the deficiencies of conventional systems the
present disclosure branches into two main directions. The former
branch is the mitigation of NBI in training UWB systems. The latter
is the mitigation in blind UWB systems.
[0105] The ability of CS technique to detect and reconstruct
unknown signals from far few numbers of measurements is explained.
There are many CS algorithms with different complexity; including
Basis Pursuit (BP), Matching Pursuit (MP), Orthogonal Matching
Pursuit (OMP), and Basis Pursuit Denoising (BPDN). Here, the
present disclosure covers the details of MP algorithm because it is
the one that will be used in the present disclosure. The present
disclosure introduces different models required to evaluate the
proposed NBI mitigation techniques. Important properties of
interferers are explained. The present disclosure focuses on the
types that are used in the simulation.
[0106] The block diagram of the system, shown in FIG. 7, involves
an UWB system and a NB system, as embodiments of the present
disclosure. Thermal noise is added at the UWB receiver. The channel
model for the UWB transmitter is different than the NBI channel.
UWB channel, MP algorithm, and NBI modeling are explained in
details.
[0107] A UWB channel model was proposed by the IEEE 802.11 0.4a
working group see A. F. Molisch, K. Balakrishnan, C. Chong, S.
Emami, A. Fort, J. Karedal, J. Kunisch, H. Schantz, U. Schuster,
and K. Siwiak, "Ieee 802.15.4a channel model-final report," Tech.
Rep., IEEE 802.15 TG4a, 2006, incorporated herein by reference. The
model is proposed by modifying the conventional model for
Saleh-Valenzuela (S-V) model. See A. Saleh and R. A. Valenzuela, "A
statistical model for indoor multipath propagation," in IEEE J.
Selected Areas Comm., Vol. 5, pp. 138-137, February 1987,
incorporated herein by reference in its entirety. It is applicable
for different environments such as indoor residential, indoor
office, industrial, outdoor, and open outdoor environments. The
multipath components arrive as clusters according to Poisson
distribution, and each path in a certain cluster also arrives with
the same distribution. Thus the inter-arrival times for the
clusters and the paths within the clusters are exponentially
distributed. The impulse response of the channel can be expressed
as:
h(t)=.SIGMA..sub.l=0.sup.L.SIGMA..sub.k=0.sup.Ka.sub.l,k.delta.(t-T.sub.-
l-.tau..sub.l,k) (2-1)
where L is the number of clusters, K.sub.l is the number of
multipath components within the l.sup.th cluster, a.sub.l,k is the
multipath gain coefficient of the k.sup.th component in the
l.sup.th cluster, T.sub.l is the delay of the l.sup.th cluster
which is defined as the Time Of Arrival (TOA) of the first arriving
multipath component within the l.sup.th cluster, and .tau..sub.l,k
is the delay of the k.sup.th multipath component relative to the
l.sup.th cluster arrival time, T.sub.l. The two dimensional model
can be reduced into one dimensional discrete model including a
mixed Poisson distribution for ray arrival times:
h(t)=.SIGMA..sub.l=0.sup.L-1.alpha..sub.l.delta.(t-.tau..sub.l)
(2-2)
where .alpha..sub.l, .tau..sub.l are the attenuation and the delay
of the l.sup.th path. The channel model was already implemented
using Matlab in A. F. Molisch, K. Balakrishnan, C. Chong, S. Emami,
A. Fort, J. Karedal, J. Kunisch, H. Schantz, U. Schuster, and K.
Siwiak, "Ieee 802.15.4a channel model--final report," Tech. Rep.,
IEEE 802.15 TG4a, 2006, incorporated herein by reference and the
present disclosure uses it directly. See A. F. Molisch, K.
Balakrishnan, C. Chong, S. Emami, A. Fort, J. Karedal, J. Kunisch,
H. Schantz, U. Schuster, and K. Siwiak, "Ieee 802.15.4a channel
model--final report," Tech. Rep., IEEE 802.15 TG4a, 2006,
incorporated herein by reference in its entirety.
TABLE-US-00002 TABLE 2 IEEE802.1.4a channel model classification
LOS Environment NLOS Environment CM-1 Residential CM-2 Residential
CM-3 Office CM-4 Office CM-5 Outdoor CM-6 Outdoor CM-7 Industrial
CM-8 Industrial CM-9 outdoor
[0108] Channel models in IEEE 802.15.4a are classified as in the
Table 2. Each model is applicable for a specific environment. Odd
numbered channels represent line-of-sight scenarios, while even
numbered channels are for non-line-of-sight (NLOS).
[0109] Channel Model#1 (CM 1) is used throughout the present
disclosure. A representative simulated impulse response and power
delay profile for CM1 is plotted in FIG. 8. The path strength of
the multipath after 150 nanosecond excess delay is negligible.
[0110] Let x.epsilon..sup.N be a vector of length N.times.1, most
of its elements are zeros and there are K nonzero elements in x.
Assume also that .PSI. is a basis matrix of dimension N.times.N.
The vector x can be represented by a linear combination as:
x=.SIGMA..sub.n=1.sup.N.theta..sub.n.psi..sub.n=.PSI..THETA.
(2-3)
where .theta.=[.theta..sub.0, .theta..sub.1, . . . ,
.theta..sub.N-1] is N+1 vector of constant coefficients. The signal
x is called K-sparse or it is sparse in the .PSI.-domain. By
utilizing the CS, the sparse signal x can be reconstructed from M
measurements where N>>M by projecting x onto a measurement
matrix .PHI. with M.times.N dimension as:
y=.PHI.x (2-4)
y=f.THETA. where f=.PHI..PSI. (2-5)
[0111] The CS technique has proven that a major factor for accurate
reconstruction process is the incoherence between .PHI. and .PSI..
See E. J. Candes, "Compressed Sampling," European Mathematical
Society, 2006, incorporated herein by reference in its
entirety.
[0112] Through an optimization problem of the l.sub.1-norm the
coefficients of the vector .theta. can be recovered from the vector
y using the following formula:
{circumflex over (.theta.)}=argmin.parallel.{tilde over
(.theta.)}.parallel..sub.1 subject to y=f{tilde over (.theta.)}
(2-6)
where B is the recovered vector. Linear programming such as BP or
MP and OMP is used to solve the problem.
[0113] In the present disclosure among many CS algorithms, MP is
used. Matching Pursuit algorithm is simple and efficient. However,
it is not optimal because it does not take the noise effect into
account. For the sparse signal, x=HO which is K-sparse on basis
.PSI., where .theta. is a vector with K.times.1 nonzero elements,
and H is a subspace matrix of dimension N.times.K that is
constructed from the basis .PSI. with N>>K. The location of
columns that construct the subspace matrix H from the basis .PSI.
is unknown, which can be achieved using MP algorithm.
[0114] Given the measurement vector, y=.PHI.x, the target of the
algorithm is to extract the K largest columns correlated to y from
a combined dictionary V=.PHI..PSI.. FIG. 9 summarizes the main
steps for the MP algorithm. The process works iteratively with
T.sub.0 maximum number of iterations. It starts by an
initialization states for the sparse vector .theta. and starts a
counter, for the number of iterations. In each turn, the algorithm
goes over all V columns, and searches for the most correlated
column vector with y then removes it from y giving a residual error
vector, e.sub.i. After each iteration, K can be approximated by
observing the magnitude of the current residual. The subspace
matrix H is constructed by examining the number of the significant
elements of {circumflex over (.theta.)} when the threshold value,
becomes smaller than the ratio between residual vector and the
measurement vector.
[0115] Compressive sensing is used to estimate the coefficients of
NBI in trained UWB systems. This can be done by exploiting the fact
that the NBI has sparse representation in the DCT domain.
Furthermore, CS is applied to estimate and construct the subspace
measurement matrix in which a sparse UWB signal lies. In blind UWB
systems, the test functions in the correlator receiver are sparse
in the frequency domain. The transmitted waveform contains only K
nonzero samples i.e. it is K-sparse, therefore NBI is effectively
eliminated. For I-UWB receivers, CS is also used to reduce the
sampling rate at the receiver side far below the Nyquist rate.
[0116] One objective of the present disclosure is to mitigate the
NBI effect on UWB systems. The bandwidth and the center frequency
of a UWB signal is denoted by .OMEGA..sub.U,f.sub.cU respectively,
while .OMEGA..sub.I, f.sub.cI are the bandwidth and the center
frequency of NBI signal and .OMEGA..sub.U>>.OMEGA..sub.I. The
performance is not affected when the interferer operates out of the
band of interest. The present disclosure is only interested in the
jammers overlaying the UWB signal's bandwidth.
[0117] Narrowband Interference Modeling
[0118] Next, the present disclosure discusses different NBIs, such
as single-tone, multi-tone and partial-band interference models.
See Si Chen; Bang-ning Zhang; Daoshen Guo; Qin-yu Zhang, "Jammer
cancellation in time-hopping impulse radio using independent
component analysis," in International Conference on Wireless
Communications & Signal Processing, WCSP, Vol., no., pp. 1-4,
13-15 Nov. 2009, incorporated herein by reference in its entirety.
Furthermore, the present disclosure discusses some licensed NBIs
like WiMAX, WLAN, and Bluetooth.
[0119] Unlicensed Narrowband Interference
[0120] The unlicensed narrowband interferers or jammers do not have
fixed center frequency or bandwidth. A single tone jammer can be
considered as the simplest form of interference, where a sinusoidal
signal with a certain single frequency, f.sub.I, lays within the
UWB signal's bandwidth. The extreme case occurs when the frequency
of the jammer coincides with the center frequency of the UWB
signal. The time domain expression of the tone jammer, v(t), and
its autocorrelation function, R.sub.v(.tau.), are expressed as:
v ( t ) = a cos ( 2 .pi. f I t ) ( 2 - 7 ) R v ( .tau. ) = a 2 2
cos ( 2 .pi. f I .tau. ) ( 2 - 8 ) ##EQU00004##
[0121] The average power of the jammer is
v = R v ( .tau. = 0 ) = .alpha. 2 2 . ##EQU00005##
The PSD of single tone interferer is the Fourier transform of its
autocorrelation which is expressed as:
S v ( f ) = a 2 4 [ .delta. ( f - f I ) + .delta. ( f + f I ) ] ( 2
- 9 ) ##EQU00006##
[0122] On the other hand, multi-tone interferer is constructed by
adding more than one tone interference signal. Assuming N.sub.v
equal power tones, the multi-tone jammer can be defined as:
v i ( t ) = I = 1 N v 2 N v cos ( 2 .pi. f I t + .phi. I ) ( 2 - 10
) ##EQU00007##
[0123] When the phase of the individual tones is random and
independent, this type of interference has Gaussian distribution
when N.sub.v>>1 according to the central limit theorem.
[0124] Partial-band interference spreads its power, v, over a
specific frequency band, so it affects a partial band of the total
UWB signal bandwidth. The PSD of the partial-band jammer is given
by:
S v ( f ) = { v .OMEGA. I , f - f cI .ltoreq. .OMEGA. I 0 ,
otherwise ( 2 - 11 ) ##EQU00008##
[0125] Licensed Narrowband Interference
[0126] The licensed narrowband interferers or jammers have fixed or
assigned frequency range. WiMAX and IEEE802.11a WLAN are OFDM based
systems where the available bandwidth divides into smaller
sub-bands. The data transmitted in each sub-band utilizes different
modulation techniques. The IEEE802.11b standard and Bluetooth
operate over the 2.4 GHz ISM band.
[0127] WiMAX is a primary NB service based on the IEEE802.16-2004
standard. It operates in the band of 2-66 GHz over an adaptable
channel bandwidth ranging from 1.25 MHz up to 20 MHz which can be
any integer multiple of 1.25 MHz, 1.5 MHz, 1.75 MHz, 2 MHz, and
2.75 MHz. The modulation adaptively changes according to the
channel conditions. With different coding rate, the system may
provide data rate up to 75 Mbps.
[0128] Another OFDM based system is the IEEE802.11a WLAN which
works in the 5.2 GHz spectrum with 20 MHz channel bandwidth. It
uses adaptive modulation and coding which changes according to the
channel conditions. Hence the system data rate might reach up to 54
Mbps. See J. Bellorado, S. S. Ghassemzadeh, L. J. Greenstein, T.
Sveinsson, V. Tarokh, "Coexistence of ultra-wideband systems with
IEEE-802.1 1 a wireless LANs," Proc. IEEE Global Telec. Conf
(GLOBECOM '03), Vol. 1, pp. 410-414, 1-5 Dec. 2003, incorporated
herein by reference in its entirety.
