U.S. patent application number 11/931629 was filed with the patent office on 2008-04-17 for linear single-antenna interference cancellation receiver.
Invention is credited to Anand G. Dabak, Eko N. Onggosanusi, Timothy M. Schmidl.
Application Number | 20080089455 11/931629 |
Document ID | / |
Family ID | 32996023 |
Filed Date | 2008-04-17 |
United States Patent
Application |
20080089455 |
Kind Code |
A1 |
Onggosanusi; Eko N. ; et
al. |
April 17, 2008 |
Linear Single-Antenna Interference Cancellation Receiver
Abstract
System and method for interference cancellation in a digital
wireless communications system. A preferred embodiment comprises
sampling a received signal wherein the received signal is
real-valued, rotating the sampled received signal by a specified
amount, extracting in-phase and quadrature phase streams from the
rotated, sampled received signal, applying an interference
suppression filter and combining the filtered streams. The output
of the combining operation can be de-correlated (by whitening) if
there is excessive correlation.
Inventors: |
Onggosanusi; Eko N.; (Allen,
TX) ; Dabak; Anand G.; (Plano, TX) ; Schmidl;
Timothy M.; (Dallas, TX) |
Correspondence
Address: |
TEXAS INSTRUMENTS INCORPORATED
P O BOX 655474, M/S 3999
DALLAS
TX
75265
US
|
Family ID: |
32996023 |
Appl. No.: |
11/931629 |
Filed: |
October 31, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10747461 |
Dec 29, 2003 |
7295636 |
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11931629 |
Oct 31, 2007 |
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60458245 |
Mar 28, 2003 |
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60509891 |
Oct 9, 2003 |
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Current U.S.
Class: |
375/350 |
Current CPC
Class: |
H04L 25/0202
20130101 |
Class at
Publication: |
375/350 |
International
Class: |
H03D 1/04 20060101
H03D001/04 |
Claims
1-38. (canceled)
39. A method for suppressing interference in a received signal
comprising: sampling the received signal to create a discrete time
sequence representing the received signal; rotating the discrete
time sequence by a specified amount; extracting in-phase and
quadrature phase streams from the rotated, sampled received signal;
applying an interference suppression filter to the in-phase and
quadrature phase streams; and combining the filtered in-phase and
quadrature phase streams.
40. The method of claim 39 further comprising after the combining,
whitening the combined streams.
41. The method of claim 40, wherein the whitening can be performed
via a temporal filter.
42. The method of claim 41, wherein the temporal filter can be
implemented via a linear predictor.
43. The method of claim 39, wherein the sampling is at a sampling
rate essentially equal to a symbol rate of the received signal.
44. The method of claim 39, wherein the in-phase stream is the real
portion of the rotated, sampled received signal and the quadrature
stream is the imaginary portion of the rotated, sampled received
signal.
45. The method of claim 43, wherein the interference suppression
filter can be designed using a zero-forcing criteria.
46. The method of claim 43, wherein the interference suppression
filter can be designed using a minimum mean square error
criteria.
47. The method of claim 43, wherein the interference suppression
filter can be designed using a maximum signal to interference plus
noise (SINR) criteria.
48. The method of claim 34, wherein the sampling is at a sampling
rate that is greater than a symbol rate of the received signal.
49. A method for suppressing interference in a received signal
comprising: sampling the received signal to create a discrete time
sequence representing the received signal, wherein the sampling is
at a sampling rate that is not less than a symbol rate of the
received signal; rotating the discrete time sequence by a specified
amount; extracting in-phase and quadrature phase streams from the
rotated, sample received signal; and applying an interference
suppression filter to the in-phase and quadrature phase
streams.
50. The method of claim 49 further comprising after the applying,
whitening the in-phase and quadrature phase streams.
51. The method of claim 50, wherein the whitening can be performed
by a spatial whitening transform, W, and wherein the spatial
whitening transform is a function of an inverse of an interference
convariance matrix estimate, wherein: R = 1 .LAMBDA. .times. m
.di-elect cons. .LAMBDA. .times. .times. e m .times. e m T ,
##EQU23## wherein e(z)=F(z)v(z) can be the residual interference
after interference suppression, F(z) is the interference
suppression matrix, .LAMBDA. is an index set depending upon where
v(z) is computed within a transmission burst, and R is the
interference covariance matrix estimate.
52. The method of claim 51, wherein the covariance matrix estimates
can be derived from transmission training sequences.
53. The method of claim 51, wherein the covariance matrix estimates
can be derived via decision feedback.
54. The method of claim 51, wherein W=R.sub.e.sup.-1.
55. The method of claim 51, wherein W=R.sub.e.sup.-1/2.
56. The method of claim 51, wherein the sampling is at a sampling
rate that is greater than a symbol rate of the received signal.
57. A circuit comprising: a sampling and coupled to a signal input,
the sampling unit containing circuitry to sample a received signal
provided by the signal input at a specified sampling rate and to
create a discrete time sequence representing the received signal; a
rotating unit coupled to the sampling unit, the rotating and
containing circuitry to rotate the discrete time sequence by a
specified amount; a pair of extractors coupled to the rotating
unit, the extractors containing circuitry to extract an in-phase
and a quadrature phase steam from an output of the rotating unit;
and a filter coupled to the pair of extractors, the filter
containing circuitry to suppress interference present in the
received signal.
58. The circuit of claim 57 further comprising a whitening unit
coupled to the filter, the whitening unit containing circuitry to
de-correlate information present in the output of the filter.
59. The circuit of claim 57, wherein the filter comprises: a pair
of filters, each filter to be applied separately to the in-phase
and the quadrature phage streams; and a combiner coupled to the
pair of filters, the combiner to sum the outputs from the pair of
filters.
60. The circuit of claim 57, wherein the filter is a space-time
interference suppression filter (STISF).
61. The circuit of claim 60 further comprising a whitening unit
coupled to the STISF containing circuitry to de-correlate
information present in the output of the STISF, wherein a transfer
function of the STISF is computed from the output of the pair of
extractors and captured training sequences from transmissions of a
desired user.
62. The circuit of claim 61, wherein the transfer function is the
sum of the output of the pair of extractors and a convolution of a
channel estimate with the captured training sequences.
62. The circuit of claim 61, wherein the whitening unit applies a
convolution of the transfer function of the STISF with a sum of the
output of the pair of extractors and a convolution of a channel
estimate with the captured training sequences.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This applciation is a Continuation of application Ser. No.
10/747,461 filed Dec. 29, 2003, which claims the benefit of U.S.
