U.S. patent application number 11/577106 was filed with the patent office on 2009-03-19 for method and system for estimating time of arrival of signals using multiple different time scales.
This patent application is currently assigned to MITSUBISHI ELECTRIC RESEARCH LABORATORIES. Invention is credited to Ismail Guvenc, Andreas F. Molisch, Zafer Sahinoglu.
Application Number | 20090075590 11/577106 |
Document ID | / |
Family ID | 37115434 |
Filed Date | 2009-03-19 |
United States Patent
Application |
20090075590 |
Kind Code |
A1 |
Sahinoglu; Zafer ; et
al. |
March 19, 2009 |
Method and System for Estimating Time of Arrival of Signals Using
Multiple Different Time Scales
Abstract
A method and system (500) estimates a time of arrival of a
signal received via a wireless communications channel. The energy
in the received signal is conditioned at multiple different time
scales to produce a conditioned signal (700). Then, a leading edge
is detected in the conditioned signal (550). The leading edge
corresponds to the time of arrival of the received signal
(551).
Inventors: |
Sahinoglu; Zafer;
(Arlington, MA) ; Guvenc; Ismail; (Santa Clara,
CA) ; Molisch; Andreas F.; (Arlington, MA) |
Correspondence
Address: |
MITSUBISHI ELECTRIC RESEARCH LABORATORIES, INC.
201 BROADWAY, 8TH FLOOR
CAMBRIDGE
MA
02139
US
|
Assignee: |
MITSUBISHI ELECTRIC RESEARCH
LABORATORIES
Cambridge
MA
|
Family ID: |
37115434 |
Appl. No.: |
11/577106 |
Filed: |
April 15, 2005 |
PCT Filed: |
April 15, 2005 |
PCT NO: |
PCT/US05/13035 |
371 Date: |
April 12, 2007 |
Current U.S.
Class: |
455/39 |
Current CPC
Class: |
H04B 17/318 20150115;
G01S 5/0221 20130101; G01S 13/76 20130101; H04B 1/71637 20130101;
H04B 17/336 20150115; H04B 17/345 20150115 |
Class at
Publication: |
455/39 |
International
Class: |
H04B 7/24 20060101
H04B007/24 |
Claims
1. A method for estimating a time of arrival of a radio signal,
comprising: conditioning, at multiple different time scales, an
energy of a received signal to produce a conditioned signal; and
detecting a leading edge of the conditioned signal, the leading
edge corresponding to a time of arrival of the received signal.
2. The method of claim 1, further comprising: estimating a distance
between two transceivers based on the time of arrival.
3. The method of claim 1, in which the received signal is an ultra
wideband radio signal.
4. The method of claim 1, in which the received signal is a
time-hopped, impulse-radio signal.
5. The method of claim 1, in which the signal is received via a
wireless channel, and further comprising: conditioning the received
signal based on characteristics of the wireless channel.
6. The method of claim 1, further comprising: conditioning the
received signal based on parameters of the signal.
7. The method of claim 1, in which the signal is received via a
wireless channel, and further comprising: conditioning the received
signal based on characteristics of the wireless channel and
parameters of the signal.
8. The method of claim 1, further comprising: applying multi-scale
wavelet coefficients to the energy of the signal during the
conditioning.
9. The method of claim 1, further comprising: applying multi-scale
filters to the energy of the signal during the conditioning.
10. The method of claim 1, further comprising: receiving the
signal; and collecting the energy of the received signal.
11. The method of claim 5, in which the characteristics of the
channel include a signal to noise ratio.
12. The method of claim 6, in which the parameters of the received
signal include a bandwidth, a frame length, a symbol length, a chip
length, and a block length of the received signal.
13. The method of claim 6, further comprising: selecting wavelet
scaling filters and coefficients of the multiple different time
scales according to the parameters of the received signal.
14. The method of claim 1, further comprising: excluding fine time
scales during the conditioning at low signal to noise ratios.
15. The method of claim 1, in which the conditioning enhances peaks
relatively near the leading edge.
16. The method of claim 4, in which multiple pulses are transmitted
for each symbol in the received signal.
17. The method of claim 16, in which the multiple pulses include
delayed versions of a first one of the multiple pulses.
18. The method of claim 1, in which the time of arrival is less
than a length of a symbol represented by the received signal.