[0129] The IEEE802.11b WLAN has a bandwidth around 22 MHz and
operates in the 2.4 GHz band as illustrated in FIG. 4. WLAN
simulates an implementation of the Direct Sequence Spread Spectrum
(DSSS) system that provides 1 Mbps, 2 Mbps, 5.5 Mbps, and 11 Mbps
payload data rates. The modulation of the system changes from DBSK
to combinations of DQPSK, QPSK and complementary code keying (CCK).
See I. Lensford. A. Stephens. and U. Nevo. "Wi-Fi (802.11b) and
Bluelooth: Enabling Coexistence:" in IEEE Network Magazine, Vol.
15, pp. 20-27, September/October 2001; and L. Sydanheimo, M.
Keskilammi and M. Kivikoski, "Performance Issues on the Wireless
2.4 GHz ISM Band in a Multisystem Environment", in IEEE Trans.
Consumer Electronics, Vol. 48, No. 3, pp. 638-643, August 2002,
each incorporated herein by reference in their entirety.
[0130] Bluetooth operates in the 2.4 GHz ISM band. It transmits
signals with small power around 1 mW, therefore it is applicable
for short-rage technology. Frequency Hopping Spread Spectrum (FHSS)
is used in Bluetooth. Bluetooth uses 1600 hop/sec to switch over 79
channels to avoid interfering with other systems operating in the
same band. Each channel has a bandwidth of 1 MHz starting at 2.402
GHz and finishing at 2.48 GHz. Though the bandwidth is large, the
common Bluetooth devices provides data rate of only 1 Mbps using
Gaussian frequency shift keying (GFSK).
TABLE-US-00003 TABLE 3 Comparison between different NB services
IEEE802.11a IEEE802.11b NB service WiMAX WLAK WLAN Bluetooth
Technique OFDM OFDM DSSS FHSS Modulation, 1/2 BPSK, 1/2, 3/4 DBPSK,
GFSK coding rate 1/2, 3/4 (BPSK, QPSK, DQPSK, (QPSK, 16-QAM) QPSK,
16-QAM), 2/3, 3/4 CCK 2/3, 3/4 64-QAM 64-QAM Spectrum GHz 2-11 5.2
2.4 2.4 Bandwidth 20 20 22 MHz Maximum data 75 54 11 1 rate
Mbps
[0131] Table 3 illustrates comparisons between the NB services. It
focuses mainly on the most important characteristics such as
modulation and coding, the operating frequency band bandwidth, and
the maximum data rate supported by each service. It will be
difficult to conside all possible NB systems. The discussion here
provides guidelines for the chosen frequencies and bandwidths.
[0132] The UWB IEEE802.11.4a channel model mainly focuses on CM1,
which the present disclosure uses in the simulation. Among many CS
algorithms the present disclosure concentrates on the MP algorithm.
See A. F. Molisch, K. Balakrishnan, C. Chong, S. Emami, A. Fort, J.
Karedal, J. Kunisch, H. Schantz, U. Schuster, and K. Siwiak, "Ieee
802.15.4a channel model--final report," Tech. Rep., IEEE 802.15
TG4a, 2006, incorporated herein by reference in its entirety.
[0133] Different unlicensed and licensed NBIs were discussed. For
the unlicensed NBI, the center frequency and the bandwidth of the
jammers can be located anywhere in the UWB signal's spectrum.
Licensed NB services are governed by standards.
[0134] Next, the present disclosure uses MP algorithm to estimate
the sparse components of the NBI in the DCT domain. Additionally,
the basis or the subspace of the transmitted UWB signal will be
constructed by the same algorithm. The algorithm aims to extract
the sparse elements from a reduced set of measurements using a
pre-defined dictionary. A dictionary is a matrix that is built up
from the signal of interest. Each column in this dictionary is a
scaled and shifted version of the signal of interest. Matching
Pursuit can be also used to estimate the columns from the designed
dictionary that fully construct the sparse signal.
[0135] Mitigation of Narrowband Interference in Systems with
Channel Training
[0136] In frequency selective channels, I-UWB pulses are distorted
because of their wide bandwidth. When such pulses are sent over
multipath environment, which cause ISI, the receiver must deal with
timing problems carefully. The timing becomes so complex in
multiple access techniques where there are many users sending on
the same channel. It is even worse when an interferer shares part
of the transmission bandwidth. The presence of interference
degrades the system performance. Most UWB system achieves
synchronization and proper channel estimation by sending a training
sequence. Some systems are designed to work in the presence of NBI
and some are designed to work in the presence of both NBI dense
ISI.
[0137] Training can be achieved by inserting a known data stream in
the beginning of each frame or by sending pilot symbols at regular
intervals during the whole transmission time. Many operations
required at the receiver side such as channel estimation,
synchronization, and data detection could be easily achieved when
the received signal contains a training sequence. However, part of
the transmitted data will be used as an overhead. Hence there is a
tradeoff between the system performance and the throughput.
Mitigation of narrowband interference can make use of the
transmitted training sequence.
[0138] Another objective of the present disclosure is to mitigate
the effect of interference on trained UWB systems based on CS
technique. Narrowband interference signals may have sparse
representation in the DCT domain. The interest of the present
disclosure is to suppress the most significant components of the
NBI signal in the DCT domain. The utilized system model is the one
proposed by Z. Wang, G. R. Arce, B. M. Sadler, J. L. Paredes, S.
Hoyos, and Z. Yu, "Compressed UWB Signal Detection with Narrowband
Interference Mitigation," in IEEE Int. Conf. on UWB, Vol. 2 pp.
157-160, September, 2008, incorporated herein by reference. In this
research, the optimum pilot symbols distribution is investigated as
well as the effect of each pilot group symbols is also studied.
Moreover, the present disclosure evaluates the performance of the
receiver in Z. Wang, G. R. Arce, B. M. Sadler, J. L. Paredes, S.
Hoyos, and Z. Yu, "Compressed UWB Signal Detection with Narrowband
Interference Mitigation," in IEEE Int. Conf. on UWB, Vol. 2 pp.
157-160, September, 2008, incorporated herein by reference in the
presence of multiuser interference. The same signaling scheme
(DS-TH) is used for multiple access.
[0139] When a random measurement matrix is applied in CS, the
captured energy of the received UWB signal by a compressive
detector may not be enough. The performance can be enhanced if the
UWB signal structure is employed in the construction of the
projection matrix. When structure is employed in designing the
projection matrix, few measurements are required to get most of the
received UWB signal energy. This is because the received UWB signal
is sparse and located in low dimensional subspace. In addition, NBI
can be represented as a sparse signal in the DCT domain. Since the
length of the representation is limited, the coefficients in the
DCT domain decay fast. The interest is to suppress the most
significant ones.
[0140] The construction of an UWB transmitter is explained. Pilot
symbol assisted modulation combined with DS spread spectrum and TH
is applied for signaling purpose. Modeling of the interference
source is discussed next. The UWB receiver design follows with
compressive measurements and data detection. The coefficients of
the NBI and UWB signal structure are estimated during the first and
second stage of the pilot symbols respectively using MP algorithm.
Simulation and results are disclosed.
[0141] An embodiment of the present model has an UWB signal path
and an interfering signal path, see FIG. 10. The UWB transmitter
consists of data symbols, DS code, TH code, and UWB pulse
generators. The NBI transmitter comprises of a NBI symbols
generator, followed by a modulation block. The transmitted UWB
signal is convolved with the channel impulse response before being
received. The received signal is also corrupted by NBI signal and
thermal noise. The noisy signal goes through an ideal BPF that has
bandwidth and center frequency matched to those of the intended
signal to be received.
[0142] The system model is an I-UWB system in which binary symbols
are represented by a sequence of pulses. The transmitted pulse,
.phi..sub.U(t), can have different shapes. Unless otherwise
specified the present disclosure uses the second derivative of the
Gaussian pulse which has duration time T.sub.pulse and unit energy.
One binary symbol is transmitted through repeating .phi..sub.U(t)
pulses in N.sub.f frames. Hence the duration time for one symbol,
T.sub.s, is T.sub.s=N.sub.fT.sub.f, where T.sub.f is the frame
duration. Each frame is further divides into N.sub.c chips, and
each chip has T.sub.c duration.
[0143] For signaling purpose, pilot symbol assisted modulation
merged with direct sequence spread spectrum (DS) and time hopping
(TH) is used. There are N.sub.d symbols in each burst including
N.sub.p pilot symbols and N.sub.s data modulated symbols, therefore
N.sub.d=N.sub.p+N.sub.s. The pilot symbols are divided into three
groups, namely N.sub.p1, N.sub.p2 and N.sub.p3. The first group
symbols are used to estimate the NBI signal subspace, the second
group symbols are applied to estimate the UWB signal subspace; and
the last group symbols gives information about the channel. During
the first pilot symbols, zeros are sent, while ones are sent during
the other two. FIG. 11 represents the signaling scheme for the
transmitted signal. Within each frame, the pulse is hopped and
appeared in certain chips according to the TH code c.sub.n. It also
illustrates the format for one symbol time where the pulse appears
in three different positions.
[0144] The transmitted signal for one burst can be represented
mathematically as:
s ( t ) = n = 0 N d N f - 1 a n b n / N f E .phi. U ( t - nT f - c
n T c ) ( 3 - 1 ) ##EQU00009##
where the DS code is a.sub.n.epsilon.{.+-.1}. b.sub..left
brkt-bot.n/N.sub.f.sub..right brkt-bot. is the binary transmitted
symbols, the TH code is c.sub.n.about.U[0, N.sub.c-1] and E is the
energy of the transmitted signal. As mentioned before b.sub.i=0 for
i.epsilon.[0, N.sub.p1-1] b.sub.i=1 for i.epsilon.[N.sub.p1,
N.sub.p-1], and b.sub.i=.+-.1 with equal probability for
i.epsilon.[N.sub.p, N.sub.d-1].
[0145] The none-periodicity introduced by the TH code gives a
smooth shape for the frequency spectrum and avoids any spectral
lines in the transmitted signal. The TH code also minimizes the
interference between users in multiple access technique, where each
user has a unique TH code.
[0146] The transmitted signal then passes through a multipath
communication channel, h(t), having T.sub.med maximum excess delay
time with L paths, where .alpha..sub.l and .tau.l are the
attenuation, and delay associated with l.sup.th path.
h(t)=.SIGMA..sub.l=0.sup.L-1.alpha..sub.l.delta.(t-.tau..sub.l)
(3-2)
[0147] To ignored ISI, the chip duration is fixed such that it is
greater than the transmitted pulse duration plus the maximum excess
delay of the channel (T.sub.c>T.sub.pulse+T.sub.med). Although
the UWB channel could have a large number of paths, only few paths
are selected which contains most of the UWB channel's energy, see
FIG. 8. Since there are many insignificant paths, UWB channels can
be modeled as sparse channels due to the large transmission
bandwidth.
[0148] The interference source, v(t), consists of two main blocks
as in FIG. 10. The first block generates the NBI symbols, and then
the modulation is performed in the second block. The channel models
for the intended UWB signal and the interferer in FIG. 10 may be
the same or may be different. When they are the same, the
IEEE802.11.4a model is used with different realizations. Some
researchers used different channel for the interferer such as fast
and frequency selective channel, or frequency nonselective slow
fading channel. The interfering signal could be passed through a
perfect channel and used additively like AWGN to jam the receiver.
When more than one NBI are present, the interference signal,
v.sub.i(t) for i=1, 2, . . . , N.sub.v-1, is modeled as the sum of
N.sub.v interferers.
[0149] There are three main stages employed at the receiver side.
The effect of the NBI is suppressed by designing a measurement
matrix that uses the estimated NBI as a null subspace. In the first
stage, the received signal is projected into a random measurement
matrix. Since no UWB symbols are transmitted, the NBI's
coefficients are estimated using CS. Subsequently, these
coefficients are used to obtain the NBI signal subspace. In the
next stage, the UWB signal subspace is constructed by making use of
the projection matrix of the estimated NBI subspace through CS.
Finally, a measurement matrix that combines the estimated null
subspace of the NBI and the constructed UWB signal subspace is
designed. This matrix has the ability to collect most of the
received UWB signal energy as well as suppress the NBI if
present.
[0150] The receiver basically consists of BPF, M mixer-integrators,
and generalized likelihood ratio test (GLRT) detector. The received
UWB signal is contaminated by white Gaussian noise w(t) with two
sided power spectral density (PSD),
N 0 2 , ##EQU00010##
and narrowband interference, v(t). The filter has one-sided
bandwidth, .OMEGA., center frequency, f.sub.c, and it affects only
the noise. The output noise becomes {tilde over (w)}(t), whereas
the desired and interfering signals aren't distorted. The received
signal at the output of the BPF is:
r(t)=.intg..sub.0.sup.th(t-.tau.)s(.tau.)d.tau.+v(t)+{tilde over
(w)}(t) (3-3)
[0151] The received signal is processed by three different
measurement matrices; denoted by .PHI..sub.i, i=1, 2, 3, each of
dimension M.times.N. They are constructed to achieve the mitigation
and demodulation requirements.