Provisional Application No. 60/458,245, filed Mar. 28, 2003,
entitled "Linear Single-Antenna Interference Cancellation Receiver
for GSM Systems", and Application No. 60/509,891, filed Oct. 09,
2003, entitled "Another Blind Single-Antenna Interference
Cancellation Receiver for GSM Systems" which applications are
hereby incorporated herein by reference.
[0002] This application is related to the following co-pending and
commonly assigned patent applications Ser. No. 10/738,508, filed
Dec. 17, 2004, entitled "Interferer Detection and Channel
Estimation for Wireless Communications Networks," Ser. No.
10/732,978, filed Dec. 11, 2003, entitled "Multiuser Detection for
Wireless Communications Systems in the Presence of Interference,"
which applications are hereby incorporated herein by reference.
TECHNICAL FIELD
[0003] The present invention relates generally to a system and
method for digital wireless communications, and more particularly
to a system and method for providing interference cancellation in a
digital wireless communications system.
BACKGROUND
[0004] Interference is a major source of concern for the designers
of wireless communications systems. Interference can reduce the
overall performance of the communications system and if severe
enough, cause the communications system to fail altogether.
Interference can come from other electrical and electronic devices
operating in the general vicinity and from other devices in the
same communications system, which are transmitting in the same (or
adjacent) frequency band.
[0005] Interference from other devices in the same communications
system can become a problem as designers of the communication
system attempt to increase network capacity. For example, one way
to increase network capacity is to increase frequency reuse, i.e.,
allow devices that are relatively close to one another to transmit
in the same frequency band. In cellular communications systems,
adjacent cell sites typically do not operate in the same frequency
bands. However, through cell site sectoring, frequency reuse can be
increased, therefore increasing network capacity. Unfortunately,
when devices, which are close to one another, transmit in the same
frequency band or in adjacent frequency bands, interference can
occur. When devices transmit within the same frequency band,
co-channel interference can occur, while adjacent channel
interference can occur if devices transmit in adjacent bands if
sufficient interband spacing is not provided.
[0006] Additionally, when multiple users are transmitting, the
information may become mixed together and it may be necessary to
extract one (or more) user's information from a received signal.
For receivers with multiple antennas, linear schemes can be used to
extract the desired information. The use of linear schemes in
receivers with single antennas may be difficult if not impossible
without the aid of additional signal manipulation.
[0007] In a GSM (Global System for Mobile Telephony) wireless
communications system, for example, information is transmitted in
transmission bursts, wherein each transmission burst may consist of
two packets of data bits with a 26 bit mid-amble located in between
the two packets. According to the GSM technical standards, one of
eight possible training sequence codes (TSC) can be used as the
mid-amble. In GSM communications systems, attempts to increase
system capacity have resulted in increased co-channel and adjacent
channel interference. Several attempts to reduce interference have
been proposed. Most of the prior art relies on using at least two
antennas at the receiver to suppress interference. However, due to
cost reasons there is generally only one antenna in GSM handsets.
With a single antenna at the receiver, one single antenna
interference cancellation (SAIC) technique is to use the joint MLSE
receiver.
[0008] A disadvantage of the prior art is that the schemes which
provide significant performance gain require the channel
information of the interferers. This may not be available since in
general the identity of the interferers is unknown. In a
synchronous network, this may require an algorithm capable of
detecting the presence and identity of the interferer(s). In an
asynchronous network, attaining such information is generally
infeasible.
SUMMARY OF THE INVENTION
[0009] These and other problems are generally solved or
circumvented, and technical advantages are generally achieved, by
preferred embodiments of the present invention which provides for a
system and method for providing interference cancellation in
wireless communications systems.
[0010] In accordance with a preferred embodiment of the present
invention, a method for eliminating interference in a received
signal comprising sampling the received signal, rotating the sample
received signal by a specified amount, extracting in-phase and
quadrature phase streams from the rotated, sampled received signal,
applying an interference suppression filter to the in-phase and
quadrature phase streams, and combining the filtered in-phase and
quadrature phase streams is provided.
[0011] In accordance with another preferred embodiment of the
present invention, a method for eliminating interference in a
received signal comprising sampling the received signal, wherein
the sampling is at a sampling rate that is not less than a symbol
rate of the received signal, rotating the sampled received signal
by a specified amount, extracting in-phase and quadrature phase
streams from the rotated, sampled received signal, and applying an
interference suppression filter to the in-phase and quadrature
phase streams is provided.
[0012] In accordance with another preferred embodiment of the
present invention, a circuit comprising a sampling unit coupled to
a signal input, the sampling unit containing circuitry to sample a
received signal provided by the signal input at a specified
sampling rate, a rotating unit coupled to the sampling unit, the
rotating unit containing circuitry to rotate the sample received
signal by a specified amount, a pair of extractors coupled to the
rotating unit, the extractors containing circuitry to extract an
in-phase and a quadrature phase stream from an output of the
rotating unit, and a filter coupled to the pair of extractors, the
filter containing circuitry to suppress interference present in the
received signal is provided.
[0013] An advantage of a preferred embodiment of the present
invention is the interference cancellation can make use of single
antenna receivers, therefore, existing receivers can be used.
[0014] A further advantage of a preferred embodiment of the present
invention is that spectral redundancy available in many modulation
schemes can be exploited to provide an additional degree of freedom
to assist in interference cancellation. The additional degree of
freedom can effectively operate as a "virtual" antenna to make a
single antenna receiver behave like a two antenna receiver.
[0015] Yet another advantage of a preferred embodiment of the
present invention is that further technique can be used to provide
greater degrees of freedom. These additional degrees of freedom can
add additional "virtual" antennas to a single antenna receiver,
permitting the use of interference cancellation techniques that
typically require a large number of antennas.
[0016] Yet another advantage of a preferred embodiment of the
present invention is that implementation can be achieved without
requiring the channel information and identity of the interferers.
Only the desired user channel information is used. Hence, the
techniques are applicable for asynchronous networks.