19. The method of claim 10, in which collecting uses a square-law
device.
20. The method of claim 10, in which collecting uses a stored
reference signal.
21. The method of claim 10, in which collecting uses a transmitted
reference signal.
22. A system for estimating a time of arrival of a radio signal,
comprising: means for conditioning, at multiple different time
scales, an energy of a received signal to produce a conditioned
signal; and means for detecting a leading edge of the conditioned
signal, the leading edge corresponding to a time of arrival of the
received signal.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention relates generally to radio
communication systems, and more particularly to determining a time
of arrival of a received signal in a wireless communications
network for radio ranging applications.
[0002] Ranging
[0003] To estimate a distance between a transmitter and a receiver
in a wireless communications network, the transmitter sends a
signal to the receiver at a time instant t.sub.1 according to a
clock of the transmitter. After receiving the signal, the receiver
immediately returns a reply signal to the transmitter. The
transmitter measures a time of arrival (TOA) of the reply signal at
a time t.sub.2. An estimate of the distance between the transmitter
and the receiver is the time for the signal to make the round trip
divided by two and multiplied by the speed of light
c , i . e . , D = t 1 - t 2 2 c . ##EQU00001##
This is also known as `ranging.
[0004] Matched Filtering
[0005] In a conventional ranging system as shown in FIG. 1A, a
signal 101 received at an antenna is pre-filtered 200 and passed to
a matched filter 300. Leading edge detection 150 can be performed
on the output of the matched filter.
[0006] As shown in FIG. 2, a typical pre-filter 200 includes a
linear low noise amplifier (LNA) 210, and a band-pass filter (BPF)
220. Generally, the output of the matched filter 300 is sampled at
a Nyquist rate to produce discrete signal decision statistics for
the edge detection.
[0007] As shown in FIG. 3, the matched filter 300 can use a time
shifted 301 template signal 310 to produces a maximum correlation
with the received signal 110 and by applying an integrator 320.
Using a sampler circuit 330, a highest peak at the output of the
matched filter 300 is considered the TOA estimate by the signal
edge detector 150, G. L. Turin, "An introduction to matched
filter," IRE Trans. on Information Theory, vol. IT-6, no. 3, pp.
311-329, June 1960. The time shifted template signal is adjusted
301 adaptively. In other words, correlations of the received signal
with shifted versions of the template signal 310 are considered. In
a single path channel, the transmitted waveform can be used as the
optimal template signal, and conventional correlation-based
estimation can be employed.
[0008] However, in the presence of an unknown multipath channel,
the optimal template signal becomes the received waveform, which is
a convolution of the transmitted waveform with the channel impulse
response. Therefore, the correlation of the received signal with
the transmit-waveform template is suboptimal in a multipath
channel. If this suboptimal technique is employed in a narrowband
system, the correlation peak may not give the true TOA because
multiple replicas of the transmitted signal partially overlap due
to multipath propagation.
[0009] In order to prevent this effect, super-resolution time delay
estimation techniques have been described, M.-A. Pallas and G.
Jourdain, "Active high resolution time delay estimation for large
BT signals," IEEE Transactions on Signal Processing, vol. 39, issue
4, pp. 781-788, April 1991.
[0010] Edge Detection on an Over-Sampled Signal
[0011] As shown in FIG. 1B, signal processing for edge detection
150 can be performed directly on the output of the pre-filter 120.
However, the high sampling rate makes the method impractical for
real-time applications.
[0012] Signal Processing Prior to Step Detection
[0013] As shown in FIG. 1C for other conventional applications 170,
e.g., electrocardiograms (ECG), acoustic signals and images, the
signals are first processed 400 so that edge detection 190 can
distinguish weak first arrival paths from noise by enhancing peaks
due to the signal, and suppressing peaks associated with noise. As
shown in FIG. 4A, a bank 410 of wavelet filters .phi. 420 can be
applied to the signal to enhance edge detection.
[0014] Leading Edge Detection
[0015] Detecting leading edges of signals has analogies with
various other fields including: object edge detection in image
processing, J. Canny, "A computational approach to edge detection,"
IEEE Trans. Pattern Anal. Machine Intel, vol. 8, pp. 679-698, 1986,
and H. Moon, R. Chellappa, and A. Rosenfeld, "Optimal edge-based
shape detection," IEEE Trans. Image Proc., vol. 11, no. 11, pp.