[0152] Full knowledge of the direct sequence code, a.sub.n, and the
time hopping code, c.sub.n, is assumed at the receiver side. M
Mixer-integrators are employed to get the compressive measurements,
with integration period, T.sub.prj, set as
T.sub.Pulse+T.sub.med.gtoreq.T.sub.prj.gtoreq.T.sub.Pulse. The
compressive measurements for the n.sup.th frame have to be started
at t=c.sub.nTc+(n-1)T.sub.f, and ended at t+T.sub.prj. At this time
the mixer-integrators are sampled at the same time, and then they
reset to zero to be ready for the next frame.
[0153] The sampling frequency should fulfill the relation
f s = 2 .times. ( f c + .OMEGA. 2 ) , ##EQU00011##
hence the data has length of
N=T.sub.prjf.sub.s.
[0154] Since the present disclosure uses CS technique for two
purposes which are ADC speed reduction and signal reconstruction,
the sampling frequency becomes large because the transmitted signal
is in the order of GHz. Actually, don't sample at rate fs because
only the projected data goes through the ADC.
[0155] During the first pilot group symbols, the received signal
get multiplied by .PHI..sub.1 which has independent and identically
distributed (i.i.d.) Bernoulli distribution. In this stage, no UWB
symbols are transmitted and the subspace of the NBI signal can be
estimated. After multiplication by the direct sequence code, the
compressive measurements of the received n.sup.th frame during the
first pilot symbols, y.sub.1[n], can be written as:
y.sub.1[n]=a.sub.n.PHI..sub.1r[n]=a.sub.n.PHI..sub.1v[n]+a.sub.n.PHI..su-
b.1w[n], n=0, . . . ,N.sub.p1N.sub.f-1 (3-4)
where r[n] is the sampled received signal of the n.sup.th frame of
size N.times.1. The digitized NBI and the digitized noise are v[n]
and w[n] respectively, both of size N.times.1. The output
y.sub.1[n] is a vector of size M.times.1. The previous equation can
be rewritten as:
y.sub.1[n]=a.sub.n.PHI..sub.1C.zeta.[n]+a.sub.n.PHI..sub.1w[n]
(3-5)
where C=[c.sub.0, c.sub.1, . . . c.sub.N-1] is the inverse DCT
matrix, and .zeta.[n] is the DCT representation of v[n]. The
estimated NBI coefficients, .zeta.[n], can be obtained in this
stage based on y.sub.1[n] because the NBI has sparse representation
in the DCT domain. Matching Pursuit (MP) algorithm is used to
estimate those coefficients.
[0156] Suppose that {tilde over (.zeta.)} is defined as {tilde over
(.zeta.)}=.SIGMA..sub.n=0.sup.N.sup.p1.sup.N.sup.f.sup.-1|{tilde
over (.zeta.)}[n]| and .zeta..sub.max=max{{tilde over
(.zeta.)}.sub.0, {tilde over (.zeta.)}.sub.1, . . . , {tilde over
(.zeta.)}.sub.N-1,}. The NBI subspace can be approximated as
C.sub.v=[c.sub.n0, c.sub.n1, . . . , c.sub.nj], where
n.sub.j.epsilon.{i.parallel..zeta..sub.i|>.mu..zeta..sub.max}.
[0157] The most significant coefficients of the NBI in the DCT
domain are suppressed by controlling the interference threshold,
.mu.. If very large value for .mu. are assigned, the constructed
NBI subspace will not suppress the interference effect. If it is
too small, unnecessary suppression is done for the zero
coefficients since the NBI is sparse. The projection matrix of the
NBI subspace signal is constructed as:
P.sub.v.sup..perp.=I.sub.N-C.sub.v(C.sub.v.sup.TC.sub.v).sup.-1C.sub.v.s-
up.T (3-6)
[0158] The received signal is then multiplied by the second
measurement matrix, .PHI..sub.2, during the second group pilot
symbols. The UWB signal structure or subspace is estimated in this
stage. During the second pilot symbols, the compressive
measurements will be:
y.sub.2[n]=a.sub.n.PHI..sub.2r[n]=.PHI..sub.2s+a.sub.n+.DELTA.N.PHI..sub-
.2v[n+.DELTA.N]+a.sub.n+.DELTA.N.PHI..sub.2w[n+.DELTA.N], n=0, . .
. ,N.sub.p2N.sub.f-1 (3-7)
where .DELTA.N=N.sub.p1N.sub.f, and s.sub.N.times.1 is the
digitized noise free received signal h(t).phi..sub.U(t) within
T.sub.prj, where represents the convolution. The second measurement
matrix is constructed as;
.PHI. 2 = .PHI. 1 P 1 v , ##EQU00012##
consequently .PHI..sub.2v[n+.DELTA.N].apprxeq.0. As a result, the
effect of the NBI is suppressed. The UWB signal subspace is
constructed from y.sub.2[n] using MP algorithm. Averaging the
second compressive measurement to reduce the noise is done
using:
y _ 2 = 1 N p 2 N f n = 0 N p 2 N f - 1 y 2 [ n ] ( 3 - 8 )
##EQU00013##
[0159] Because of the multipath channel, the received UWB signal is
a shifted and scaled version of the transmitted UWB pulse,
.phi..sub.U(t).
[0160] A dictionary, .PSI..sub.c, can be designed such that each
column is a time shifted version of .phi..sub.U(t). Let .PSI..sub.u
be the sampled form of .PSI..sub.c with a rate of f.sub.s. Each
column of .PSI..sub.u is normalized to have a unit energy. The
f.sup.th column is given by:
.PSI..sub.uj(n)=.phi..sub.U(f.sub.s-j/f.sub.s), n=0,1, . . .
,f.sub.sT.sub.prj-1 (3-9)
[0161] Only K paths with the largest gains out of the total UWB
channel paths are considered. This gives the received signal sparse
representation (K-sparse). As a result, the UWB signal structure
can be represented as s=H.sub.u.theta..sub.u where H.sub.u is a
matrix of dimension N.times.K constructed from K relevant column
vectors of .PSI..sub.u, and .theta..sub.u is a K.times.1 vector of
non-zero coefficients. Given .PSI..sub.u, .PHI..sub.2 and y.sub.2,
MP algorithm can be used to estimate the K vectors from that
construct the UWB signal subspace H.sub.u.
[0162] Finally, the third group pilot symbols and the data
modulated symbols are multiplied by the third measurement matrix
.PHI..sub.3. This matrix has the ability to collect most of the
received UWB signal energy as well as suppress the NBI if present.
The construction of .PHI..sub.3 utilizes the NBI and UWB subspaces
using the formula:
.PHI..sub.3=G({tilde over (H)}.sub.u.sup.T{tilde over
(H)}.sub.u).sup.-1{tilde over (H)}.sub.u.sup.T (3-10)
where G is an i.i.d. random matrix of dimension M.times.N, and
H ~ u = P 1 V H ^ u . ##EQU00014##
The compressive measurements multiplied by a.sub.n during both the
third pilot group symbols and the data modulated symbols are given
respectively by:
y.sub.3[n]=.PHI..sub.3s+a.sub.n+{tilde over
(.DELTA.)}N.PHI..sub.3v[n+{tilde over (.DELTA.)}N]+a.sub.n+{tilde
over (.DELTA.)}N.PHI..sub.3w[n+{tilde over (.DELTA.)}N], n=0, . . .
,N.sub.p3N.sub.f-1 (3-11)
y.sub.d|j[n]=b.sub.j.PHI..sub.3s+a.sub.n-{circumflex over
(.DELTA.)}N.PHI..sub.3v[n+{circumflex over
(.DELTA.)}N]+a.sub.n+{circumflex over
(.DELTA.)}N.PHI..sub.3w[n+{circumflex over (.DELTA.)}N], n=0, . . .
,N.sub.f-1 (3-12)
where {tilde over (.DELTA.)}N=(N.sub.p1+N.sub.p2)T.sub.f, {tilde
over (.DELTA.)}N=(N.sub.p+j)N.sub.f, and b.sub.j.epsilon.{.+-.1} is
the data modulated with j=0, 1, . . . , N.sub.s-1. The term
.PHI..sub.3s gives information about the channel and it can be
obtained from y.sub.3[n] within the same burst. Averaging
y.sub.3[n] over multiple frames is used as a template to demodulate
the transmitted symbols. The maximum likelihood estimation of
.PHI..sub.3s is given by:
.PHI. 3 s ^ = 1 N p 3 N f n = 0 N p 3 N f - 1 y 3 [ n ] = .PHI. 3 s
+ a n + .DELTA. ~ N W _ where w _ = 1 N p 3 N f n = 0 N p 3 N f - 1
v [ n + .DELTA. ~ N ] + w [ n + .DELTA. ~ N ] ( 3 - 13 )
##EQU00015##
is a vector of length N.times.1 compromises of the sum of a WGN
with variance
N 0 .OMEGA. N p 3 N f ##EQU00016##
and the residual NBI which can be also modeled as Gaussian
noise.
[0163] Since the transmitter sends b.sub.j.epsilon.{.+-.1} with
equal probability, two hypotheses must be distinguished by the
detector:
H.sub.0:y.sub.d|j[n]=-.PHI..sub.3s+a.sub.n+{circumflex over
(.DELTA.)}N.PHI..sub.3v[n+{circumflex over
(.DELTA.)}N]+a.sub.n+{circumflex over
(.DELTA.)}N.PHI..sub.3w[n+{circumflex over (.DELTA.)}N],
(b.sub.j=-1), n=0,1, . . . ,N.sub.f-1 (3-14)
H.sub.1:y.sub.d|j[n]=-.PHI..sub.3s+a.sub.n+{circumflex over
(.DELTA.)}N.PHI..sub.3v[n+{circumflex over
(.DELTA.)}N]+a.sub.n+{circumflex over
(.DELTA.)}N.PHI..sub.3w[n+{circumflex over (.DELTA.)}N],
(b.sub.j=1), n=0,1, . . . ,N.sub.f-1 (3-15)
[0164] The statistics of the GLRT detector is defined as:
T ( y d j ) = ( .PHI. 3 s + .PHI. 3 p ) T ( N 0 .OMEGA..PHI. 3
.PHI. 3 T ) - 1 ( b j .PHI. 3 s + .PHI. 3 d ) where p = 1 N p 3 N f
n = 0 N p 3 N f - 1 w [ n + .DELTA. ^ N ] + v [ n + .DELTA. ^ N ] ,
and d = 1 N f n = 0 N f - 1 w [ n + .DELTA. ~ N ] + v [ n + .DELTA.
~ N ] . ( 3 - 16 ) ##EQU00017##
[0165] The detector estimates {circumflex over
(b)}.sub.j=T(y.sub.d|f)>0; otherwise {circumflex over
(b)}.sub.j=-1. The first bracket in the previous equation is the
average of y.sub.3[n] over N.sub.p3N.sub.f frames used as a
template, whereas the last bracket represents the average of the
measurement vector during the data transmission over N.sub.f
frames.
[0166] Suppose that there are m=1, 2, . . . , N.sub.u secondary
users in addition to the primary user. The users transmit their
information at the same time with the intended one and there is no
delay of propagation, see FIG. 13. Each user has its own DS code,
TH code, and data. Therefore, collision or interference occurs if
the TH codes are matched. This may amplify the intended pulse,
reduce its level or make it zero depend on the DS code, the
information of the interfering users, the number of users as well
as the TH codes relative to the current transmitted pulse of the
intended user. The kth user has transmitted waveform over a burst
represented by:
s.sup.k(t)=.SIGMA..sub.n=0.sup.N.sup.d.sup.N.sup.f.sup.-1a.sub.n.sup.kb.-
sub..left brkt-bot.n/Nf.right brkt-bot..sup.k {square root over
(E)}.phi..sub.U(t-nT.sub.f-c.sub.n.sup.kT.sub.c) (3-17)
where a.sub.n.sup.k and c.sub.n.sup.k are the DS, and the TH codes
for the k.sup.th user. The other parameters are similar to those
related to the intended user.