[0017] The foregoing has outlined rather broadly the features and
technical advantages of the present invention in order that the
detailed description of the invention that follows may be better
understood. Additional features and advantages of the invention
will be described hereinafter which form the subject of the claims
of the invention. It should be appreciated by those skilled in the
art that the conception and specific embodiment disclosed may be
readily utilized as a basis for modifying or designing other
structures or processes for carrying out the same purposes of the
present invention. It should also be realized by those skilled in
the art that such equivalent construction do not depart from the
spirit and scope of the invention as set forth in the appended
claims
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] For a more complete understanding of the present invention,
and the advantages thereof, reference is no made to the following
descriptions taken in conjunction with the accompanying drawings,
in which:
[0019] FIG. 1 is a diagram of a transmission burst in a GSM
communications system;
[0020] FIG. 2 is a diagram of a detailed view of the 26-bit GSM
training sequence field;
[0021] FIG. 3 is a diagram of the transmissions from three GSM
devices with no timing offset;
[0022] FIG. 4 is a diagram of a portion of a receiver, according to
a preferred embodiment of the present invention;
[0023] FIG. 5 is a diagram of a process for interference
cancellation in a receiver, according to a preferred embodiment of
the present invention;
[0024] FIG. 6 is a diagram of a portion of a receiver, according to
a preferred embodiment of the present invention;
[0025] FIG. 7 is a diagram of a receiver circuit, according to a
preferred embodiment of the present invention;
[0026] FIG. 8 is a diagram of a process for interference
cancellation in a receiver, according to a preferred embodiment of
the present invention;
[0027] FIG. 9 is a data plot of link level performance for several
single antenna interference cancellation algorithms, according to a
preferred embodiment of the present invention; and
[0028] FIG. 10 is a data plot of link level performance for several
single antenna interference cancellation algorithms, according to a
preferred embodiment of the present invention.
DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS
[0029] The making and using of the presently preferred embodiments
are discussed in detail below. It should be appreciated, however,
that the present invention provides many applicable inventive
concepts that can be embodied in a wide variety of specific
contexts. The specific embodiments discussed are merely
illustrative of specific ways to make and use the invention, and do
not limit the scope of the invention.
[0030] The present invention will be described with respect to
preferred embodiments in a specific context, namely a GSM network
operating in synchronous mode. The GSM technical standard can be
found in a series of technical documents, wherein a general
description can be found in Document 01,02, entitled "General
Description of GSM Public Land Mobile Network (PLMN), Revision
6.0.0" published January 2001, which is incorporated herein by
reference. The invention may also be applied, however, to other
wireless communications networks which make use of real-valued
modulation schemes such as GMSK, BPSK, and M-PAM. Examples of these
networks include but are not limited to GSM-EDGE, GPRS, and so
on.
[0031] With reference now to FIG. 1, there is shown a diagram
illustrating a transmission burst 100 in a GSM communications
system. Data transmitted in the transmission burst 100 are carried
in a pair of 57-bit data fields 105. Two 3-bit fields, referred to
as tail bit fields 110, can be used to keep adjacent transmission
bursts separate. In many wireless communications systems,
transmissions are usually preceded with a field located at the
beginning of the transmission. This field is commonly referred to
as a preamble and can be used to carry a specific sequence of bits
(typically referred to as a training sequence) that can help a
receiver detect and decode the transmission. Note that while the
use of a preamble is common, it is not the only place within in a
transmission to place a training sequence. For example, in a GSM
transmission burst, the training sequence is located in the middle
of the transmission burst. The transmission burst 100 contains a
26-bit training sequence field 115, which may be separated from the
pair of 57-bit data fields 105 by a pair of stealing bit fields
120. Since the training sequence is not at the beginning of the
transmission, it referred to as being a mid-amble. Note that the
discussion of field specifies (the number of bits in a field, the
position of a field, and so forth) is used to enable the discussion
using a currently available wireless communications system. It
should be evident that the field specifies should have no impact
upon the validity of the present invention.
[0032] With reference now to FIG. 2, there is shown a diagram
illustrating a detailed view of the GSM 26-bit training sequence
field 115. The GSM 26-bit training sequence field 115 can be broken
up into three smaller fields, a 5-bit cyclic prefix field 205, a
16-bit training sequence field 210, and a 5-bit cyclic postfix
field 215. According to the GSM technical standards, the 5-bit
cyclic prefix field 205 contains a copy of the last 5 bits of the
16-bit training sequence field 210 while the 5-bit cyclic postfix
field 215 contains a copy of the first 5 bits of the 16-bit
training sequence field 210. According to the GSM technical
specifications, there are up to eight (8) unique training sequences
that may be used in a signal GSM communications system.
[0033] As discussed previously, interference from other devices
from within the same communications network can come in two forms,
co-channel and adjacent channel interference. Regardless of the
form of interference, the net result may be that the overall
performance of the source of the interference and receiver of the
interference may be degraded since the transmissions of both the
device causing the interference and the device being interfered
with are being damaged. Since the number of training sequences is
limited (eight in the case of a GSM communication system), it can
be possible to use the a priori knowledge of the training sequences
to improve the channel estimation performance at a receiver.
[0034] With reference now to FIG. 3, there is shown a diagram
illustrating the transmissions of three GSM devices, wherein there
is no timing offset. Each of three acts of axes (305, 310, and 315)
display a series of GSM transmission bursts from a single device.
Note that each device uses a different training sequence; TSC0 for
the transmission displayed on axis 305, TSC2 for the transmission
displayed or axis 310, and TSC1 for the transmission displayed on
axis 315. Note that the GSM communications system displayed in FIG.
3 is a synchronous system, wherein all of the devices transmit at
essentially the same time. For example, first GSM transmission
bursts 307, 312, and 317 are all transmitted at the same time, as
are second GSM transmission bursts 308, 313, and 318. Also note
that there is no (or less than a single symbol) timing offset
between the transmissions of the three devices. A vertical line 320
denotes the beginning of the second GSM transmission bursts 308,
313, and 318 in all three devices.
[0035] Note that it may be possible that a timing offset exists
between the arrival times of transmissions from different devices.
A timing offset may exist even if transmissions within a wireless
communications system are designed to occur at the same time. For
example, if a clock of a transmitter has drifted away from clocks
of other transmitters, then the transmitter with the inaccurate
clock can begin its transmission at an incorrect time.
Alternatively, differences in the distance traveled by various
transmissions (propagation delay) can also account for a timing
offset. For example, even if transmissions are initiated at the
same time, a transmission that is traveling a long distance will
arrive later than a transmission that is traveling a short
distance. A timing offset can vary from nanoseconds to
milliseconds. When a timing offset is large, it can sometimes be
expressed in terms of symbol intervals (an amount of time equal to
the transmission of a single symbol).