1209-1227, November 2002; voice activity detection in speech
processing, S. G. Tanyer and H. Ozer, "Voice activity detection in
non-stationary noise," IEEE Trans. Speech and Audio Processing,
vol. 8, no. 4, pp. 478-482, July 2000, A. Q. Z. Qi Li; Jinsong
Zheng; Tsai, "Robust endpoint detection and energy normalization
for real-time speech and speaker recognition," IEEE Trans. Speech
and Audio Processing, vol. 10, no. 3, pp. 146-157, March 2002, and
J. Sohn, N. S. Kim, and W. Sung, "A statistical model-based voice
activity detection," IEEE Signal Processing Lett., vol. 6, no. 1,
pp. 1-3, January 1999; and spike-detection in biomedical
engineering, Z. Nenadic and J. W. Burdick, "Spike detection using
the continuous wavelet transform," IEEE Trans. Biomedical
Engineering, vol. 52, no. 1, pp. 7487, January 2005, S.
Mukhopadhyay, G. C. Ray, "A new interpretation of nonlinear energy
operator and its efficacy in spike detection," IEEE Trans.
Biomedical engineering, vol. 45, no. 2, pp. 180-187, February 1998;
and electrocardiograms, C. Li, C. Zheng, and C. Tai, "Detection of
ECG characteristic points using wavelet transforms," IEEE Trans.
BiomedicalEngineering, vol. 42, no. 1, pp. 21-28, January 1995)
[0016] Detecting drastic changes in signals is described
extensively in the prior art. When statistics of the signal are
known before and after a change-point, an optimal detection can be
achieved by tracking log-likelihood ratios of the signals from two
hypothesized distributions.
[0017] Considering more basic techniques, a simplest approach for
detecting edges of a signal is to pass the signal through a
gradient operator, such as [-1 0 1]). However, this technique does
not consider the effects of noise. The performance of the gradient
operator can be improved by using a filtered derivative techniques
for smoothing.
[0018] Scale-space filtering, as shown in FIG. 4A, was first
described by A. Witkin, "Scale-space filtering: A new approach to
multi-scale description," Proc. IEEE Int. Conf. Acoust., Speech,
Signal Processing (ICASSP), vol. 9, pp: 150-153, March 1984. The
input signal 170 is smoothed at various time scales with Gaussian
distributions of different variances .phi. 420. Local minima and
maxima of the derivative of the smoothed signal, at various time
scales, which can also be obtained by filtering an initial signal
with derivatives of Gaussian distributions at various time scales,
correspond to the edges of the signal at different scales.
Zero-crossings of a convolution of the signal with the second
derivatives of Gaussian distributions, at various scales, can
identify the edges. However, this technique does not reveal a
direction of the edge, i.e., whether the edge is a rising-edge or a
falling-edge, nor, a sharpness of the edge. Witkin describes a
coarse-to-fine tracking of the edges in the scale-space image, by
exploiting the correlations across the scales, to identify and
localize major singularities in the signal.
[0019] The scale-space representation of signals uses a
wavelet-theory framework, and a wavelet transform modulus maxima
(WTMM) for the identification of major edges in the signal is used
by A. Mallat and W. L. Hwang, "Singularity detection and processing
with wavelets," IEEE Trans. Information Theory, vol. 38, no. 2, pp.
617-643, March 1992, and A. Mallat and S. Zhong, "Characterization
of signals from multi-scale edges," IEEE Trans. Pattern Analysis
and Machine Intelligence, vol. 14, no. 2, pp. 710-732, July
1992.
[0020] By analyzing an evolution of the wavelet transform exponent
across scales, local Lipschitz exponent, which measure a local
regularity of the signal, can be estimated. That effectively
`denoises` the signal using the Lipschitz exponent, and other a
priori information.
[0021] A direct multiplication of wavelet transform data, at
various scales, can be used to enhance signal edges and suppress
the noise, Y. Xu, J. B. Weaver, D. M. Healy, and J. Lu, "Wavelet
transform domain filters: a spatially selective noise filtration
technique," IEEE Trans. Image Processing, vol. 3, no. 6, pp.
747-758, July 1994.