[0167] In a network, the average number of bits that are
transmitted successfully or average rate of successful bit delivery
is known as the throughput. In multiuser systems, the throughput
decreases as the number of users increases. Throughput can be
represented mathematically using the following formula:
Throughput=(1-BER)R.sub.s (3-18)
where R.sub.s is the symbol rate in bps. In the simulation, the
throughput is calculated for different number of the secondary
users N.sub.u.
[0168] In one embodiment of the present disclosure the mitigation
of NBI in trained UWB systems is evaluated. The diagram in FIG. 14
depicts the main steps that are used to investigate the mitigation
process based on CS. As mentioned the transmission sequence
contains the three groups of pilot symbols, and the data modulated
symbols. DS-TH is used for signaling where each symbol is repeated
in N.sub.f frames at different chips. The signal then goes through
an IEEE802.11.4a channel. The NBI system also generates its own
symbols, and sends them over an NBI channel.
[0169] At the receiver side, the received UWB signal is captured
using BPF. The measurement is taken using three measurement
matrices. First the corrupted received signal at the BPF's output
is multiplied by .PHI..sub.1 which has Bernoulli distribution. This
measurement vector is used to estimate the NBI subspace using CS.
Second, the received signal is multiplied by .PHI..sub.2 which is
constructed according to the estimated NBI subspace. Based on this
measurement vector, the UWB signal subspace is estimated using CS.
Third, the received signal is multiplied by .PHI..sub.3 that has
the ability to null out the NBI and collect the UWB's signal
energy. After averaging over the third group pilot symbols, the
measurement vector now is used as a template in the demodulation
process. Again the received signal is multiplied by .PHI..sub.3 but
the measurement vector is applied as the input to the GLRT detector
with previous template. Finally, the detector does the decision
process.
[0170] An investigation of the pilot symbols distribution is
considered. Then fix the distribution of the pilot symbol and study
different related parameters such as the number of frames per
symbol, N.sub.f, and the interference threshold, .mu.. After that,
the performance of the system is evaluated under the effect of
different unlicensed and licensed NBIs. Finally, the system is
tested in the presence of both NBI and multiuser interference. In
addition, system throughput is examined under the effect of
multiuser interference as well as NBI's effect.
[0171] To investigate the best distribution of pilot symbols in the
presence of NBI, the following parameters are selected. The
transmitted signal is the second derivative Gaussian pulse with
duration T.sub.pulse=0.75 ns and center frequency, f.sub.cU=3 GHz.
The bandwidth of the receiver BPF is 8 GHz; hence the sampling
frequency is GHz. The IEEE802.11.4a Channel Model 1 (CM 1) which
represents residential line-of-sight (LOS) environment is used. One
thousand symbols (N.sub.d=1000) are transmitted over many
realizations randomly generated from CM1. The mean root square
delay spread is about 17 nanosecond, and the channel response is
normalized to have unit energy. The projection time covers the
whole received multipath arrivals. The sampling rate is reduced
to
M N = 20 % ##EQU00018##
through CS, where N is the length of the received signal. The chip
duration is T.sub.c=32 ns, and the number of chips is N.sub.c=25.
The frame duration is T.sub.f=T.sub.cN.sub.c=800 ns, and the number
of frames per symbol is N.sub.f=5, therefore
T.sub.s=T.sub.fN.sub.f=4 .mu.s. The delivered data rate is
R.sub.s=250 kbps. The total number of pilot symbols is N.sub.p=45
and interference threshold, .mu.=10.sup.-2 The performance is
evaluated for SNR=-21 dB and SIR=-20 dB. All those parameters are
fixed in the simulation unless stated otherwise.
[0172] The signal power is calculated over the whole time spanned
by the multipath arrivals and the noise is added over the total
duration time. The added noise will only have effect during the
signaling time. This is why communication can be achieved at
relatively low SNR.
[0173] In the following, the present disclosure considers three
different cases. In every case, one pilot at a time is fixed and
trade off the remaining two to keep N.sub.p constant. The fixed
pilot is assigned moderate value. The results are depicted in three
figures. The figures are divided into two subplots. The difference
between the subplots is in the center frequency of the NBIs. The
center frequencies of the NBIs are either f.sub.cl1=f.sub.cl2=1.6
GHz or f.sub.cl1=f.sub.cU=3 GHz. Each subplot contains three
different NBIs with different bandwidth combinations. Three
different bandwidth combinations are investigated:
(.OMEGA..sub.I1=20 MHz, .OMEGA..sub.I2=10 MHz), (.OMEGA..sub.I1=40
MHz and .OMEGA..sub.I2=20 MHz) and (.OMEGA..sub.I1=100 MHz
.OMEGA..sub.I2=50 MHz). For fair comparison all interferers are
adjusted to have the same power. The results are illustrated in
terms of BER as a function of N.sub.p1 or N.sub.p2. Note as the
number of symbols in one group increase the other will decrease to
keep N.sub.p=45.
[0174] First, the number of pilot symbols in the third group,
N.sub.p3=10, is fixed to evaluate the number of pilots required for
subspaces estimation for the NBI and UWB signals, see FIG. 15. The
BER curves as function of N.sub.p1 can be divided into three
different regions. For values of N.sub.p1 between 0 and 5 there is
a gradual improvement in the system performance. From 5 to 15
symbols the tradeoff between N.sub.p1 and N.sub.p2 has a minimal
effect on the performance. As N.sub.p1 increases more than 15 the
performance starts to degrade at a slow pace. The symbols in
N.sub.p1 are necessary to reduce the NBI's effect, however
communication can still be achieved at N.sub.p2=0.
[0175] In the second case, the NBI signal subspace estimation and
the acquired channel information are investigated by fixing
N.sub.p2=15. FIG. 16 indicates that no communication is possible
when neither NBI signal subspace estimation nor channel information
is being used. The NBI that has large bandwidth (.OMEGA..sub.I1=100
MHz .OMEGA..sub.I2=50 MHz) becomes less sparse since more
coefficients appear in the DCT domain. Consequently, more symbols
are required in N.sub.p1 to optimize the BER as the two subplots
demonstrate. The situation is even worse when the two frequencies
are unequal. Increasing N.sub.p3 results in a gradual reduction in
the BER provided that N.sub.p1 is not less than the minimum
requirements. For the simulated scenarios, a minimum of N.sub.p1=5
is required.
[0176] Finally, the UWB signal subspace estimation and the channel
information are studied when N.sub.p1 is fixed as depicted in FIG.
17. The third group, N.sub.p3, must not be zero in order to know
the channel characteristics and consequently have an acceptable
system performance. On the other hand, communication can be
established at N.sub.p2=0 in all bandwidth combinations. For the
simulated scenarios, the BER decreases as N.sub.p2 increases until
N.sub.p2=15, and N.sub.p3=25.
[0177] From the previous simulations, the optimal distribution is a
weak function of the center frequency or bandwidth of the NBI. The
system performance is a strong function of N.sub.p3 as FIG. 16 and
FIG. 17 illustrate. For limited power interference, the BER
degrades as the center frequency of the NBI is shifted to
f.sub.cl1i=f.sub.cU. The BER degrades as the center frequency of
the NBI is shifted to f.sub.cl1=f.sub.cU. However, the degradation
due to increasing the NBI's bandwidth together with shifting the NB
I's center frequency is larger because it results in more
significant coefficients of the NBI in the DCT domain. The sparsity
is also affected and subsequently, the mitigation of NBI won't be
the same. The distribution of the pilot symbols in Z. Wang, G. R.
Arce, B. M. Sadler, J. L. Paredes, S. Hoyos, and Z. Yu, "Compressed
UWB Signal Detection with Narrowband Interference Mitigation," in
IEEE Int. Conf. on UWB, Vol. 2 pp. 157-160, September, 2008,
incorporated herein by reference for the NBI that has
f.sub.cl1=f.sub.cl2=1.6 GHz and (.OMEGA..sub.I1=20 MHz,
.OMEGA..sub.I2=10 MHz), was N.sub.p1=5, N.sub.p2=30 and N.sub.p3=10
which isn't optimal as FIG. 15 shows. Based on the simulations, the
distribution at N.sub.p1=5, N.sub.p2=15 and N.sub.p3=25 leads to
better performance as shown in FIG. 16 and FIG. 17.
[0178] In the remaining simulations, the pilot symbols distribution
is fixed according to the previous investigations as: N.sub.p1=5,
N.sub.p2=15 and N.sub.p3=25. The effect of the frame repetition,
N.sub.f, is examined in FIG. 18. The performance is evaluated for
f.sub.cl1=f.sub.cl2=1.6 GHz and (.OMEGA..sub.I1=20 MHz and
.OMEGA..sub.I2=10 MHz). Similar behavior is expected for the other
combinations of interferers. The BER is reduced as more frames
being used to represent one symbol. With no repetition, around 9 dB
more is needed to have similar performance of N.sub.f=5. The
simulation shows that, increasing N.sub.f from 5 to 10 saves around
3 dB at very low BER. Note that this is not affair comparison as
the rate is reduced by a factor of 2.
[0179] In the preceding simulations, the interference threshold,
.mu.=10.sup.-2, was fixed. The effect of this factor on the system
performance is plotted in FIG. 19. For the region where
0<.mu.<0.04, the performance improves as u increases. The
small improvement is because the suppressed coefficients used to
construct the NBI subspace is decreased. Few columns are being
involved in the construction of the estimated NBI subspace, the
performance enhances. Herein the noisy coefficients are eliminated
and consequently the noise level is reduced. This is equivalent to
avoid picking up the non-significant coefficients and avoid
collecting more noise. For .mu.>0.1, the performance starts to
degrade. In those range, the constructed NBI subspace is not enough
to suppress the interference effect. In other words, few NBI's
coefficients are involved in the construction process.
[0180] The third part of the simulation addresses different NBI
types that might jam the UWB systems. Different NBIs are studied
under the same distribution of the pilot symbol. The unlicensed
NBIs to be investigated are considered as the sum of two QPSK
signals. The effect of the center frequency of the NBI and its
bandwidth are studied.
[0181] FIG. 20 demonstrates six different scenarios. Sold lines are
used to represent the three traces where the center frequencies of
the two QPSK jammers are f.sub.cl1=f.sub.cl2=1.6 GHz, while dashed
lines are used when the center frequencies are 3, and 1.6 GHz. When
one center frequency of the NBI (.OMEGA..sub.I1=20 MHz,
.OMEGA..sub.I2=10 MHz) matches f.sub.cU, this results in a loss of
1 dB at BER=1.times.10.sup.-4. For the f.sub.cl1=f.sub.cl2=1.6 GHz
NBI, no more than 2 dB is needed to work at BER=10.sup.-4 if the
bandwidth of the NBI increases from (.OMEGA..sub.I1=20 MHz,
.OMEGA..sub.I2=10 MHz) to (.OMEGA..sub.I1=100 MHz,
.OMEGA..sub.I2=50 MHz). However, more than 8 dB is needed if the
bandwidth of the NBI increases from (.OMEGA..sub.I1=20 MHz,
.OMEGA..sub.I2=10 MHz) to (.OMEGA..sub.I1=200 MHz,
.OMEGA..sub.I2=50 MHz) and at the same time f.sub.cl1 changes to
match f.sub.cU. The considered distribution of the pilot symbols
isn't optimal for the last case; hence such huge difference is
obtained.
[0182] Next, the system performance is investigated for different
licensed NBIs. FIG. 21 considers WiMAX, IEEE802.11a WLAN (WLANa),
IEEE802.11b WLAN (WLANb), and Bluetooth. Those NBIs have fixed
center frequencies and bandwidths according to the regulation as
discussed.
[0183] WLANa signal has the least effect in system performance
because it operates at 5.2 GHz away from the center frequency of
the transmitted pulse at f.sub.cU=3 GHz, see FIG. 21. On the other
hand, the performance degradation due to WLANb at 2.4 GHz is large
which is very close to transmitted pulse at 3 GHz. Although
Bluetooth signal has very low bandwidth, the randomness of the
center frequency of the Bluetooth signal causes large degradation
in the performance. It is desired to point out that Bluetooth and
the estimation process of its subspace are changed in every
transmission.
[0184] In the last part, the system is evaluated in the presence of
multiuser interference in addition to the NBI. The utilized
signaling scheme for the multiuser system is DS-TH coding.
Synchronized data transmission is assumed for the intended and the
secondary user(s). The NBI has center frequencies of the
f.sub.cl1=f.sub.cU=13 GHz, f.sub.cl2=1.6 GHz with bandwidth
(.OMEGA..sub.I1=40 MHz and .OMEGA..sub.I2=20 MHz). FIG. 22 shows
that the system performance degrades as more users are present
together with the NBI. For the given system parameters, two
secondary users resulted in a minimal effect on the BER. This
indicates the ability of the DS-TH code to reduce the interference.