[0036] With reference now to FIG. 4, there is shown a diagram
illustrating a portion of a receiver 400, wherein addition signal
manipulation can be used to provide an additional degree of freedom
to assist in interference cancellation, according to a preferred
embodiment of the present invention. FIG. 4 provides a high-level
view of circuitry responsible for interference cancellation in the
receiver 400. Note that FIG. 4 does not show typical parts that may
be found in a receiver, such as an antenna, radio frequency
hardware, decoding hardware, and so forth. A received signal, r(t),
as received by an antenna (not shown) of the receiver 400 and after
filtering to remove out-of-band interferers and amplifying to bring
signal levels to a compatible level by radio frequency hardware
(also not shown), may be sampled at baud-rate by a baud-rate
sampling unit 405. The sampling of the received signal creates a
discrete time sequence representing the received signal. After the
sampling, the discrete time sequence can be provided to a linear
interference suppression unit 410. According to another preferred
embodiment of the present invention, sub-baud rate processing can
be used in place of baud-rate processing.
[0037] The linear interference suppression unit 410 can include a
derotation unit 415, which can be used to apply a specified
rotation to the discrete time sequence. After derotation, the
discrete time sequence can be provided to a real-valued unit 420
and an imaginary-valued unit 422, which can be responsible for
extracting the real portion and the imaginary portion of the
discrete time sequence, e.g., the discrete time sequence can be
split into two sequences, with one sequence containing the real
portion of the discrete time sequence and the other sequence
containing the imaginary portion of the discrete time sequence. The
real sequence can represent an in-phase portion and the imaginary
sequence can represent a quadrature portion of the discrete time
sequence.
[0038] Each of the two sequences (the real sequence and the
imaginary sequence) can then undergo filtering via two filter units
425 and 427. A detailed explanation of the operation of the filter
units 425 and 427 is provided below. After filtering, the two
sequences can be recombined by a combining unit 430. A net effect
of the filtering by the filter units 425 and 427 and the combining
unit 430 is interference suppression. After combining, the output
may be colored. If the coloring is severe, then the output may be
whitened (de-correlated) by a whitening unit 435 prior to minimum
least squares error equalization.
[0039] For discussion purposes, a signal model, along with
assumptions and notation shall be laid out. Note that the signal
model presented below is for a GSM communications system. However,
a comparable signal model can be provided for other types of
communications systems. A baseband received signal can be sampled
at a baud (symbol) rate to facilitate disrete-time processing. A
Gaussian Minimum Shift Keying (GSSK) modulated signal can be
accurately approximated using a linear approximation expressible
as: x .function. ( t ) = p = - .infin. .infin. .times. .times. j p
+ 1 .times. a p .times. C 0 .function. ( t - pT ) , a p .di-elect
cons. { .+-. 1 } , ##EQU1## where T is a single symbol duration and
C.sub.0(t) is the GMSK waveform of duration 47.
[0040] Assuming that there are {tilde over (K)} co-channel users in
the communications system, the baseband receive signals can be
expressed as: r ~ .function. ( t ) = k = 1 K ~ .times. .times. p =
- .infin. .infin. .times. .times. j p + 1 .times. a k , p .times. h
~ k .function. ( t - pT ) + n ~ .function. ( t ) , .times. r ~ m =
r ~ .function. ( mT ) = j m + 1 .times. k = 1 K ~ .times. .times. l
= 0 L .times. .times. ( j - 1 .times. h ~ k , l ) .times. a k , m -
l + n ~ m , ##EQU2## where {tilde over (h)}(t) is the overall
channel impulse response including C.sub.0(t), {tilde over
(h)}.sub.i={tilde over (h)}(IT), and LT is the channel delay
spread.
[0041] With reference now to FIG. 5, there is shown a diagram
illustrating a process 500 for interference cancellation in a
receiver, wherein addition signal manipulation can be used to
provide an additional degree of freedom to assist in interference
cancellation, according to a preferred embodiment of the present
invention. A received signal, r(t), after being received by a
receiver and sampled (block 505) at a sampling rate essentially
equal to the received signal's baud rate can be expressed as: r ~ m
= r ~ .function. ( mT ) = j m + 1 .times. k = 1 K ~ .times. .times.
l = 0 L .times. .times. ( j - 1 .times. h ~ k , l ) .times. a k , m
- l + n ~ m ##EQU3## Note that a.sub.k can be modulated using
binary phase shift keying (BPSK) and therefore is real-valued.
[0042] Two independent real-valued channels can be obtained from
{tilde over (r)}.sub.m by first performing a derotation (block 510)
with a factor of (-j).sup.m+1 followed by extracting a real
(in-phase) and imaginary (quadrature) part of the resulting signal
(block 515). The two independent real-valued channels can be
expressed in vector form as: [ Re .function. ( j - ( m + 1 )
.times. r ~ m ) Im .function. ( j - ( m + 1 ) .times. r ~ m ) ] =
.times. k = 1 K .times. .times. l = 0 L .times. [ Re .function. ( j
- l .times. h ~ l ( k ) ) Im .function. ( j - l .times. h ~ l ( k )
) ] .times. a m - l ( k ) + [ Re .function. ( j - ( m + 1 ) .times.
n ~ m ) Im .function. ( j - ( m + 1 ) .times. n ~ m ) ] .times.
.revreaction. r ~ m = k = 1 K .times. .times. l = 0 L .times. h l (
k ) .times. a m - l ( k ) + n ~ m = k = 1 K .times. [ h .times. 0 (
k ) .times. h .times. 1 ( k ) h .times. L ( k ) ] .times. a m - l (
k ) + n ~ m . ( 1 ) ##EQU4##
[0043] This effectively provides a single-input 2-output
real-valued channel. Essentially, the spectral redundancy stemming
from the fact that a.sub.k is a real-valued symbol is exploited. It
can be shown that the two independent real-valued channels (shown
above) are uncorrelated from one another. The same holds true for
the noise components. Note that the GMSK-specific feature above may
arise from the GMSK waveform, C.sub.0(t), and the rotation
(-j).sup.m+1. The above technique of exploiting spectral redundancy
can also be applicable to any general real-valued modulation scheme
such as BPSK and M-PAM. For BPSK and M-PAM, the derotation (for
example, as performed by the derotation unit 415 (FIG. 4)) may not
be needed. In this case, the sampled received signal can be
directly processed by in-phase and quadrature extractors (for
example, the real-valued unit 420 and an imaginary-valued unit 422
(FIG. 4)).