[0022] Using the product of multi-scale wavelet coefficients to
detect sharp edges in signals is described by A. Swami and B. M.
Sadler, "Steps change localization in additive and multiplicative
noise via multi-scale products," Proc. IEEE Asilomar Conf. Signals,
Systems, Computers, vol. 1, pp. 737-741, November 1998, B. M.
Sadler and A. Swami, "On multi-scale wavelet analysis for step
estimation," Proc. IEEE Int. Conf. Acoust., Speech, Signal
Processing (ICASSP), vol. 3, pp. 1517-1520, May 1998, S.
MacDougall, A. K. Nandi, and R. Chapman, "Multiresolution and
hybrid Bayesian algorithms for automatic detection of change
points," IEEE Proceedings-Vision, Image, and Signal Processing,
vol. 145, no. 4, pp. 280-286, August 1998, J. Ge and G.
Mirchandani, "Softening the multi-scale product method for adaptive
noise reduction," Proc. IEEE Asilomar Conf. Signals, Systems,
Computers, vol. 2, pp. 2124-2128, November 2003, L. Zhang and P.
Bao, "A wavelet-based edge detection method by scale
multiplication," Proc. IEEE Int. Conf. Pattern Recognition, vol. 3,
pp. 501-504, August 2002, and M. Beauchemin and K. B. Fung,
"Investigation of multi-scale product for change detection in
difference images," Proc. IEEE Int. Geoscience and Remote Sensing
Symp. (IGARSS), vol. 6, pp. 3853-3856, September 2004.
[0023] Ultra Wideband
[0024] Ultra wideband signals are drastically different than
conventional wireless signals. Not only is the signal spread over a
huge frequency range, but in addition, the extremely short pulses
that constitute the signal are also spread out over time. For
example, the signal can cover anywhere from 500 MHz to several GHz
of the radio spectrum, and bursts of ultra-low power pulses are
often in the picosecond, i.e., 1/1000th of a nanosecond, range. The
pulses are transmitted across all frequencies at once. Furthermore,
UWB signals are subject to dense multipath propagations.
[0025] FIG. 4B compares the potential effect of the differences
between a conventional signal 451 and an ultrawideband signal 452.
Missing the peak at time 461 for the conventional signal 451 will
have minimum effect on estimating the correct TOA, while missing
the peak at time 462 for the UWB signal 452 can be completely
erroneous.
[0026] However, as the bandwidth of the UWB signal increases, the
signal is less spread in time and a rising edge of the received
signal becomes sharper. In precision ranging applications,
detecting the arrival time of the rising edge of the received
signal at desired accuracies is important. Therefore, it is desired
to use UWB signals to provide precise positioning capabilities.
[0027] Prior art matched filters are described by W. Chung and D.
Ha, "An accurate ultra wideband (UWB) ranging for precision asset
location," Proc. IEEE Conf. Ultrawideband Syst. Technol. (UWBST),
pp. 389-393, November 2003, B. Denis, J. Keignart, and N. Daniele,
"Impact of NLOS propagation upon ranging precision in UWB systems,"
Proc. IEEE Conf. Ultrawideband Syst. Technol. (UWBST), pp. 379-383,
November 2003, and K. Yu and I. Oppermann, "Performance of UWB
position estimation based on time-of-arrival measurements," Proc.
IEEE Conf. Ultrawideband Syst. Technol. (UWBST), pp. 400-404, May
2004.
BRIEF DESCRIPTION OF THE DRAWINGS
[0028] FIG. 1A is a block diagram of prior art leading edge
detector with a matched filter;
[0029] FIG. 1B is a block diagram of a prior art leading edge
detector without a matched filter;
[0030] FIG. 1C is a block diagram of a prior art leading edge
detector with a signal conditioner;
[0031] FIG. 2 is a block diagram of a pre-filter for the leading
edge detector of FIG. 1A;
[0032] FIG. 3 is a block diagram of a matched filter for the
leading edge detector of FIG. 1A;
[0033] FIG. 4A is a block diagram of the signal conditioner of the
leading edge detector of FIG. 1C;
[0034] FIG. 4B compares peaks in conventional signals with peaks in
ultra wideband signals;
[0035] FIG. 5A is block diagram of a ranging system and method;
[0036] FIG. 5B is a timing diagram of a transmitted time hopping
impulse radio signal to be detected;
[0037] FIG. 6A is a block diagram of the signal energy collector
that produces observation samples using signal energy
collection;
[0038] FIG. 6B is a block diagram of the signal energy collector
that produces observation samples using matched filtering;
[0039] FIG. 6C is a block diagram of the signal energy collector
that produces observation samples using transmitted reference
structure;
[0040] FIG. 7 is a detailed block diagram of a ranging method using
a wavelet filter bank; and
[0041] FIG. 8 is a detailed block diagram of a ranging method using
a multi-scale filter bank.