This is a direct function of the system's spreading gain.
[0185] Finally, throughput versus the SNR is plotted in FIG. 23 as
the number of the interfering user changes. As expected, throughput
decreases when more users jam the intended one and vice-versa. At
large SNR, throughput is almost constant as one has up to five
secondary users. Moreover, the reduction in the throughput at such
SNR is lower than 10 kbps as the number of users increases up to 25
users. At very low SNR, the effect of the multi user interference
becomes large and clear. This multiuser study quantifies the amount
of degradation due to the presence of other users. It also serves
as a motive for future study where the entire compressive sensing
algorithm is redesigned to possible reject other users. The
challenge is in the similarity between the intended dictionary and
the one to be nullified.
[0186] Here, the mitigation of NBI in trained UWB systems is
investigated based on CS. The speeds of the ADC as well as the NBI
effects are reduced through CS. This part of the present disclosure
first investigates the optimum pilot symbols distribution as well
as the effect of each pilot group symbols. The present disclosure
concludes that there are a minimum required number of symbols in
the first group N.sub.p1 after which the performance saturates. For
the considered scenarios, N.sub.p1=5 was enough to achieve good
system performance at low SIR and low NBI's bandwidth, this value
is satisfied for weaker NBIs i.e. SIR>-20 dB. Communications can
be achieved with N.sub.p2=0. However, the performance can be
enhanced if the UWB signal structure is employed in the
construction of the projection matrix, i.e. N.sub.p2>0. The
number of pilot symbols in the third group N.sub.p3 is directly
proportional to the performance.
[0187] The present disclosure studied different parameters that may
affect the system performance such as the number of frame per
symbol and the interference threshold, .mu.. The BER is reduced as
more frames are being used to represent one symbol. Simulations
also show that the value of the interference threshold should be
chosen carefully. The performance improves as p increases over a
certain range where the number of the suppressed coefficients used
to construct the NBI subspace is decreased. Herein the present
disclosure eliminates the noisy coefficients and consequently the
noise level is reduced.
[0188] The mitigation process was also applied when licensed NB
services are present. Based on the simulation, the performance of
the system degrades as the NBI's center frequency locates closer to
that of the transmitted pulse. Generally, increasing the NB I's
bandwidth will reduce the sparsity of the NBI signal. More than one
NBI with unequal center frequencies also results on a reduction in
the sparsity of their equivalent NBI signal. Therefore, the
interference threshold should be changed or the system needs to
redistribute the pilot symbols to have acceptable performance.
[0189] Furthermore, the system behavior is studied in the presence
of multiuser interference besides the NBI. As expected, simulation
shows that when more users being active the system performance
degrades and vice-versa. This also causes a reduction in the system
throughput. Future optimization for CS in the presence of
multiusers is motivated.
[0190] Mitigation of Narrowband Interference in Blind Systems
[0191] Channel estimation is an important element that determines
the performance of a given communications system especially in the
presence of interference. Channel estimation can be done by
training the system with a priori known data or it can be done
blindly. Communication systems that don't use training sequences
are known as blind systems. They are capable to do several
processes blindly such as channel estimation, synchronization, and
demodulation. The effect of the NBI on UWB systems can be
eliminated using CS in two different systems; trained systems and
blind systems. In one embodiment, the present disclosure
concentrates on blind systems see A. Oka and L. Lampe, "A
Compressed Sensing Receiver for Bursty Communication with UWB
Impulse Radio," in Intl. Conf. on Ultra-Wideband, pp. 279-284,
September 2009; A. Oka and L. Lampe, "Compressed Sensing Reception
of Bursty UWB Impulse Radio is Robust to Narrow-Band Interference,"
in IEEE Global Telecommunications, December, 2009; and A. Oka and
L. Lampe, "Compressed Sensing Reception of Bursty UWB Impulse Radio
is Robust to Narrowband Interference," in IEEE GLOBECOM,
November-December 2009, each incorporated herein by reference.
[0192] One objective of this part of the present disclosure is to
study the performance of CS in blind UWB systems in the presence of
NBI. Specifically, this part of the present disclosure studies the
performance for different licensed and unlicensed NBIs and extends
the mitigation technique in A. Oka and L. Lampe, "Compressed
Sensing Reception of Bursty UWB Impulse Radio is Robust to
Narrow-Band Interference," in IEEE Global Telecommunications,
December, 2009, incorporated herein by reference for two NBIs. The
speeds of the ADC as well as the NBI effects are reduced through
CS. The channel models in A. Oka and L. Lampe, "Compressed Sensing
Reception of Bursty UWB Impulse Radio is Robust to Narrow-Band
Interference," in IEEE Global Telecommunications, December, 2009,
incorporated herein by reference for the UWB signal and the NBI
were fixed with only two different realizations. In the present
disclosure, the channels are randomly selected from different UWB
channel realizations in every burst transmission. The present
disclosure evaluates the effect of the burst size, the type of the
modulated window and the baud rate. The present disclosure also
goes over the parameters that are related to the mitigation process
such as the NBI's bandwidth and bandwidth of the transmitted
pulse.
[0193] The present disclosure addresses the problem of utilizing CS
to blind UWB system in the presence of NBI. The configuration of
UWB transmitter is explained first. The interference source follows
next with some details. More details about NBI modeling are
mentioned. The receiver has two main parts, analog-front-end and
DSP-back-end which are clarified in details. Since the major
processes are done in the receiver, all functions are elaborated
and the constructions of the related blocks are explained.
Simulation and some results are given.
[0194] UWB Transmitter Configuration
[0195] The proposed system contains two main transmission paths,
UWB signal path and interference path as shown in FIG. 24. The UWB
signal's transmitter consists of UWB symbol generator, UWB pulse
shaper, UWB channel, and signal attenuator. The interfering signal
has a similar path. The received signal is corrupted by NBI signal
and thermal noise. The corrupted signal goes through an ideal BPF
that has bandwidth and center frequency matched to those of the
intended signal to be received.
[0196] The transmitter sends burst of data represented by a burst
of pulses. The transmitter comprises three blocks, including baud
clock, payload bits, and IR pulse generator as shown in FIG. 24.
The baud clock generates a clock signal at frequency
f.sub.baud=1/T.sub.baud. It determines the timing of the pulse
within the same burst. Moreover, the start of every burst is also
set by this clock through down-conversion of its frequency to
f.sub.burst. The payload bits block produces information bits,
B.sup.k. In every burst, the transmitter sends K pulses after that
it remains silent till the start of the next burst. The supplied
bits, drown equally probable from {+1, -1}, amplitude modulate an
IR pulse, .phi..sub.U(t). The pulse shape of UWB signal is
generated by modulating a Hanning window with an RF carrier at the
desired center frequency. Thus, the pulse .phi..sub.U(t) will have
a center frequency f.sub.cU, bandwidth .OMEGA..sub.U and interval
T.sub.pulse.
[0197] The time and the frequency domain of the modulated pulse is
plotted in FIG. 26. The pulse has pulse duration, T.sub.pulse=1 ns,
center frequency, f.sub.cU=4 GHz, and a 6-dB bandwidth of about
.OMEGA..sub.U=2 GHz.
[0198] The correct TOA, T.sub.d, for each burst is uniformly
distributed in the interval [0, .gamma.]. The transmitter sends K
pulses per burst per transmission. Then it keeps silent during a
period of T.sub.burst. After that, it sends pulses, followed by the
silent period. The process continues till the transmitter completes
sending all the information.
[0199] In FIG. 27, illustration for three burst transmission is
sketched where there are four bits per burst. The transmitted
waveform for a burst of data transmission can be written as:
s(t)=.SIGMA..sub.k=0.sup.K-1B.sup.k.PHI..sub.U(t-kT.sub.baud-T.sub.d)
(4-1)
[0200] The UWB waveform is then passed through an UWB channel,
c.sub.U(t), according to IEEE802.15.4a channel model CM1 presented
in the present disclosure. The impact of path-loss due to distance
between the UWB transmitter and the UWB receiver, d.sub.U, is
represented by
d - p U ##EQU00019##
where p is the path-loss exponent.
[0201] Interference Configuration
[0202] The interfering symbols are generated at rate 1/T.sub.1,
where T.sub.1 is the baud rate of the NBI. As for UWB signal, the
symbols are shaped first using .phi..sub.1(t). Then the interfering
signal, v(t), is passed through channel c.sub.1(t). The channel of
the NBI might be an IEEE802.11.4a channel model as used for the UWB
signal but with different realization. Alternatively, it may be
other channel model as FIG. 7 shows that perfect channel can be
also used. The impact of path-loss due to the distance between the
NBI and the UWB receiver, d.sub.1, is represented by
d - p U . ##EQU00020##
[0203] UWB Receiver Configuration
[0204] The received signal is contaminated by both two sided
PSD,
N 0 2 , ##EQU00021##
additive White Gaussian Noise (AWGN), w(t), and narrowband
interference, v(t); see FIG. 24. A correlator receiver with digital
notch filter is employed to detect the transmitted signal and
mitigate the NBI. The receiver in FIG. 28 has two main parts,
analog front-end and DSP back-end. Those parts are presented with
more details in the present disclosure. The DSP back-end applies
simple quadratic problem optimization. Quadratic programs can be
easily solved by optimization techniques like
interior-point-methods.
[0205] In blind systems, CS is used to achieve two main things. The
first one is reducing the speed of the ADC or the sampling rate.
The other is the utilization of a sparse signal to detect a certain
waveform's structure. According to the present disclosure when the
length of a signal is N samples, according to Nyquist theorem it
requires at least M mixer-integrators to reconstruct the original
shape of the signal being transmitted where M>N. However, with
M<<N the original signal can be--with high
probability--estimated perfectly without degradation using CS.
Hence the speed of the ADC is reduced to by a factor of M/N. The
transmitted signal contains K nonzero samples and the test
functions are also sparse in the frequency domain. The sparsity of
the transmitted signal helps in the demodulation process, while the
sparsity of the test functions emphasis that the NBI has only small
effect in the measurements being taken. Subsequently the location
of the NBI is detected as well as its effect is effectively
eliminated.
[0206] The analog front end part contains a BPF and M
mixer-integrators. Each mixer compares the signal with one of the
basis. The receiver first utilizes BPF, g(t), to capture the
intended UWB signal and limit the noise. The BPF should have a
center frequency which coincides with the frequency of the
desirable UWB signal f.sub.c and bandwidth equal to the bandwidth
of the transmitted UWB signal .OMEGA., i.e. .OMEGA..sub.U and
f.sub.c=f.sub.cU. FIG. 29 demonstrates the time and the frequency
domain of a BPF with a center frequency of 4 GHz and almost a flat
bandwidth around 2 GHz. The design of the filter should ensure that
the desired UWB signal passes the filter without distortion.
[0207] Ignoring the path-loss, the signal at the output of the BPF
can be written as:
r(t)=.SIGMA..sub.k=0.sup.K-1B.sup.kh(t-kT.sub.baud-T.sub.d)+w(t)+i(t)
(4-2)
where h(t)=.phi..sub.U(t)*c.sub.U(t)*g(t) is the total impulse
response of length denoted by second. The last two terms are the
response of the filter to the noise and to the interference
respectively. M mixer-integrators follow the BPF with highly
frequency selective test functions. The number of correlators is
smaller than required by Shannon-Nyquist sampling theorem. The
output from those mixers is taken simultaneously at
t=.lamda..sub.h(K-1)T.sub.baud.
[0208] The test functions .PSI..epsilon..sup.M.times.N are
sinusoidal waveforms of amplitude 1/ {square root over (N )}
designed to have a rapid decay through windowing technique. In
addition, their frequencies are deterministically and uniformly
distributed in the interval
[ f c - .OMEGA. 2 , f c + .OMEGA. 2 ] . ##EQU00022##
so they are sparse in the frequency domain. Tukey window or tapered
cosine, w[n], is used here, to be compared with see A. Oka and L.