[0044] The additional degree of freedom (achieved by exploiting the
spectral redundancy and creating two independent real-valued
channels from the received signal) can be used to fully suppress a
single interferer. Alternatively, if there is more than one
interferer, then the single degree of freedom can be used to
partially suppress the multiple interferers. The interference
suppression can be performed by filtering the two independent
real-valued channels and then combining the results of the
filtering (block 520). The filters (w.sub.1(z) and w.sub.2(z)) can
have N+1 taps which can result in an increase in the number of
states for the MLSE equalizer by a factor of 2.sup.N times. A
detailed discussion of the filters (w.sub.1(z) and w.sub.2(z)) is
provided below.
[0045] The filters (w.sub.1(z) and w.sub.2(z)) can be chosen to
suppress interference. Several different criteria can be used, such
as, zero-forcing (ZF), minimum mean square error (MMSE), and
maximum signal to interference plus noise ratio (SINR). The
following describes a design of the filters using a maximum SINR
criteria. Proceeding from equation (1) above, set the number of
taps for each filter to N+1 and let: .times. .times. r m = [ r ~ m
r ~ m - 1 r ~ m - N ] .di-elect cons. 2 .times. ( N + 1 ) , .times.
n m = [ .times. .times. n ~ m .times. .times. n ~ m .times. -
.times. 1 .times. .times. n ~ m .times. - .times. n ] .about.
RealGaussian .function. [ O 2 .times. ( N + 1 ) , .sigma. 2 2
.times. I 2 .times. ( N + 1 ) ] , .times. a m ( k ) = [ a m ( k ) a
m - 1 ( k ) a m - L - N ( k ) ] .di-elect cons. BPSK L + N + 1
.times. .times. Then , .times. r m = k = 1 K .times. .times. H k
.times. a m ( k ) + n m == H 1 .times. a m ( 1 ) + k = 2 K .times.
H k .times. .times. a m ( k ) + n m = .times. H 1 .times. a m ( 1 )
+ v m ( 2 ) ##EQU5## where H.sub.k is the 2(N+1).times.(L+N+1)
block Toeplitz matrix formed from {h.sub.0.sup.(k),h.sub.1.sup.(k),
. . . ,h.sub.L.sup.(k)}.
[0046] The combined filter (combining both filters w.sub.1(z) and
w.sub.2(z)) w=[w.sub.1,0 w.sub.2,0 w.sub.1,1 w.sub.2,1 . . .
w.sub.1,N w.sub.2,N].sup.T.epsilon..sup.2(N+1) operates upon the
two independent real-valued channels to produce a single stream
output as follows:
y.sub.m=w.sup.Tr.sub.m=w.sup.TH.sub.1a.sub.m.sup.(1)+w.sup.T.nu..sub.m=u.-
sup.Ta.sub.m.sup.(1)+w.sup.T.nu..sub.m (3) where u denotes the
effective desired user channel after interference suppression. In
this case, the SINR can be defined as: SINR = E .function. [ ( u T
.times. a m ( 1 ) ) 2 ] E .function. [ ( w T .times. r m - u T
.times. a m ( 1 ) ) 2 ] . ( 4 ) ##EQU6## It can be shown that a
SINR-maximizing solution is expressible as: w = R rr .times. - 1
.times. H 1 .times. u , u = evec max .function. [ H 1 T .times. R
rr - 1 .times. H 1 ] .times. .times. R rr - 1 = E .function. [ r m
.times. r m T ] = k = 1 K .times. .times. H k .times. H k T +
.sigma. 2 2 .times. I 2 .times. ( N + 1 ) ( 5 ) ##EQU7## where
evec.sub.max[X] denotes the eigenvector for matrix X corresponding
to the maximum eigenvalue. Note that by definition in equation (3),
u=H.sub.1.sup.Tw. (6)
[0047] When channel estimates of all K users are available (e.g.,
via joint least-squares channel estimation and knowledge of
training sequences for the users), the above solution can simply
use the channel estimates to derive an optimal combining filter. In
blind implementation, where only a channel estimate of the desired
user is available (e.g., via a single user channel estimation), the
data covariance matrix, C.sub.rr, can be estimated via the sample
covariance matrix by averaging multiple snapshots of
r.sub.mr.sub.m.sup.T.
[0048] The solution discussed above can permit a blind adaptive
implementation using a wide variety of adaptive filtering
techniques. This can be possible by noting that for a given u, w is
essentially a linear MMSE filter that minimizes the mean square
error in the denominator of SINR (equation (4)). The solution may
begin with an initial estimate for u, then adaptively obtain w, and
then refine u using equation (6). This may be done iteratively. An
adaptive implementation can be beneficial, especially for
time-varying channels (wherein the channel varies significantly
within one transmission burst) and highly asynchronous networks
(wherein the interferers and hence the interferer's channels and
statistics change within a transmission burst).
[0049] Using the training code sequence of the desired user, it can
also be possible to obtain a SINR-maximizing solution, wherein SINR
is defined in a deterministic sense, rather than a stochastic sense
as in equation (4). Collecting M snapshots of r.sub.m in equation
(2) within a period of the training code sequence (for a GSM
communications system, the training code sequence is made up of 26
symbols per transmission burst), [r.sub.0 r.sub.1 . . .
r.sub.M-i]=H.sub.1.left brkt-bot.a.sub.0.sup.(1) a.sub.1.sup.(1) .
. . a.sub.M-1.sup.(1).right brkt-bot.+[.nu..sub.0 .nu..sub.1 . . .
.nu..sub.M-1] R=H.sub.1A.sub.1+V. (7) Similar to the stochastic
approach, the combining filter can operate as follows:
y.sup.T=w.sup.TR=w.sup.TH.sub.1A.sub.1+w.sup.TV=u.sup.TA.sub.1+w.sup.TV.
The deterministic SINR can then be defined as: SINR = u T .times. A
1 2 w T .times. R - u T .times. A 1 2 . ( 8 ) ##EQU8## It can be
shown that the SINR-maximizing solution in this case is:
w=(RR.sup.T).sup.-1RA.sub.1.sup.Tu,
u=evec.sub.max[(A.sub.1A.sub.1.sup.T).sup.-1A.sub.1R.sup.T(RR.sup.T).sup.-
-1RA.sub.1.sup.T]. (9) It can be shown that the above solution can
be equivalent to:
w=evec.sub.max[(RR.sup.T).sup.-1RA.sub.1.sup.T(A.sub.1A.sub.1.sup.T).sup.-
-1A.sub.1R.sup.T]
u=(A.sub.1A.sub.1.sup.T).sup.-1A.sub.1R.sup.Tw=H.sub.1.sup.Tw,
Wherein H.sub.1 is the single user least square channel estimate of
the desired user. Therefore, if a better channel estimate can be
obtained via a different method, it can be used in place of
H.sub.1. Additionally, this shows that channel estimation can be
performed separately from SINR maximization.
