Note: Descriptions are shown in the official language in which they were submitted.
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JOINT SPACE-TIME OPTIMUM FILTER (JSTOF) USING CHOLESKY AND
EIGENVALUE DECOMPOSITIONS
Field of the Invention
The present invention relates to wireless
communications systems, such as cellular communications
systems, and, more particularly, to filtering received
wireless signals to reduce unwanted interference.
Background
Interference canceling matched filters (ICMF) and joint
demodulation (JDM) has been investigated to meet
requirements for a Downlink Advanced Receiver Performance
(DARP) that is standardized by the third generation mobile
communications system and the Third Generation Partnership
Project (3GPP). Some of these proposals are set forth in the
following articles and documents.
1. Liang et al., A Two-Stage Hybrid Approach for
CCI/ISI Reduction with Space-Time Processing, IEEE
Communication Letter Vol. 1, No. 6, Nov. 1997.
2. Pipon et al., Multichannel Receives
Performance Comparison In the Presence of ISI and CCI,
1997 13th Intl. Conf. on Digital Signal Processing,
July 1997.
3. Spagnolini, Adaptive Rank-One Receiver for
GSM/DCS Systems, IEEE Trans. on Vehicular Technology,
Vol. 51, No.5, Sept. 2002.
4. Feasibility Study on Single Antenna
Interference Cancellation (SAIC) for GSM Networks, 3GPP
TR 45.903 Version 6Ø1, Release 6, European
Telecommunications Standards Institute, 2004.
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5. Radio Transmission and Reception (Release 6),
3GPP TS 45.005 Version 6.8.0; European
Telecommunications Standards Institute, 2005.
6. Stoica et al., Maximum Likelihood Parameter
and Rank Estimation in Reduced-Rank Multivariate Linear
Regressions, IEEE Trans. On Signal Processing, Vol. 44,
No.12, Dec. 1996.
Kristensson et al., Blind Subspace Identification
of a BPSK Communication Channel, Proc. 30t'' Asilomar
Conf. On Signals, Systems and Computers, 1996.
Golub et al., Matrix Computations, 3d Edition,
1996.
Trefethen et al., Numerical Linear Algebra, 1997.
Press et al., Numerical Recipes in C, 2nd Edition,
1992.
Current Global System for Mobile communications (GSM)
cellular systems have to address the co-channel interference
(CCI) on the mobile station (MS) side, as well as address
the DARP requirements. Some single channel structures and
pre-filters have been used to aid in canceling the
interference and provide some channel impulse response (CIR)
estimation. Moreover, some systems have used maximization of
the signal-to-interference to design jointly a single
channel space-time filter and the CIR estimation for a
single channel. Other systems have used a constrained
minimization of the mean-square error to design a single
channel space filter. Other systems have used a single
channel space filter that is designed by a rank-one
approximation of the ML channel estimation. The target
applications for these systems have been a base station
where a physical antenna array including a plurality of
antennas is available.
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Suamnary
Generally speaking, the present disclosure relates to a
filter for reducing co-channel interference within a
communications receiver. More particularly, the filter may
include a multi-channel, space-time filter circuit that
filters signal parts that have been split from a
communications signal by jointly estimating space-time
filter weights and multi-channel impulse responses (CIRs)
based upon a Cholesky decomposition. A multi-channel matched
filter circuit receives multi-channel signals from the
multi-channel, space-time filter circuit and has a filter
response that is provided by a channel impulse response
estimation from the space-time filter circuit. A standard
filter can be operative when an interference level is below
a pre-determined threshold and can be formed as a matched
filter and cross-correlation circuit and switch mechanism
for switching the signal parts into the matched filter and
cross-correlation circuit.
In one aspect, the multi-channel, space-time filter
circuit includes a plurality of multiplier and delay
circuits that each receive n signal parts. The multiplier
and delay circuits are operative based on space-time filter
weights. Each multiplier and delay circuit comprises two
multiplier circuits and a delay circuit. Each multiplier and
delay circuit is operative at one symbol delay. A joint
optimal filter weights and channel estimator is operatively
connected to the multi-channel, space-time filter circuit
and receives training sequence (TS) symbols and timing
uncertainty data and generates space-time filter weights for
the multi-channel, space-time filter circuit. A summer
circuit sums data from the multiplier and delay circuits for
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each channel. An equalizer circuit is operative with the
multi-channel, matched filter circuit.