Lampe, "Compressed Sensing Reception of Bursty UWB Impulse Radio is
Robust to Narrow-Band Interference," in IEEE Global
Telecommunications, December, 2009, incorporated herein by
reference where the equation for computing its coefficients is
given by:
w [ n ] = { 1 2 [ 1 + cos ( 2 .pi. .alpha. ' [ n - .alpha. ' 2 ] )
] , 0 .ltoreq. n < .alpha. ' 2 1 , .alpha. ' 2 .ltoreq. n < 1
- .alpha. ' 2 1 2 [ 1 + cos ( 2 .pi. .alpha. ' [ n - 1 + .alpha. '
2 ] ) ] , 1 - .alpha. ' 2 .ltoreq. n .ltoreq. 1 ( 4 - 3 )
##EQU00023##
[0209] The sampled m.sup.th test function multiplied by the window
can be written as:
.psi. i = 1 N sin ( 2 .pi. f I n f s ) w [ n ] , n = 0 , 1 , , N -
1 , .A-inverted. i = 0 , 1 , , M - 1 ( 4 - 4 ) ##EQU00024##
[0210] The shape of this window is controlled by a factor
0.ltoreq..alpha.'.ltoreq.1. The window becomes a rectangle window
when .alpha..ltoreq.0 and resembles a Hanning window if
a'.gtoreq.1. Hence the shape of function approximately doesn't
change if the controlled factor is greater than one or lower than
zero. FIG. 30 represents the frequency domain for three basis
functions designed for three values of .alpha.'=0.1, 0.5 and 0.9.
By making use of Tukey window, the functions get narrower as
.alpha.' increased. The basis functions must be known at the DSP
back-end; however they are simple because they don't require any
tuning.
[0211] Beside the sinusoidal waveforms, the basis functions can be
other signals. The present disclosure focuses on the sinusoidal
signals explained previously. Unless otherwise stated, the
controlled factor is fixed to be .alpha.'=0.9.
[0212] For the quantity
M N f s 2 .OMEGA. , ##EQU00025##
if sample at the Nyquist frequency, f.sub.s should equal to
2.OMEGA.. When M=N, there is no loss and the Nyquist rate is
achieved. While the bandwidth is calculated at the 3 dB point, a
factor, .alpha., is injected to the quantity to be
Mf s 2 .alpha..OMEGA. N . ##EQU00026##
This factor is included to enhance and support practical pulses
because there are no ideal band-limited pulses. The factor
Mf s 2 .alpha..OMEGA. N ##EQU00027##
is called the sampling-factor with .alpha.=1.5. Perfect sampling
will occur when
Mf s 2 .alpha..OMEGA. N = 1 , while Mf s 2 .alpha..OMEGA. N < 1
##EQU00028##
represents the under-sampling case. In the last case where
M<<N, the sampling rate at the receiver side is reduced
further and the receiver complexity is reduced.
[0213] The output of the m.sup.th mixer is given as:
y.sub.m=.intg..sub.0.sup..lamda..sup.h.sup.+.gamma.+(K-1)T.sup.baudr(t).-
psi..sub.m(t)dt (4-5)
[0214] The measurement vector y=[y.sub.0, y.sub.1, . . . y.sub.M-1]
is used in the DSP back-end to demodulate the payload, B.sup.k, via
QP algorithm.
[0215] The main objective of the DSP back-end is to estimate the
payload transmitted information vector B=[B.sup.0, B.sup.1, . . . ,
B.sup.K-1] and actual TOA uncertainty . When an NBI(s) signal is
presented in the band of interest, correlating the test functions
with the received signal gives a vector with large value(s)
whenever the NBI and any one of the test functions have the same
frequency. The first task is to find the position of this value.
The location of the interferer is detected then its effect is
reduced by a digital notch filter. Since the affected measurements
are dropped, lose small amount of the UWB signal's energy may be
lost. However, using such rapidly decaying basis will ensure that
the loss is limited.
[0216] Suppose that the number of interferers is denoted by
n.sub.1. An algorithm searches for the index or the indices of the
maximum absolute measurement value(s) in the measurement vector y
using the relation:
{circumflex over (m)}.sub.i=argmax.sub.m.epsilon.{0,1, . . .
,M-1}|y.sub.m|, i=1,2, . . . ,n.sub.1 (4-6)
[0217] When n.sub.1=1, let D be an even number, the notch filter
drops D+1 measurements around the index {circumflex over (m)}
resulting in y.sub.notched.epsilon..sup.M-(D+1), with the proper
sub-matrix of .PSI..
y notched = [ y 0 , y 1 , , y m ^ - D 2 - 1 , y m ^ + D 2 + 1 , , y
M - 2 , y M - 1 ] ( 4 - 7 ) .PSI. = [ .psi. 11 .psi. 12 , , .psi. 1
N .psi. ( m ^ - D 2 - 1 ) 1 .psi. ( m ^ - D 2 - 1 ) 2 , , .psi. ( m
^ - D 2 - 1 ) N .psi. ( m ^ + D 2 + 1 ) 1 .psi. ( m ^ + D 2 + 1 ) 2
, , .psi. ( m ^ + D 2 + 1 ) N .psi. M 1 .psi. M 2 , , .psi. M N ] (
4 - 8 ) ##EQU00029##
[0218] A major issue is how to set the value of D? The value of D
is related to the bandwidth of UWB signal, .OMEGA..sub.U, bandwidth
of NBI signal, .OMEGA..sub.I, and the number of measurements, M. It
can be also related to A which is the frequency band that separates
any two successive test functions,
.DELTA. = .OMEGA. U M . ##EQU00030##
Hence, it may be written
D = .beta. .OMEGA. I .DELTA. , ##EQU00031##
where .beta. is a safety factor to account for leakage into
adjacent measurements. The value of .beta. is set to 4 as in see A.
Oka and L. Lampe, "Compressed Sensing Reception of Bursty UWB
Impulse Radio is Robust to Narrow-Band Interference," in IEEE
Global Telecommunications, December, 2009, incorporated herein by
reference.
[0219] Depending on the indices of the maximum absolute values in
the measurement vector, there might be an overlapping between the
notched measurements when n.sub.I=2 for example. Consequently the
notched vector may not be
y.sub.notched.epsilon..sup.M-(D.sup.1.sup.+1+D.sup.2.sup.+1). Let
the index or the location of the second maximum absolute
measurement value be greater than the index of the first maximum
absolute measurement value, mathematically {circumflex over
(m)}.sub.2>{circumflex over (m)}.sub.1. If there is no
overlapping, the notched measurement vector is written as:
y notched = [ y 0 , y 1 , , y m ^ 1 - D 1 2 - 1 , y m ^ 1 + D 1 2 +
1 , , y m ^ 2 - D 2 2 - 1 , y m ^ 2 + D 2 2 + 1 , , y M - 1 ] ( 4 -
9 ) ##EQU00032##
[0220] In this case, because of the first interferer the
measurements
m ^ 1 - D 1 2 , m ^ 1 - D 1 2 + 1 , , m ^ 1 + D 1 2 - 1 , m ^ 1 + D
1 2 ##EQU00033##
are notched. Additionally, the measurements
m ^ 2 - D 2 2 , m ^ 2 - D 2 2 + 1 , , m ^ 2 + D 2 2 - 1 , m ^ 2 + D
2 2 ##EQU00034##
are dropped because of second the interferer. It is clear that no
overlapping occurs when
m ^ 2 - D 2 2 > m ^ 1 + D 1 2 . ##EQU00035##
Although, there is an overlapping if
m ^ 2 - D 2 2 .ltoreq. m ^ 1 + D 1 2 . ##EQU00036##
[0221] Through either knowing the number of the presented
interferers or finding the magnitudes which are larger than a
specified threshold (the number of the active interferers), can be
determined. The affected points are then subtracted and removed by
digital notch filter employed in the DSP back-end. Therefore the
interference signal is effectively mitigated.
[0222] Let f.sub.s be a virtual sampling rate that is large enough,
and the sampling time T.sub.s=1/f.sub.s. Since the length of the
channel impulse response is .lamda..sub.h seconds, the number of
samples in the response will be
.LAMBDA..sub.h=[.lamda..sub.hf.sub.s] samples. The discrete time
representation of the channel can be written as h[n]=[h[0],h[1], .
. . , h[.LAMBDA..sub.h-1]].sup.T. The maximum TOA uncertainty,
.gamma., and the baud interval, T.sub.baud, are constructed to be
multiple of T.sub.s. Hence the number of samples in the maximum
possible TOA uncertainty becomes .GAMMA.=.gamma.f.sub.s samples,
and the samples between two consecutive bits will be
N.sub.baud=f.sub.xT.sub.baud samples. While each transmission
includes K bits and .GAMMA. maximum possible TOA uncertainty, the
maximum length of the payload is
.LAMBDA..sub.x=.GAMMA.+(K-1)N.sub.baud samples. Because of the
convolution process, the maximum number of samples in each burst
including the channel is N=.LAMBDA.h+.LAMBDA.x-1.
[0223] Additionally, the actual TOA uncertainty quantization is
Y=round(T.sub.df.sub.s) samples. Small quantization error occurs
which can be ignored when the sampling rate is large enough.
[0224] The received sampled waveform, r.epsilon..sup.N,
becomes:
r=x+w+i (4-10)
where i, w.epsilon..sup.N are the sampled forms of i(t) and w(t),
respectively. H.epsilon..sup.N.times..LAMBDA..sup.X is the
convolutional matrix (Toeplitz form) of n[n] as in A. Oka and L.
Lampe, "Compressed Sensing Reception of Bursty UWB Impulse Radio is
Robust to Narrowband Interference," in IEEE GLOBECOM,
November-December 2009, incorporated herein by reference.
x.epsilon..sup..LAMBDA..sup.X is the virtual discrete time
representation of the payload with K nonzero samples (K-sparse).
Each sample has a random amplitude of {+1, -1}, and has a random
position separated by N.sub.baud samples; mathematically
.LAMBDA..sup.k=Y+kN.sub.baud, k=0, 1, . . . , K-1. Since the
samples are spaced equally by N.sub.baud knowing the location of
the first bit handles the locations of the remaining ones provided
N.sub.baud. Hence the effective sparsity of the signal is only one
rather than K. The sampled measurement vector, y, is the
simultaneous sampling of the output of all correlators after
multiplying the received signal by test functions which can be
written as:
y=.PSI.r=.PSI.x+.PSI.w+.PSI.i (4-11)
[0225] Assume that all transmitted signals
x.epsilon..sup..LAMBDA..sup.X are equiprobable and are contained in
the set .chi.. This set has burst length of
.parallel.x.parallel..sub.0=K. The K nonzero entries of level {-1,
+1} are equally spaced by N.sub.baud samples. The locations of
those nonzero samples are calculated based on the relation:
l.sup.k=l.sup.0+kN.sub.baud where k=0, 1, . . . , K-1 and
l.sup.0.epsilon.[0, .GAMMA.], as FIG. 31 depicts that. There is a
one-to-one mapping. To sum up, any possible transmitted signal,
{-1, +1}.sup.K, has its own payload and random TOA uncertainty
(B,Y) which is mapped in the set x to the corresponding vector
x(B,Y). Therefore, the ML algorithm can be used to estimate the
received discretized signal {circumflex over (x)} first. Then the
result is mapped to estimate the payload {circumflex over
(B)}({circumflex over (x)}) and TOA ({circumflex over (x)}), in
other words P(y|B,Y)=P(y|x).
[0226] Let us ignore the interference term in equation above for
the time being. Given x was transmitted, the ML demodulator used to
detect the intended signal will be:
x ^ = arg min x .di-elect cons. X ( y - .PSI. x ) T ( .PSI. T .PSI.
T ) - 1 ( y - .PSI. x ) ( 4 - 12 ) ##EQU00037##
where g is the convolutional matrix (Toeplitz form) of g(t). Let
.xi.[n] be a vector that represents one of the possible transmitted
signals x.epsilon..sup..LAMBDA..sup.X. This candidate vector has
very large values U in positions where it's unlikely to include
nonzero samples in the original transmitted signal and equals one
in the remaining positions. For n=0, 1, . . . , .LAMBDA..sub.x-1,
the vector [n] is defined as:
.xi. ( a , l 1 , l 2 ) [ n ] = { 1 , n = l + kN baud , l .di-elect
cons. { a + l 1 , a + l 2 } k .di-elect cons. { 0 , 1 , , K - 1 } ,
otherwise ( 4 - 13 ) ##EQU00038##
[0227] The ML demodulation problem equation can be rewritten
as:
{tilde over
(x)}argmin.sub.x.epsilon.R.LAMBDA.X.parallel..XI.(a,l.sub.1.sub.,l.sub.2.-
sub.)x.parallel..sub.1.sub.=K(y-.PSI.x).sup.T(.PSI.gg.sup.T.PSI..sup.T).su-
p.-1(y-.PSI.x) (4-14)
where .XI.(a, l.sub.1, l.sub.2)=diag{.xi.(a, l.sub.1, l.sub.2)}.