[0050] After interference suppression (filtering and combining) and
before being provided to an MLSE equalizer, it may be necessary to
whiten (de-correlate) the interference suppressed signal (block
525). The interference suppressed signal can be severely colored
(as a result of the filtering and combining operations). If this is
the case, then the interference suppressed signal can be whitened
(for example, by a whitening unit 435 (FIG. 4)). Severe coloring
can impact the performance of MLSE. The whitening can be
implemented adaptively using linear prediction filtering.
Alternatively, it can be shown that the correlating function of the
residual interference (plus noise) takes the following form: C
.function. ( .DELTA. ) = w T .function. ( k = 2 K .times. .times. H
k .times. D .DELTA. .times. H k T + .sigma. 2 2 .times. .delta.
.DELTA. .times. I 2 .times. ( N + 1 ) ) .times. w , ##EQU9##
wherein D.sub.A is the shifted identity matrix. A whitening filter
can then be derived using spectral factorization. Note that the
process 500 may not be limited to co-channel interference
suppression alone, the process 500 can also suppress adjacent
channel interference. Notice that the above correlation function
depends on the interferer(s)'s channel information. Alternatively,
the whitening filter can be derived from a linear prediction
formulation where the interference is modeled as an auto-regressive
(AR) process with order-N, where (N+1) is the whitening filter
length. Using this formulation, the whitening filter can be derived
from the interference estimate (received signal minus desired
signal obtained from the TSC and/or decision feedback) without
requiring the channel information of the interferer(s).
[0051] With reference now to FIG. 6, there is shown a diagram
illustrating a portion of a receiver 600, wherein addition signal
manipulation can be used to provide multiple additional degrees of
freedom to assist in interference cancellation, according to a
preferred embodiment of the present invention. FIG. 6 provides a
high-level view of circuitry responsible for interference
cancellation in a receiver 600. Note that FIG. 6 does not show
typical parts that may be found in a receiver, such as an antenna,
radio frequency hardware, decoding hardware, and so forth.
Previously, the multiple stream input signals (the I and Q streams)
may be processed into a single stream upon interference
suppression. The receiver 600 attempts to preserve those multiple
streams upon interference suppression. A received signal, r(t), as
received by an antenna (not shown) of the receiver 600 and after
filtering to remove out-of-band interferers and amplifying to bring
signal levels to a compatible level by radio frequency hardware
(also not shown), may be sampled at a rate greater than baud-rate
by a sampling unit 605, meaning that the received signal, r(t), is
being oversampled. For example, the received signal may be
oversampled by a factor of 2.times., 4.times., 6.times., 8.times.,
or any integral multiple of the baud-rate. The sampling of the
received signal creates a discrete time sequence representing the
received signal. After the sampling, the discrete time sequence can
be provided to a space-time interference suppression unit 607.
[0052] The space-time interference suppression unit 607 can include
a derotation unit 610, which can be used to apply a specified
rotation to the discrete time sequence. After derotation, the
discrete time sequence can be provided to a real-valued unit 615
and an imaginary-valued unit 617, which can be used for extracting
the real portion and the imaginary portion of the discrete time
sequence. The real sequence can represent an in-phase portion and
the imaginary sequence can represent a quadrature portion of the
discrete time sequence. The two sequences (the real sequence and
the imaginary sequence) can then undergo filtering by a space-time
interference suppression filter 620, which makes use of a matrix
filter. Note that once again, the spectral redundancy of a GMSK
modulated signal has been exploited to provide an additional degree
of freedom. However, by oversampling the received signal by a
factor of Q, an additional (Q-1) degrees of freedom can be
provided. Furthermore, the splitting of the discrete time sequence
into two sequences doubles the degrees of freedom to a total of
2(Q-1) degrees of freedom. The output of the space-time
interference suppression unit 607 may be colored and if the
coloring is severe enough, a spatial whitening unit 650 can be used
to whiten the output prior to being provided to an equalizer (not
shown).
[0053] The space-time interference suppression unit 607 and the
spatial whitening unit 650 can have as input an interference
suppression filter matrix, F(z), and a spatial whitener, W,
respectively. Both the interference suppression filter matrix,
F(z), and the spatial whitener, W, can be computed from the
discrete time sequence and a training sequence of the desired user
and then provided to the space-time interference suppression unit
607 and the spatial whitening unit 650 by a channel estimation and
computing unit 622.
[0054] The channel estimation and computing unit 622 can include a
channel estimation unit 625, which can compute a channel estimate,
h(z), from the discrete time signal. The channel estimation
(produced by the channel estimation unit 625) can then be provided
to a convolution unit 630, wherein it can be convolved with the
training code sequence of the desired user (snapshots of which can
be taken from the received signal). Output of the convolution unit
630 can be combined by a combining unit 635 with the discrete time
signal to produce an interference component, V(z). The interference
component, V(z), can be used to compute the interference
suppression matrix, F(z), by a interference suppression matrix
compute unit 640. The interference component, V(z), can also be
used to compute the spatial whitener, W, by convolving it (via a
convolution unit 645, for example) with the interference
suppression matrix, F(z), to produce a residual interference after
interference suppression, e(z). The residual interference after
interference suppression, e(z), can then be provided to a spatial
whitener compute unit 655, wherein the spatial whitener, W, is
computed. Note that details of the computations will be discussed
below. An alternative embodiment of the receiver circuitry 600 can
be found displayed in FIG. 7.
[0055] Once again, to discuss the design of the receiver 600, a
signal model, along with assumptions and notation shall be laid
out. As discussed previously, a GMSK modulated signal can be
approximated as: x .function. ( t ) = p = - .infin. .infin. .times.
.times. j p + 1 .times. a p .times. C 0 .function. ( t - pT ) , a p
.di-elect cons. { .+-. 1 } , ##EQU10## wherein T is a single symbol
duration and C.sub.0(t) is the GMSK waveform of duration 4T.