Brief Description of the Drawings
Various objects, features and advantages will become
apparent from the following detailed description, when
considered in light of the accompanying drawings, in which:
FIG. 1 is a block diagram of a Joint Space-Time Optimum
Filter based Downlink Advanced Receiver Performance (DARP)
capable receiver in accordance with an exemplary embodiment;
FIG. 2 is a more detailed block diagram of the Joint
Space-Time Optimum Filter and Multi-Channel Matched Filters
shown in FIG. 1 in accordance with an exemplary embodiment;
FIG. 2A is a block diagram of a method in accordance
with an exemplary embodiment;
FIG. 3 is a graph showing the Joint Space-Time Optimum
Filter based DARP capable receiver performance for various
DARP test cases;
FIG. 4 is a graph showing the Joint Space-Time Optimum
Filter receiver performance in accordance with an exemplary
embodiment with additive white Gaussian noise (AWGN),
compared with and without an auto-switching strategy;
FIG. 5 is a graph showing the Joint Space-Time Optimum
Filter receiver performance in accordance with an exemplary
embodiment with DTS-5, compared with and without auto-
switching;
FIG. 6 is a graph comparing the performance of single
with multiple Viterbi equalizers in accordance with an
exemplary embodiment, using 8-bit SD limiter in the
simulation;
FIG. 7 is a graph showing the performance of Joint
Space-Time Optimum Filter Receiver and a modified test case
in accordance with an exemplary embodiment;
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FIG. 8 is a schematic block diagram of an exemplary
model wireless communication device that can be used in
accordance with an exemplary embodiment; and
FIG. 9 is a table comparing the three approaches for
performing Cholesky decomposition, QR decomposition, and
singular value decomposition (SVD) computations in
accordance with the present disclosure.
Detailed Description of the Preferred Embodiznents
Several non-limiting embodiments will now be described
more fully hereinafter with reference to the accompanying
drawings, in which preferred exemplary embodiments are
shown. These embodiments may, however, be embodied in many
different forms and should not be construed as limited to
the embodiments set forth herein. Rather, these embodiments
are provided so that this disclosure will be thorough and
complete, and will fully convey the scope to those skilled
in the art. Like numbers refer to like elements throughout,
and prime notation is used to indicate similar elements in
alternative embodiments.
In accordance with one embodiment, Co-Channel
Interference (CCI) on a mobile station (MS) side in a
current Global System for Mobile (GSM) communications system
is addressed, as well as the compliant requirement of a
Downlink Advanced Receiver Performance (DARP) standard by
the Third Generation Partnership Project (3GPP).
The illustrated embodiment in FIG. 1 provides a multi-
channel pre-filter that is operable for canceling the
interference and providing channel impulse response (CIR)
estimation adaptively and optimally. The pre-filter can use
two major components in one non-limiting example: (1) a
multiple-input-multiple-output (MIMO) based Joint Space-Time
Optimum Filter (JSTOF); and (2) a multiple-input-single-
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output (MISO) based multi-channel matched filter. In a
typical mobile station using a single available antenna, a
virtual antenna array can be configured internally by the
combination of over sampling and the separation of real and
imaginary parts that receive samples.
In one non-limiting embodiment, a signal from the
virtual antenna array is fed to the JSTOF, where the optimum
weights for the MIMO-based interference canceling filter are
estimated. At the same time, the multi-channel CIRs for the
desired signal are jointly estimated. The output of the
JSTOF allows the interference to be filtered and fed to a
MISO-based multi-channel matched filter. The filter response
of the matched filter is provided by the CIR estimation from
the JSTOF.
The output of the multi-channel matched filter passes
to a Viterbi equalizer which removes the inter-symbol
interference (ISI) and provides soft decisions for further
processing. A single channel response required by the
equalizer can be formed by a combination of the convolved
CIRs from the JSTOF. This pre-filter can also automatically
switch to the conventional or standard filter in the
conventional receiver in any AWGN dominant cases and switch
back to the JSTOF-based receiver in any interference
dominant cases. This auto-switching capability reduces the
loss in AWGN dominant cases.
An example of the pre-filter or interference canceling
filter for the JSTOF-based and DARP-capable receiver is
shown at 10 in FIG. 1, in which the oversampling ratio is 2
and the number of the virtual antennas is 4(M = 4), as also
indicated by XI(k) through X4(k). Throughout this description
the pre-filter 10 can be referred to as the interference
canceling filter or JSTOF filter, and acts as a pre-filter
in a DARP compliant receiver. A receiver incorporating this
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filter 10 could be described as a JSTOF receiver as is shown
by the dashed line at 11 in FIG. 1.
FIG. 1 shows examples of the various circuit blocks
used for the filter 10. An input signal is received into a
derotation circuit 12. The derotated output signal is split,
with a portion passing into a filter 14 of a conventional
receiver that includes a 2:1 switch 16, and an output into a
matched filter 18 and a cross-correlation circuit 20 that
receives shortened training sequence (TS) symbols. The 2:1
switch 16 is operable to allow switching between the filter
14 and the JSTOF-based and DARP-capable pre-filter 10.