[0042] System Structure and Method Operation
[0043] As shown in FIG. 5A, we provide a system and method 500 for
estimating a time of arrival (TOA) of a signal 501 received via a
wireless channel 502 at a radio transceiver in a wireless
communications network. The TOA in a ranging application can be
used to determine a distance between two transceivers. For the
purpose of this description, the transceiver is estimating the TOA
for a received signal. However, it should be understood that the
transceiver can transmit and receive. In a preferred embodiment,
the received signal 501 is an ultra wideband radio signal.
[0044] The signal 501 is received at an antenna of a transceiver.
Energy of the signal is collected 600. The collected signal energy
is conditioned 700 using multiple different time scales.
Furthermore, the conditioning can be improved by considering
characteristics 520 of the channel and signal parameters 540.
Leading edge detection 550 is then preformed on the condition
signal energy to estimate the TOA 551.
[0045] Our method is significantly different than the prior art. We
use multiple different time scales. In one embodiment, we apply
products of multi-scale wavelet coefficients during the signal
conditioning 700, see FIG. 7. In an alternative embodiment, we
apply multi-scale filters during the conditioning, see FIG. 8.
Multiple different time scales have never been used for
conditioning a collected energy of a radio signal to perform
leading edge detection for the purpose of radio ranging.
[0046] The signal energy conditioner 700 takes the channel
characteristics 520, e.g., signal to noise ratio (SNR), etc., and
the signal related parameters 540, e.g., bandwidth, frame, symbol,
chip, and block lengths the signal, into consideration to improve a
performance of the energy edge detector 550. The signal related
parameters 540 can be used to select appropriate wavelet time
scaling filters and coefficients of the multiple different time
scales, while the channel characteristics 520 are used in selecting
the different time scales involved in the product calculation.
[0047] At relatively low SNRs, e.g., less than 20 dB, fine time
scales are excluded from the product determinations, because a high
noise level cannot be smoothed out at fine time scales. Therefore,
the fine time scales, unless they are removed, can cause erroneous
peaks.
[0048] We use multi-time scale analysis of the received signal
energy to conditioning the signal. The conditioning enhances peaks
relatively near to the leading edge of the received signal 501, and
suppresses noise. Then, edge detection methods can be applied to
the output of the conditioner 700.
[0049] Signal Model
[0050] The received signal can be an ultra-wideband signal (UWB).
Specifically, a time-hopped impulse-radio signal (TH-IR). However,
it should be understood, that the signal can be of other forms, as
known in the art.
[0051] As shown in FIGS. 5B-5C, for the ultra wideband signal 501,
wireless impulse radio transceivers allocate time in terms of
symbol time (T.sub.S) 595, frame times (T.sub.F) 575, blocks times
(T.sub.B) 585, and chip times (T.sub.C) 565. Frames are longer than
blocks, which are longer than chips. Each frame can include
multiple blocks. Each block can include multiple chips, and each
symbol (T.sub.S) 595 can include multiple frames 565.
[0052] As shown in FIG. 5B, a single radio pulse 555 is transmitted
in each frame 565 within a block 585 at a predetermined position
(time) in a chip 565. As shown in FIG. 5C, multiple pulses 555 and
556 are transmitted for each symbol. The later pulses are delayed
(D) 640 versions of the first pulse. It should be understood that
more than two pulses can be transmitted for each symbol.