Assuming that there are {tilde over (K)} co-channel users in the
communications system, the baseband receive signals can be
expressed as r ~ .function. ( t ) = p = - .infin. .infin. .times. j
p + 1 .times. a p ( 1 ) .times. h ~ ( 1 ) .function. ( t - pT ) + k
= 2 K .times. p = - .infin. .infin. .times. j p + 1 .times. a p ( k
) .times. h ~ ( k ) .function. ( t - pT ) + n ~ .function. ( t ) =
p = - .infin. .infin. .times. j p + 1 .times. a p ( 1 ) .times. h ~
( 1 ) .function. ( t - pT ) + v ~ .function. ( t ) , ##EQU11##
wherein {tilde over (h)}(t) is the overall channel impulse
response, including C.sub.0(t) with delay spread LT, n(t) is the
thermal noise, and {tilde over (v)}(t) is the total interference
plus noise.
[0056] With reference now to FIG. 8, there is shown a diagram
illustrating a process 800 for interference cancellation in a
receiver, wherein addition signal manipulation can be used to
provide multiple additional degrees of freedom to assist in
interference cancellation, according to a preferred embodiment of
the present invention. A received signal r(t), after being received
by a receiver and sample (block 805) at a sampling rate Q times the
received signals baud rate can be expressed as: r ~ m = [ r ~ Qm r
~ Qm + 1 r ~ Qm + ( Q - 1 ) ] , where .times. .times. r ~ Qm + q =
r ~ .function. ( ( Qm + q ) .times. T Q ) . ( 10 ) ##EQU12## It can
then be shown that r ~ m = p = - .infin. .infin. .times. j p + 1
.times. a p ( 1 ) .function. [ h ~ ( 1 ) .function. ( ( m - p )
.times. T ) h ~ ( 1 ) .function. ( ( m - p ) .times. T + T Q ) h ~
( 1 ) .function. ( ( m - p ) .times. T + Q - 1 Q .times. T ) ] + v
~ m = p = - .infin. .infin. .times. j p + 1 .times. a p ( 1 )
.times. h ~ m - p + v ~ m = j m + 1 .times. l = 0 L .times. ( j - l
.times. h l ( 1 ) ) .times. a m - l ( 1 ) + v ~ m . ##EQU13##
[0057] In essence, Q times oversampling provides an additional
(Q-1) degrees of freedom. Note that a.sub.k in BPSK modulated,
hence is real-valued. From equation (10), the total number of
degrees of freedom can be doubled by first performing a derotation
with a factor of (-j).sup.m+1 (block 810) followed by extracting
the real and imaginary parts of the resulting signal (block 815).
This can be expressible as: [ Re .function. ( j - ( m + 1 ) .times.
r ~ m ) Im .function. ( j - ( m + 1 ) .times. r ~ m ) ] = l = 0 L
.times. [ Re .function. ( j - l .times. h ~ l ( 1 ) ) Im .function.
( j - l .times. h ~ i ( 1 ) ) ] .times. a m - l ( 1 ) + [ Re
.function. ( j - ( m + 1 ) .times. v ~ m ) Im .function. ( j - ( m
+ 1 ) .times. v ~ m ) ] .revreaction. r m = l = 0 L .times. h l
.times. a m - l + v m , ( 11 ) ##EQU14## wherein the superscripts
(1) indicating user 1 (the desired user) are suppressed for
notational conciseness. This can then provide a single-input
2Q-output real-valued channel. Once again, the spectral redundancy
inherent in the real-valued symbol a.sub.k can be exploited.
[0058] The oversample received signal r.sub.m can then be processed
by a space-time interference suppression matrix filter as follows
(block 820): y m = n = 0 N .times. G n .times. r m - n = G 0
.times. r m + n = 1 N .times. G n .times. r m - n , ( 12 )
##EQU15## wherein G.sub.n .epsilon..sup.2Q.times.2Q is the n-th tap
of the space-time matrix filter. A detailed discussion of the
space-time matrix filter is provided below. In the z-domain,
y(z)=G(z)r(z)=G(z)(h(z)a(z)+v(z)). The processed 2Q-vector signal
y.sub.m can serve as input to a desired user equalizer of type such
as MLSE, DFE, or any other type of equalizer. The effective ISI
channel for the equalizer can be expressed as
h.sub.eq(z)=G(z)h(z).
[0059] The design of the filters (w.sub.1(z) and w.sub.2(z))
involved the use of an algorithm that maximizes SINR. A different
optimization can be used to design the space-time matrix filter
G(z). The space-time matrix filter G .function. ( z ) = G 0 + n = 1
N .times. G n .times. z - n ##EQU16## can be decomposed into two
parts:
[0060] G(z)=WF(z), where W = G 0 .times. .times. and .times.
.times. F .function. ( z ) = I 2 .times. Q + n = 1 N .times. F n
.times. z - n . ( 13 ) ##EQU17## The following criteria can be
used: [0061] The first stage F(z) can be designed to suppress the
total interference component v(z), without affecting the desired
signal component h(z). Therefore, the first tap in F(z) may be
I.sub.2Q (an identity matrix). Note that this stage may be
optional. The stage can be deactivated by setting N to 0.
Additionally, F(z) can also increase the effective channel
constraint length (before equalization) by N. [0062] The second
stage W may be chosen to spatially whiten the residual interference
component after space-time interference suppression.
[0063] Using the assumption that the only available channel
estimate for the desired user is available via the use of a channel
estimation algorithm, such as a single-user correlator, single-user
least square, joint least square, and so forth. This means that the
algorithm is blind to the interference parameters. Given that the
received signal r(z) and the desired user channel estimate h(z),
the interference component v(z) can be estimated as follows:
v(z)=r(z)-h(z)a(z), (14) wherein a(z) can be an estimate of the
desired user data. The desired user data can be obtained by: [0064]
v(z) can be estimated only within the mid-amble every transmission
burst. In this case, a(z) is the desired user's training sequence,
which is completely known. [0065] If additional data is desired, a
decision-directed approach can be used. A preliminary data estimate
(either hard or soft) can be obtained using the output of a matched
filter or even the space-time interference suppression filter. The
estimate can then be used in conjunction with the training sequence
of the desired user to obtain a longer estimate of v(z).
Alternatively, a per-survivor processing (PSP) technique can be
used to obtain more accurate preliminary data estimates at the
expense of complexity.
[0066] The interference estimate v(z) can then be used to compute
F(z) according to an optimization criterion as follows: min F 1 ,
.times. .times. , F N .times. m .di-elect cons. .LAMBDA. .times. v
m + n = 1 N .times. F n .times. v m - n 2 = min F 1 , .times.