The other portion of the output signal from the
derotation circuit 12 is split into even samples and odd
samples as part of the virtual antenna 24 and split again
into real and imaginary signals to form the respective Xz(k)
through X4(k) input signals into a JSTOF circuit 30, also
referred to as a multi-channel, space-time filter circuit.
The output signals from the JSTOF circuit are passed into a
multi-channel matched filter circuit 32, and its output
signal is passed into a rescaling circuit 34 and then into a
multiplexer circuit 36 as data (dl). The multiplexer circuit
36 also receives a channel (cl) response. When the
conventional filter 14 is connected, the multiplexer 36
receives the data (d2) and channel (c2) response from the
matched filter circuit 18 and cross-correlation circuit 20.
Signals are passed into a Viterbi equalizer 38 as a soft
decision output.
Further details of the JSTOF and the multi-channel
matched filters are shown in FIG. 2, where the number of
time-delayed samples used in the JSTOF circuit is 2 (N = 2).
The various inputs Xl (k) through X4(k) are received into the
JSTOF, which is shown in greater detail. The JSTOF circuit
30 includes channelized multipliers, also termed mixers 40,
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42, delay units 44 and summers 46, which input into multi-
channel matched filters 48 for each of the four illustrated
channels, and signals from the matched filters are passed
into a summer 50. A joint optimal filter weights and channel
estimator circuit 52 receives TS symbols and timing
uncertainty signals to produce the weights (WppT) used for
the mixers 40, 42.
It thus is possible as described to integrate a pre-
filter function into a conventional GSM receiver by adding a
pre-filter branch parallel to a conventional matched filter
as shown in FIG. 1. The conventional software/hardware
Viterbi equalizer 38 can be used without change. In one non-
limiting example, an integrated DARP-capable receiver has
been tested against DARP test cases by simulations, which
indicates that the receiver provides 1.6 dB to 6.9 dB margin
over a specified performance in terms of the frame error
rate (FER) for one of the AMR speech channels.
FIG. 2a is a flow-chart illustrating a high-level
method associated with the described system in which the
various steps are shown as non-limiting examples. The
various steps begin with the 100 series reference numerals.
The incoming communications signal is derotated (Block 100)
and passed into the virtual antenna. The communications
signal is split into even and odd samples (Block 102), and
each even and odd sample is then split into real and
imaginary signal parts (Block 104). The communications
signals from the virtual antenna are passed into the JSTOF
circuit, where the communications signals are multiplied and
delayed (Block 106) and then summed (Block 108), all as part
of a first multiple-in, multiple-out (MIMO) Joint Space Time
Optimum Filter (JSTOF) . After summing, summed signals are
passed into the multi-channel, multiple-input single-output
(MISO) matched filter circuit (Block 110) and then summed
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(Block 112) and passed as a single out signal into the
Virterbi equalizer (Block 114) in which a soft decision is
made (Block 116).
In operation, the derotation circuit 12 is operable
with GMSK modulated signals and the frequency offset that is
part of that signaling protocol. Before any derotation, the
signal constellation is dynamic and after derotation the
signal constellation becomes static, i.e., any symbols are
typically concentrated on 0' and 180 , with symbols rotated
to those two points. Thus, the GMSK signal can be treated as
a typical binary phase shift keying (BPSK) signal. The
derotation at the front end is used for even and odd
samplings, which is useful because of the over-sampling
rate. For example, in a conventional receiver, this is
typically at the rate of 1, i.e., one sample per symbol.
The virtual antenna 24 can increase the sampling rate
to two samples per symbol in a serial manner coming from the
baseband filter to form two separate channels of even and
odd. Before this process, the odd/even samples were serially
interleaved. These signals are then further split into the
real and imaginary signal parts to form the four independent
channels of the virtual antenna. It should be noted that in
some embodiments other numbers of virtual antennas/channels
may be used (e.g., one or more), as will be appreciated by
those skilled in the art.
As best shown in FIG. 2, these signals are then passed
into the multiplier 40,42 and unit delay circuits 44, e.g.,
a one symbol delay, and thus the signal is processed with a
multiply and delay, followed by a multiply operation as
evident by the two multipliers 40, 42 and one delay circuit
44. This operation is followed by a summation in summer 46
as illustrated. This portion of the system is operable as a
multi-channel, two-dimensional filter. One dimension occurs
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because of the delay in time and another dimension is
introduced from the virtual antenna, i.e., a spatial
dimension as described and thus the two dimensions form a
space-time filter.
It is evident each incoming signal is used in
conjunction with other channels, and multipliers receive
weights from the Joint Optimal Filter Weights and Channel
Estimator 52. The weights coming from the Joint Optimal
Filter Weight and Channel Estimator 52 are passed into the
multipliers.