[0053] The predetermined position of the single pulse or multiple
pulses can be different for different symbols. Typically, the
position of the pulse in the frame indicates the value of the
symbol. The received time hopping (TH) impulse radio (IR) signal
501 can be represented by
r ( t ) = j = - .infin. .infin. d j .omega. m p ( t - jT f - c j T
c - .tau. toa ) + n ( t ) , ( 1 ) ##EQU00002##
where a frame index is j, a frame duration is T.sub.f, a number of
pulses per symbol is N.sub.s, a chip duration is T.sub.c, a symbol
duration is T.sub.s, the TOA of the received signal is
.tau..sub.toa, and a possible number of chip positions per frame
N.sub.h is given by N.sub.h=T.sub.f/T.sub.c. An effective pulse
after the channel impulse response is given by
.omega. m p ( t ) = E l = 1 L .alpha. l .omega. ( t - .tau. l ) , (
2 ) ##EQU00003##
where the received UWB pulse is .omega.(t) is a pulse energy E, a
fading coefficients .alpha..sub.i, and delays of the multipath
components are .tau..sub.1. Additive white Gaussian noise (AWGN)
with zero-mean and double-sided power spectral density N.sub.0/2
and variance .sigma..sup.2 is denoted by n(t). No modulation is
considered for the ranging process.
[0054] In order to avoid catastrophic collisions, and smooth the
power spectral density of the transmitted signal, time-hopping
codes c.sub.j.sup.(k), that can take values in {0, 1, . . . ,
N.sub.h-1} are assigned to different transceivers. Moreover,
random-polarity codes d.sub.j{=.+-.1} provide additional processing
gain for detecting the signal, and smoothing the signal
spectrum.
[0055] For simplicity of this description, we assume that the
signal arrives in one frame duration, i.e.,
.tau..sub.TOA<T.sub.f, and there is no inter-frame interference
(IFI), i.e., T.sub.f.gtoreq.(L+c.sub.max)T.sub.c, or, equivalently,
N.sub.c.gtoreq.L+c.sub.max, where c.sub.max is a maximum value of
the TH sequence. It should be understood that multiple frames can
be used for a symbol.
[0056] Note that the assumption of .tau..sub.TOA<T.sub.f does
not restrict us. In fact, it is enough to have
.tau..sub.TOA<T.sub.s to work when the frame is large enough and
a predetermined TH codes are used. Moreover, even if
.tau..sub.TOA>T.sub.s, an initial energy detection can be used
to determine the arrival time within a symbol uncertainty.
[0057] Signal Energy Collection
[0058] UWB signals are quite unlike conventional signals in a
number of ways. First the signal is spread over an extremely large
frequency range. Second, the pulses that constitute the signal are
spread over time. Third, the signal suffers from multipath
propagation, and fourth, the amount of energy in the pulses is very
low. For example, FCC regulations require UVWB systems to emit
energy at less than -41.3 dBm/Hz, over a spectrum from 3.1 GHz to
10.6 GHz. The low power requirement results in increased
sensitivity of UWB signals to interference and fading. Therefore,
in the case the signal is a wideband signal, we provide three
different ways that energy can be collected 600 in an optional step
to produce the signal for the energy conditioner 700.
[0059] Square-Law Device
[0060] As shown in FIG. 6A, the energy collector 600 includes a
linear low noise amplifier (LNA) 601, a band-pass filter (BPF) 605,
a square-law device 610, an integrator 620, and a sampler circuit
630, serially connected to each other. The square-law device
outputs a squared form of an input signal, as known in the art. The
sampling circuit uses a sampling interval of t.sub.s, which is
equal to the block length T.sub.B, The output of the integrator 620
are observation samples z(n), as analytically expressed as:
z [ n ] = j = 1 N s .intg. ( j - 1 ) T f + ( c j + n - 1 ) T b ( j
- 1 ) T f + ( c j + n ) T b r ( t ) 2 t ( 3 ) ##EQU00004##
[0061] Signal parameters 540 can include signal bandwidth, frame
duration 575, block duration 585, chip duration 565, and symbol
duration 595, etc. The integrator 620 intervals are determined
according to the signal parameters 520.