Consequently, the previous equation can be simplified more and more
to be a QP problem with two constraints as:
z ~ = min f T z + 1 2 z T Qz , Subject to : z .di-elect cons. 2
.LAMBDA. x : z .gtoreq. 0 , [ .xi. ( a , l 1 , l 2 ) T , .xi. ( a ,
l 1 , l 2 ) T ] z = K ( 4 - 15 ) Q = ( T .PSI. T ( .PSI. T .PSI. T
) - 1 .PSI. - T .PSI. T ( .PSI. T .PSI. T ) - 1 .PSI. - T .PSI. T (
.PSI. T .PSI. T ) - 1 .PSI. T .PSI. T ( .PSI. T .PSI. T ) - 1 .PSI.
) ( 4 - 16 ) f = [ - y notched T ( .PSI. T .PSI. T ) - 1 .PSI. y
notched T ( .PSI. T .PSI. T ) - 1 .PSI. ] ( 4 - 17 )
##EQU00039##
[0228] The following equation used to extracts {tilde over
(x)}.epsilon..sup..LAMBDA..sup.X from {tilde over
(z)}.epsilon..sup.2.LAMBDA..sup.X calculated in (4-15):
{tilde over (x)}.sub.n={tilde over (z)}.sub.n-{tilde over
(z)}.sub.(n+.LAMBDA..sub.X.sub.), n=0,1, . . . ,.LAMBDA..sub.X-1
(4-18)
[0229] The fastest one among several algorithms used to solve the
QP problems is the interior-point algorithm. See S. Boyd and L.
Vandenberghe. Convex Optimization. Cambridge University Press,
2004, incorporated herein by reference in its entirety. Since the
QP problem in hand has only equalities and lower bounds, the
problem is efficiently solved using medium-scale algorithm through
Matlab in the present disclosure.
[0230] The detection process aims to estimate the signal
{circumflex over (x)} first, map {circumflex over (x)} to estimate
the payload {circumflex over (B)}({circumflex over (x)}) and TOA
({circumflex over (x)}). Hence the DSP back-end accomplishes the
demodulation process through two steps. Estimating the arrival of
the burst is the first one which is achieved by solving the QP
problem using .xi.(a=0, l.sub.1=0, l.sub.2=.GAMMA.) to get {tilde
over (x)}.sup.(1). The TOA can be estimated by correlating {tilde
over (x)}.sup.(1) with the template .xi.(0,0,0) using the
relation:
{circumflex over (Y)}=argmax.sub.n'.epsilon.{0,1 . . .
.GAMMA.}.SIGMA..sub.n|{tilde over (x)}.sup.(1)[n-n']|.xi.(0,0,0)[n]
(4-19)
[0231] The second step is to solve the QP problem using .xi.(a=0,
l.sub.1=0, l.sub.2=.GAMMA.). The result {tilde over (x)}.sup.(2)
and the first step's result are used to detect the payload sequence
using the following formula:
{circumflex over (B)}.sup.k=sign({tilde over (x)}.sup.(2)[
+kN.sub.baud]), k=0,1, . . . ,K-1 (4-20)
[0232] The vector {tilde over (x)}.sup.(2) should contain K nonzero
samples, but because of the noise and incorrect estimation of it
may include more than K samples with different magnitudes. The
estimated TOA is used to determine the location of the first
nonzero sample in {tilde over (x)}.sup.(2). The remaining K-1 are
handled easily as they are equally spaced by N.sub.baud samples.
Finally the payload bits {circumflex over (B)}.sup.k are detected
by taking only the sign of the determined locations in {tilde over
(x)}.sup.(2).
[0233] In one embodiment of the present disclosure the mitigation
of the NBI in blind UWB systems is evaluated. The diagram in FIG.
32 summarizes the main steps that are used to simulate the system.
To sum up, the UWB system generates K bits in the first step, and
shapes them. Next, the resultant signal goes through an
IEEE802.11.4a channel. The UWB signal amplitude is scaled based on
the traveled distance if the path-loss is considered. The NBI
system also generates its own symbols, shapes them, and finally
sends them over the interference channel.
[0234] At the receiver side, the received UWB signal is captured
using BPF. Then the measurement is taken using the test functions
followed by an algorithm that determines the number of active
interferers. Based on this number, a digital notch filter
suppresses the effects of those NBIs. Finally, the QP performs a
joint decoding through two stages. The arrival of the current burst
is estimated first. The payload is then demodulated in the second
stage based on the estimated arrival.
[0235] All simulations are accomplished with f.sub.s=10 GHz. For
residential LOS environment, IEEE802.11.4a CM1 is used. The channel
models for the UWB and the NBI signals are randomly selected from
100 realizations generated from CM1 that has a dispersion time
around 50 nanosecond and normalized to have unit energy. A Hanning
modulated pulse centered at frequency f.sub.cU=4 GHz is used to
shape the UWB symbols with duration interval T.sub.pulse=1 ns,
which yields .OMEGA..sub.U=2 GHz. Moreover, the transmission rate
is
f baud = f Nyquist 8 = 2 .OMEGA. U 8 500 Mbaud ##EQU00040##
which causes an ISI to be extended over 25-50 pulses. The test
functions are sinusoid waveforms generated to have frequencies that
are deterministically selected from the band
[ f c + .OMEGA. U 2 , f c - .OMEGA. U 2 ] . ##EQU00041##
They are also designed to have a rapid decay using Tukey window.
The maximum TOA is .gamma.=1 ns which yields .GAMMA.=10 samples.
Since one of main objectives is to reduce the ADC through CS, the
sampling-factor is adjusted to be 0.25 which implies 75% reductions
in the sampling frequency. For the unlicensed NBI, the center
frequency of the UWB pulse, the center frequency and the bandwidth
of the jammers can be located anywhere in the UWB signal's
spectrum. So assume that there is a partial band jammer and 2
partial bands jammer with two equal bandwidths. The 2 partial bands
jammer causes interference in two bands at specific center
frequencies. The partial band is fixed such that it has a center
frequency equal to that of the modulated UWB pulse in order to
produce as much as possible interference for the intended system
i.e. f.sub.cl=f.sub.cU=4 GHz. The location of the 2 partial bands
jammer is adjusted to be similar to one partial band which has
bandwidth equal to summation of the two bands in the 2 partial
bands jammer.
[0236] In this case the center frequencies are located at
f cl 1 , 2 = f cU .+-. .OMEGA. I 2 = 4 GHz .+-. .OMEGA. I 2
##EQU00042##
where .OMEGA..sub.I is the bandwidth of each band. While for the
licensed NB services, the center frequencies and the bandwidth are
fixed as illustrated. All those parameters are fixed unless stated
otherwise.
[0237] At the beginning, the impact of the number of bits per
burst, K, is considered. For a specific NBI, the performance is
evaluated from the BER point of view. The performance is evaluated
for K=2,4, and 8 bit per burst and SNR=9 dB which is fixed for the
following simulations unless otherwise stated. FIG. 33 shows the
case of a partial band interferer that has .OMEGA..sub.I=20 MHz and
f.sub.cl=f.sub.cU=4 GHz.
[0238] If the mitigated with the unmitigated case are compared, it
is clear that the performance is enhanced as K increases. Moreover,
sending the information using large burst size outperforms sending
it using small burst size. This is because of the equally spaced
pulses and the low probability of error in arrival estimation which
reduces the BER. At higher SIR, it is expected that there will be
no benefit from the mitigation process since the NBI becomes very
week and actually notch out the desired measurements.
[0239] Before changing the type and the location of the NBI, the
type of the UWB modulated pulse is investigated. Three different
windows are chosen including Hanning, Gaussian, and Hamming
modulated pulses. For fair comparison, they're adjusted to produce
similar 6-dB bandwidth of .OMEGA..sub.U=2 GHz. The performance is
discussed for the same NBI as shown in FIG. 34. For K=2, a partial
band jammer is assumed with f.sub.cl=f.sub.cU=4 GHz. The Hanning
and Hamming modulated pulses exhibit almost the same performance.
When the SIR becomes greater than 3 dB, the Gaussian modulated
pulse needs to increase the SIR by around 3 dB to get the same BER
compared with Hanning and Hamming. As a result, Hanning modulated
pulse is chosen to be used in the remaining scenarios.
[0240] The interference can take different models. When an
interferer jams a system, it won't affect the performance being
evaluated provided that its center frequency is out of the band of
interest. In other words, the received signal at the output of the
BPF doesn't contain any NBI. In the NBI free case, the performance
should be almost similar to the case when the NBI is located out of
the band of interest. Again for the unlicensed NBIs, assume a
partial band jammer and 2 partial bands jammer with two equal
bandwidths. For the licensed NBIs, the present disclosure studies
them two at a time. For example, WiMAX, IEEE802.11b WLAN are added
together and considered as two jammers in the mitigation
process.
[0241] In FIG. 35 a partial band jammer is assumed to jam the UWB
system with K=2. Slight enhancement is achieved by doubling the
bandwidth since the power spreads over large bandwidth (20 MHz)
compared with the 10 MHz. If the NBI is mitigated, the performance
enhances in the rage of -3<SIR<6 dB. At higher SIR, no
benefit is gained since the NBI's power is very low where actually
the desired signal is dropped.
[0242] Similarly, the same system is evaluated in the presence of 2
partial bands jammer. The center frequencies for the two bands are
adjusted at f.sub.cl=4 GHz+5 MHz, f.sub.cl2=4 GHz-5 MHz.
.OMEGA..sub.I1=.OMEGA..sub.I2=10 MHz, and for the other case
f.sub.cl1=4 GHz+10 MHz, f.sub.cl2=4 GHz-10 MHz and
.OMEGA..sub.I1=.OMEGA..sub.I2=20 MHz. In this case, the enhancement
due to the mitigation against the jammers is large and clear as
FIG. 36 illustrates. Such setting in the center frequencies of the
jammers are in order to make them equivalent to two different
partial bands. The 2 partial bands jammer is one signal which
contains two bands, leading two low power in the bands. For the
considered SIR, the power in the band of a partial band jammer with
.OMEGA..sub.I=10 MHz is greater than that of the 2 partial bands
with
.OMEGA..sub.I1=.OMEGA..sub.I2=10 MHz Therefore, the performance
improves by increasing the bandwidth i.e. the NBI's effect
decreases.
[0243] One object is to see the behavior of the intended system as
a function of the jammer's bandwidth. For the two types of the
unlicensed interferers the BER is investigated versus the jammer
bandwidth for .OMEGA..sub.I=.OMEGA..sub.I1=.OMEGA..sub.I2, SNR=9
dB, and SIR=-3 dB which implies that the interfering signal is
double the UWB signal. As the NBI's power becomes very high, BER
should decrease as the bandwidth of the jammer increases since the
power spreads over large band. An UWB system that uses two bit per
burst transmission is used (K=2) to send 100,000 symbols. The
performance is plotted in FIG. 37. The dual-band interferer has
less effect compared with the single-band case since the power at
the effecting bands are so low compared with that of the partial
band NBI. At bandwidth between 75-to-100 MHz, the two cases have
the same effect on the system performance.
[0244] The effect of the licensed NB services restricts the
selected frequency band. For WiMAX the possible range is large, so
it can be studied for example at 4 GHz together with IEEE802.11a
WLAN (WLANa) operating at 5.2 GHz in order to have two licensed
interferers to the intended system. The modulated UWB pulse is
designed to have a center frequency at f.sub.cU=4.5 GHz and
.OMEGA..sub.U=2 GHz. The two jammers are added together and
consider as one signal when calculating the SIR. Though, they are
considered as two NBIs in the mitigation process.
[0245] Bluetooth and IEEE802.11b WLAN (WLANb), operating in the ISM
band (2.4 GHz), need to change center frequency of the transmitted
pulse. Coexistence of WiMAX interferer at 3.5 GHz with Bluetooth or
with IEEE802.11b WLAN is also possible. Hence an UWB modulated
pulse at f.sub.cU=3 GHz be subject to interference from those NB
services. Bluetooth and IEEE802.11b WLAN interferers or WiMAX and
Bluetooth interferers are two different cases which are evaluated.
The UWB system sends the data with K=8 and the SNR=27 dB.
[0246] The bandwidth of the WiMAX signal is set to its maximum
(.OMEGA..sub.I=20 MHz). The maximum bandwidth equals 20 MHz, 1 MHz,
22 MHz for WLANa, Bluetooth, and WLANb, respectively. The
performance in WLANb and Bluetooth case outperforms that of WiMAX
and Bluetooth as shown in FIG. 38. There are two main reasons for
this; the bandwidth of the WiMAX is smaller than that for the WLANb
by 2 MHz and its center frequency is closer to f.sub.cU. Hence the
affected band in the two cases is so different and consequently the
corrupted and the notched measurements are also different. The
center frequencies of WLANb and Bluetooth are the same which make
them behave as one NBI, though it is changing for the Bluetooth
because of the frequency hopping. The performance is affected more
as the interferer's bandwidth decreases.