.times. , F N .times. m .di-elect cons. .LAMBDA. .times. e m 2 , (
15 ) ##EQU18## wherein e(z)=F(z)v(z) can be the residual
interference after interference suppression and .LAMBDA. is an
index set depending upon where v(z) is computed within a
transmission burst. The optimization criterion in equation (15) can
be viewed as a linear prediction problem. The solution can be
obtained using any of many adaptive filtering algorithms or
analytically as follows. Let .LAMBDA.={N,N+1, . . . , M} and
define: v = [ v N v N + 1 v M ] .di-elect cons. 2 .times. Q
.function. ( M - N + 1 ) , f = vec .function. ( [ F 1 F 2 F N ] )
.di-elect cons. 4 .times. Q 2 .times. N ##EQU19## A = [ e N - 1 T e
N - 2 T e 0 T e N T e N - 1 T e 1 T e M + 1 T e M - 2 T e M - N T ]
I 2 .times. Q . ##EQU19.2## Then, the solution to equation (15) can
be given as: f opt = min f .times. v - Af 2 = ( A H .times. .times.
A ) - 1 .times. A H .times. v . ( 16 ) ##EQU20## From f.sub.opt, F
opt .function. ( z ) = I 2 .times. .times. Q + n = 1 N .times.
.times. F n , opt .times. z - n ##EQU21## can be obtained.
[0067] The spatial whitening transformation, W, can be obtained
from the residual interference estimate
e(z)=F.sub.opt(z){circumflex over (.nu.)}(z). First, an estimate of
the spatial covariance matrix can be obtained as follows R = 1
.LAMBDA. .times. m .di-elect cons. .LAMBDA. .times. .times. e m
.times. e m T , ( 17 ) ##EQU22## which can then be used to derive
the spatial whitening transformation: W=R.sub.c.sup.-1/2. (18) Note
than when N=0, e(z)=.nu.(z). Note also that W may be a function of
an inverse of Re, i.e., the exponent of Re may have other values,
such as -1 (or -1/3, -1/4,- 1/5,, and so forth) instead of just
-1/2 as shown in Equation (18) above.
[0068] For asynchronous communications systems where the
interference may be present only within a part of a transmission
burst, some decision-directed algorithm can be used to adapt the
matrix filter, G(z), to changes in the interference structure. The
algorithm can start from mid-amble (since the desired user training
sequence is known) and then adapt from the center to the beginning
and the end of each transmission burst. In this case, an efficient
algorithm to update matrix inverses can also be used. The
decision-directed adaptive algorithm can be based upon a host of
standard adaptive filtering algorithms, such as, NLMS and RLS
(Kalman filtering).
[0069] The computation of a square-root of a matrix is needed to
compute the spatial whitening transformation (see equation (18)).
This can increase receiver complexity significantly since it
involves the computation of a symmetric matrix factorization.
However, when an equalizer that uses matched filtering as a
front-end is used, the square-root operation may be circumvented.
In this case, the equalizer requires only the channel correlation
estimates. The channel correlation polynomial can be expressed as:
p(z)=.parallel.WF(z)h(z).parallel..sup.2=h(z).sup.TF(z).sup.TR.sub.e.sup.-
-1F(z)h(z), (19) which does not require computing the square-root
of R.sub.e.sup.-1. Such simplification can also be done for an MLSE
equalizer when a front-end matched filter is used. In this case,
the branch metric definition may need to be modified to take into
account the noise correlation after matched filtering FIG. 7
displays an embodiment of receiver circuitry 700 that takes
advantage of this simplification.
[0070] After interference suppression (filtering and combining) and
before being provided to an MLSE equalizer, it may be necessary to
whiten (de-correlate) the interference suppressed signal (block
825). The interference suppressed signal can be severely colored
(as a result of the filtering and combining operations). If this is
the case, then the interference suppressed signal can be whitened
(for example by a whitening unit 650 (FIG. 6)). Severe coloring can
impact the performance of MLSE. The whitening can be implemented
adaptively using linear prediction filtering. Note that the process
800 may not be limited to co-channel interference suppression
alone, the process 800 can also suppress adjacent channel
interference.
[0071] With reference now to FIG. 9, there is shown a data plot
illustrating a link level performance comparison of several single
antenna interference cancellation algorithms in an environment with
a single co-channel interferer, according to a preferred embodiment
of the present invention. A first curve 905 displays the
performance of a conventional MLSE algorithm, a second curve 910
displays the performance of a MLSE algorithm with pre-whitening
prior to MLSE, a third curve 915 displays the performance of a
successive interference canceling algorithm, a fourth curve 920
displays the performance of a joint MLSE algorithm, a fifth curve
925 displays the performance of an embodiment of the proposed
interference suppression scheme (as displayed in FIG. 5) with no
whitening and a sixth curve 930 displays the performance of an
embodiment of the proposed interference suppression scheme (as
displayed in FIG. 5) with whitening. The performance results show
that the joint MLSE algorithm outperforms the proposed interference
suppression scheme with and without whitening. Note however, that
the proposed interference suppression schemes permit a blind
implementation, which is not possible with joint MLSE or successive
interference cancellation.
[0072] With reference now to FIG. 10, there is shown a data plot
illustrating a link level performance comparison of several single
antenna interference cancellation algorithms (with and without
oversampling) in an environment with a single co-channel
interferer, according to a preferred embodiment of the present
invention. A first and second curve 1005 and 1010 display the
performance of conventional MLSE with oversampling factors of one
(1) and two (2), a third and fourth curve 1015 and 1020 display the
performance of an embodiment of the present invention (as displayed
in FIG. 8, with N=0) with oversampling factors of one and two, a
fifth and sixth curve 1025 and 1030 display the performance of an
embodiment of the present invention (as displayed in FIG. 8, with
N=1) with over sampling factors of one and two. The performance
results show that 2.times. oversampling can provide significant
gait over baud-rate sampling in the embodiments of the present
invention. However, oversampling does not provide a performance
gain for conventional MLSE receiver.
[0073] Although the present and its advantages have been described
in detail, it should be understood that various changes,
substitutions and alterations can be made herein without departing
from the spirit and scope of the invention as defined by the
appended claims.
[0074] Moreover, the scope of the present application is not
intended to be limited to the particular embodiments of the
process, machine, manufacture, composition of matter, means,
methods and steps described in the specification. As one of
ordinary skill in the art will readily appreciate from the
disclosure of the present invention, processes, machines,
manufacture, compositions of matter, means, methods, or steps,
presently existing or later to be developed, that perform
substantially the same function or achieve substantially the same
result as the corresponding embodiments described herein may be
utilized according to the present invention. Accordingly, the
appended claims are intended to include within their scope such
processes, machines, manufacture, compositions of matter, means,
methods, or steps.
* * * * *