[0062] Stored-Reference
[0063] As shown in FIG. 6B, for the collector 600', with a sampling
interval of t.sub.s, which is equal to block length T.sub.b, the
received signal 501 is correlated 615 with a stored reference
signal 503. The stored reference signal can be pre-stored in the
receiver. The resulting output is sampled at by sampler circuitry
630 according to
s tmp ( t ) = j = 0 N s - 1 d j .omega. ( t - jT f - c j T c ) , (
4 ) z n ( sr ) = .intg. ( n - 1 ) t s ( n - 1 ) t s + N s T f r ( t
) s tmp ( t - ( n - 1 ) t s ) t , ( 5 ) ##EQU00005##
[0064] Transmitted Reference
[0065] As shown in FIG. 6C, for the collector 600'', with a
sampling interval of t.sub.s, which is equal to the block length
T.sub.B, the received signal is correlated 616 with a delayed
version (D) 640 of the signal, see FIG. 5C. The resulting output is
sampled at the sampler circuitry 630 according to
z n ( tr ) = j = 1 N s .intg. ( j - 1 ) T f + ( c j + n - 1 ) t s (
j - 1 ) T f + ( c j + n ) t s r ~ ( t ) r ~ ( t - D ) t , ( 6 )
##EQU00006##
[0066] Signal Conditioner
[0067] As shown in FIG. 7, the signal conditioner 700 enhances the
signal and suppresses noise prior to energy edge detection 550. The
signal parameters 540 can be used to optimize selection of wavelet
filter types 720 and coefficients for the time scaling in the
wavelet filter bank 710. Wavelets are a class of function used to
localize a given function in both space and scaling. Channel
characteristics 520, such as an estimated SNR 521 are provided as a
feedback to a branch selector 740 for selecting the appropriate
wavelet filter bank outputs for a product determination 745. At a
low SNR, erroneous peaks can occur. This is due to the fact that
the fine scale wavelet filters maintain high frequency components
of a high noise level. These peaks can distort the output of the
product 745, and can be misleading in the signal energy edge
detection 550. Therefore, if the SNR level is low, then the fine
time scales are removed from the product determination in the
signal energy conditioner 700. The smoothing branch 730 is used for
noise suppression, and it typically contains a filter function in
the form of a Gaussian curve.
[0068] The product output is fed to the signal energy edge detector
550. The signal energy edge detector 550 can use conventional edge
detection techniques, as known in the art, such as threshold-based,
threshold based with search back, maximum likelihood based, and the
like.
[0069] Alternatively, signal energies from coarse to fine time
scales in a multi-scale filter bank 810 can be used to improve the
performance of the leading edge detector 550. In FIG. 8, the
filters are arranged, from the bottom to the top, in a coarse to
fine time scale order. The coarser filters have a greater smoothing
effect than the finer filters. For example, the coarsest filter can
consider 64 samples over a relatively large amount time, and the
finest filter considers only one sample over a small amount of
time. Of course, the exact amount of time, for a particular
application, depends on the signaling frequency. If the SNR is less
than 20 db, then the finest time scale is excluded.
[0070] Because the energy values at different time scales are
correlated, their product is expected to enhance the peaks due to
signal existence. A rectangular filter h.sub.2[n] at a time scale s
is given by
h.sub.2[n]=u[n+2.sup.p]=u[n],
where s=1, 2, . . . , S is a time scale number ranging from finer
scales to coarser scales, S=.left brkt-bot.log.sub.2Nb.right
brkt-bot., and u[n] is a step function. A convolution of h.sub.2[n]
with the energy vector z produces energy concentration of our
signal at various time scales, given by
y s [ n ] = k z [ k ] h 2 [ n - k ] . ##EQU00007##
[0071] Because the values y.sub.s[n] are correlated across multiple
different time scales, we can use direct multiplication 815 to
enhance the peaks closer to the leading edge of the signal, and
suppress noise components, i.e.,
P S ( MEP ) [ n ] = s = 1 S y s [ n ] , ##EQU00008##
where P.sub.S.sup.(MEP)[n] denotes the product of convolution
outputs from scale l, which is the energy vector itself, through
scale S, which is the output of the conditioner 800. Then, the
location (time) of the strongest path is estimated as
t ^ MEP = [ arg max l .ltoreq. n .ltoreq. N s { P S [ n ] } ] T b
##EQU00009##
by a global maxima detector 820.
[0072] After the strongest energy block is estimated, a search-back
process in the detector 550 can accurately estimate the time of
arrival of the leading edge of the signal. Therefore, a search back
window length 840 is provided to the leading edge detector 550.
[0073] It is to be understood that various other adaptations and
modifications may be made within the spirit and scope of the
invention. Therefore, it is the object of the appended claims to
cover all such variations and modifications as come within the true
spirit and scope of the invention.
* * * * *