[0247] The bandwidth of the UWB pulse also has an effect in the
notched measurements. For Hanning window with pulse duration around
1 nanosecond the 6-dB bandwidth is .OMEGA..sub.U=2 GHz, see FIG.
26. As the pulse duration increases to 2 nanosecond the 6-dB
bandwidth decreases to .OMEGA..sub.U=1 GHz. In other words, the
6-dB bandwidth is .OMEGA..sub.U=2/T.sub.pulse. This parameter is
related to the number of corrupted measurements being dropped.
Comparing two different bandwidth for the same modulated pulse, the
performance is shown in FIG. 39 for K=2, and 4 bit per burst.
Meanwhile this parameters has an effect on the baud rate, the ratio
of transmission remains as before i.e.
f buad = f Nyquist 8 ##EQU00043##
[0248] where f.sub.Nyquist=2.OMEGA..sub.U.
[0249] When .OMEGA..sub.U increases the number of the notched
measurements is reduced and preserves the important information of
the transmitted pulse. Therefore, the performance enhances as FIG.
39 illustrates. When .OMEGA..sub.U decreases more of the
measurements
( D .varies. 1 .OMEGA. U ) ##EQU00044##
are notched out.
[0250] Consequently the performance degrades. Similar to previous
observation in FIG. 33, as K increases the performance
improves.
[0251] The baud rate is also another important parameter. Here it
is desired to know how much data can be transmitted compared to the
Nyquist rate without degrade the system performance.
[0252] The system in A. Oka and L. Lampe, "Compressed Sensing
Reception of Bursty UWB Impulse Radio is Robust to Narrow-Band
Interference," in IEEE Global Telecommunications, December, 2009,
incorporated herein by reference was studied at baud rate
f baud = f Nyquist 8 , ##EQU00045##
where f.sub.Nyquist=2.OMEGA..sub.U. Three different baud rates are
compared in FIG. 40 including
f baud = f Nyquist 8 = 500 Gbaud , f Nyquist 4 = 1000 Gbaud and f
Nyquist 2 = 2000 Gbaud ##EQU00046##
with K=2.
[0253] A partial band NBI is present with bandwidth and center
frequency of .OMEGA..sub.I=20 MHz, f.sub.cl=4 GHz,
respectively.
[0254] The ISI is proportional to the transmission rate.
Consequently, as the baud rate increases more pulses are being
overlapped which degrade the system performance.
[0255] Here, the mitigation of the NBI in blind UWB systems is
evaluated. The speeds of the ADC as well as the NBI effects are
reduced through CS. The present disclosure extends the mitigation
technique in A. Oka and L. Lampe, "Compressed Sensing Reception of
Bursty UWB Impulse Radio is Robust to Narrow-Band Interference," in
IEEE Global Telecommunications, December, 2009, incorporated herein
by reference to consider the effect of two licensed or unlicensed
NBIs. The present disclosure also studies different parameters that
may affect the system performance such as the burst size, the type
of the modulated window and the baud rate. In addition, the present
disclosure examines the performance of the system in the presence
of different licensed and unlicensed NBIs. The present disclosure
also goes over the parameters that are related to the mitigation
process such as the NBI's bandwidth and the bandwidth of the
transmitted pulse.
[0256] As the present disclosure uses more bit per burst, the
difference between the mitigated and the unmitigated case
increases. Though, this difference becomes low as the SIR increases
because the NBI becomes so weak. Moreover, sending the information
using large burst size outperforms sending it using small burst
size since the probability of making an error in one bit decreases
as the burst size increases. The simulation shows that the BER is a
weak function of the considered modulated widow. Additionally, the
performance is highly affected when the NBI's center frequency is
shifted to the center frequency of the transmitted pulse.
[0257] For a partial band jammer, slight enhancement is achieved by
doubling the bandwidth since the power spreads over larger
bandwidth. While in the dual-band jammer case, the enhancement due
to the mitigation against the jammers is evident. At higher SIR,
more benefit is not obtained since the NBI's power is very low
where the present disclosure actually drops the desired signal. For
the considered scenarios, it is demonstrated that the BER is a
strong function of the NBI's bandwidth.
[0258] In the simulation, the present disclosure also considers
different bandwidth of the transmitted pulse, .OMEGA..sub.U. When
.OMEGA..sub.U increases the number of the notched measurements is
reduced and the present disclosure preserves the important
information of the transmitted pulse. Therefore, the performance
enhances. When .OMEGA..sub.U decreases the present disclosure
notches out many of them. Consequently the performance degrades
since the power of the NBI is now concentrated in a relatively
larger band.
[0259] The present disclosure mainly focuses on studying the
mitigation of NBI in trained and blind UWB systems based on CS. The
mitigation technique in the trained system needs to have some
knowledge about the NBI signal's subspace, while in blind systems
other parameters are more dominant such as the bandwidth of the
NBI, the bandwidth of UWB transmitted pulse and the number of
measurements (mixer-integrators). In both systems, CS is applied to
reduce the speed of the ADC by using mixer-integrators lower than
the required by Shannon theorem.
[0260] The present disclosure describes a method including pilot
symbol distribution that optimizes the BER in trained UWB systems.
In blind systems the present disclosure extends the mitigation
process to mitigate the effect of two licensed and unlicensed
NBIs.
[0261] It was shown that due to the large bandwidth of the UWB
signals, they require a very high speed ADC and they may interfere
with other narrowband systems. Hence, an UWB receiver should handle
those two problems in an efficient way.
[0262] Since narrowband signals have sparse representation in the
DCT domain, they can be estimated using CS. The mitigation
technique needs to have knowledge about the NBI signal's subspace.
The present disclosure estimated the sparse components of the
interferer using MP and then used knowledge to suppress the most
significant coefficients. This was achieved by adjusting the value
of the interference threshold, .mu.. The present disclosure
established that, this value should not be very large in order to
have a good NBI's subspace estimation and shouldn't be very low to
avoid excessive noise level.
[0263] Moreover, the present disclosure provides pilot symbols
distribution that optimizes the BER. The present disclosure
describes a system in which a minimum required number of symbols in
the first group N.sub.P1 after which the performance saturates.
Communications can be achieved with N.sub.p2=2, however, the
performance can be enhanced if the UWB signal structure is employed
in the construction of the projection matrix. The number of pilot
symbols in the third group N.sub.p3 is directly proportional to the
performance; hence more symbols should be assigned to get
information about the channel.
[0264] In one embodiment in the presence of strong and different
licensed and unlicensed NBIs, the location of the NBI relative to
the center frequency of the transmitted pulse determines the amount
of the degradation in the system performance. Additionally, the
present disclosure evaluated the system in the presence of
multiuser interference. Simulations show that when more users being
active the system performance degrades.
[0265] Further, the present disclosure considered the mitigation of
narrowband interference in blind systems. The mitigation process
needs to locate the center frequency of the NBI. Then a digital
notch filter is employed to drop out the affect measurements around
the estimated interferer based on some parameters such as the
bandwidth of the NBI, the bandwidth of UWB transmitted pulse and
the number of measurements (mixer-integrators). The main parameter
in hand is the bandwidth of the NBI. Hence, it should be available
at the intended receiver.
[0266] The performance is highly affected by the NBI's center
frequency relative to the center frequency of the transmitted
pulse. The present disclosure demonstrated that the BER is a strong
function of the NBI's bandwidth. The performance enhances as the
NBI's bandwidth increases since the power spreads over large
bandwidth. As the UWB signal's bandwidth increases the number of
the notched measurements reduces and the present disclosure
preserves the important information of the transmitted pulse.
Moreover, simulation shows that the BER is a weak function of the
considered modulated windows.
[0267] The mitigation process in the blind and trained systems is
totally different since it depends on various parameters. The
inverse DCT transformation matrix of interferer should be known; in
this case the trained system is used. On the other hand, the blind
system can be effectively used, if the NBI's bandwidth is
known.
[0268] The present disclosure considered NBI mitigation in UWB
systems based on CS. There are still several open problems whose
solution could add a great benefit in the field of interest. The
present disclosure may summarize them in the following points:
[0269] Extend the trained CS based UWB system to perform MUltiuser
Detection (MUD). Both the NBI and the multiuser interference are
mitigated. Before NBI mitigation, the receiver jointly decodes all
users first. Then subtracts the decoded information from the
received noisy signal.
[0270] In Multiuser systems the dictionary is redesigned to nullify
the other users. Different waveforms for the different users are
used. Future work may compare and study different signaling schemes
that can be used for multiuser techniques.
[0271] The amount of degradation due to the presence of other users
is quantified. The method may include using compressive sensing
algorithm to possibly reject other users. The challenge is in the
similarity between the intended dictionary and the one to be
nullified.
[0272] A receiver that changes the interference threshold,
adaptively in order to enhance the BER. The same receiver may
adaptively select the best pilot symbols distribution that
optimizes the system performance.
[0273] A blind UWB system for multiuser signal detection.
[0274] The method may know the NBI's bandwidth by approximation. An
algorithm is used to estimate the number of the active NBIs. A
threshold to handle the NBI as a random signal can be used to
detect weather the NBI is active or not.
[0275] Next, a hardware description of a device according to
exemplary embodiments is described with reference to FIG. 41. In
FIG. 41, the device includes a CPU 4100 which performs the
processes described above. The process data and instructions may be
stored in memory 4102. These processes and instructions may also be
stored on a storage medium disk 4104 such as a hard drive (HDD) or
portable storage medium or may be stored remotely. Further, the
claimed advancements are not limited by the form of the
computer-readable media on which the instructions of the inventive
process are stored. For example, the instructions may be stored on
CDs, DVDs, in FLASH memory, RAM, ROM, PROM, EPROM, EEPROM, hard
disk or any other information processing device with which the
device communicates, such as a server or computer.
[0276] Further, the claimed advancements may be provided as a
utility application, background daemon, or component of an
operating system, or combination thereof, executing in conjunction
with CPU 4100 and an operating system such as Microsoft Windows 7,
UNIX, Solaris, LINUX, Apple MAC-OS and other systems known to those
skilled in the art.
[0277] CPU 4100 may be a Xenon or Core processor from Intel of
America or an Opteron processor from AMD of America, or may be
other processor types that would be recognized by one of ordinary
skill in the art. Alternatively, the CPU 4100 may be implemented on
an FPGA, ASIC, PLD or using discrete logic circuits, as one of
ordinary skill in the art would recognize. Further, CPU 4100 may be
implemented as multiple processors cooperatively working in
parallel to perform the instructions of the inventive processes
described above.
[0278] The device in FIG. 41 also includes a network controller
4106, such as an Intel Ethernet PRO network interface card from
Intel Corporation of America, for interfacing with network 77. As
can be appreciated, the network 77 can be a public network, such as
the Internet, or a private network such as an LAN or WAN network,
or any combination thereof and can also include PSTN or ISDN
sub-networks. The network 77 can also be wired, such as an Ethernet
network, or can be wireless such as a cellular network including
EDGE, 3G and 4G wireless cellular systems. The wireless network can
also be WiFi, Bluetooth, or any other wireless form of
communication that is known.
[0279] The device further includes a display controller 4108, such
as a NVIDIA GeForce GTX or Quadro graphics adaptor from NVIDIA
Corporation of America for interfacing with display 4110, such as a
Hewlett Packard HPL2445w LCD monitor. A general purpose I/O
interface 4112 interfaces with a keyboard and/or mouse 4114 as well
as a touch screen panel 4116 on or separate from display 4110.
General purpose I/O interface also connects to a variety of
peripherals 4118 including printers and scanners, such as an
OfficeJet or DeskJet from Hewlett Packard.
[0280] A sound controller 4120 is also provided in the device, such
as Sound Blaster X-Fi Titanium from Creative, to interface with
speakers/microphone 4122 thereby providing sounds and/or music.
[0281] The general purpose storage controller 4124 connects the
storage medium disk 4104 with communication bus 4126, which may be
an ISA, EISA, VESA, PCI, or similar, for interconnecting all of the
components of the device. A description of the general features and
functionality of the display 4110, keyboard and/or mouse 4114, as
well as the display controller 4108, storage controller 4124,
network controller 4106, sound controller 4120, and general purpose
I/O interface 4112 is omitted herein for brevity as these features
are known.
[0282] See Evaluation of Compressed Sensing in UWB Systems with
NBI, by Saleh Ahmed Alawsh, A thesis presented to the dean of
graduate studies at King Fahd University of Petroleum and Minerals,
Dhahran, Saudi Arabia, April 2013, incorporated herein by reference
in its entirety.
* * * * *