The weights are also an 8 x 4 dimensional matrix in one
non-limiting example, i.e., 32 weights. As to the training
sequence symbols input into the Joint Optimal Filter Weights
and Channel Estimator 52, there are typically in some non-
limiting examples about 26 known symbols and it is known
which training sequence a packet contains. A +/-3 or seven
positions search in a non-limiting example can be used to
find the timing. The impulse response of the multi-channel
matched filter (hopt) can be used such that the system
matches the channel response and makes the signal stronger
after the matched filter.
As shown in FIG. 1, rescaling can occur as a hardware
or software convenience, although it is not required. This
rescaling circuit 34 allows greater operation for a 4-bit or
5-bit input as a non-limiting example to the Viterbi
equalizer 38. The dynamic range of the signal can be
readjusted such that the signal can be sent into a 4-bit or
5-bit circuit.
As noted before, the multiplexer 36 can take the
signals d2 and c2 for the data and channel response from the
conventional filter receiver 14 or the signals d, and cl for
the data and channel response from the JSTOF receiver 10 to
allow a switch-over between the two. The JSTOF receiver will
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introduce some loss if there is no interference, i.e., just
pure white noise. In this case the conventional receiver 14
can be used and will work adequately. So, the circuits can
switch back to the conventional filter without loss
introduced by the JSTOF receiver and its circuits. The
switching is based on the estimation of the SINROUT minus
SINRINP. If the quantity is below a threshold, the system
determines there is little interference and the interference
canceling of the JSTOF receiver is not required. Thus, the
filter of the conventional receiver 14 is used by switching
the 2:1 switch 16.
The circuit is operable in beam forming systems and
other systems. This type of system also allows the signal-
to-noise ratio to be improved and the bit error rate (BER)
to be improved. This could impact top level protocols and
phone calls and other communications matters for use with
these circuits.
The multi-channel structure of the JSTOF-based filter
10 is used in one embodiment, and the MIMO-based JSTOF
circuit 30 provides a space-time filter weight and channel
estimations that are different from prior art solutions.
This circuit provides the ability to combat the interference
efficiently for both synchronous and asynchronous
interferences and yield high performance. Some simulations
have shown that none of the solutions in some prior art
techniques provide the required performance against the DARP
test cases.
This MISO-based multi-channel matched filter circuit 32
is a feature that improves the overall error rate
performance and reduces the complexity of the equalizer by
avoiding multi-channel Viterbi equalizers. The built-in
automatic switching between JSTOF-based and conventional
receivers reduce the loss in AWGN cases.
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Suitable receiver structures can be used in order to
meet the DARP requirements. An Interference Canceling
Matched Filter (ICMF) can use an example of the virtual
antenna as described and beamforming to combat the
interference. The circuit is sensitive to the estimation
errors of the Channel Impulse Response (CIR) of the desired
signal. A Joint Demodulation (JD) showed good performance
for the various test cases. In addition to the difficulty in
combating the asynchronous interferers, there may be heavy
computational complexity involved in finding the CIR of an
interferer.
In one embodiment, the virtual antenna 24 is operable
with adaptive space-time filtering, allowing the Joint
Spatial-Temporal Optimum Filter (JSTOF) circuit 30 to be
used. One difference from the ICMF is that the spatial-
temporal filter weights used to suppress the interference
and the CIR estimation of the desired signal are jointly
estimated and optimized in the JSTOF while the two are
separately estimated in an ICMF. The JSTOF circuit 30 can be
a Multiple-Input-Multiple-Output (MIMO) circuit that takes
advantage of the rank deficiency nature of the desired CIR
matrix in the space-time setup. Simulations have shown a
satisfactory performance for the various DARP test cases.
Computational load is deemed acceptable given that fixed-
point Cholesky factorization and EVD/SVD are feasible.
This method has some simplicity and low computational
complexity. It is also robust because the system makes few
assumptions about the source of the interference. In
addition, the system can continue to use the existing
equalizer structure, as the solution is integrated as a pre-
processing step on the input data. This would allow the
system to use the HW equalizer accelerators if available.
In order to support the evaluation of this technique,
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the system level Block Error Rate (BLER) simulator was
extended to support all of the interferer models/scenarios
being used by the 3GPP DARP Specification.
There now follows a description of the simulation
performance for DARP test cases using the JSTOF circuit. It
should be understood that space-time processing for joint
interference reduction and channel estimation has been used
in a base station, where an array of M antennas is
available. Assuming that the equivalent channel response for
the single desired user can be modeled as an L-tap Finite
Impulse Response (FIR) filter, a snapshot sample of the
received baseband signal can be expressed as
L-1
x(k) _ E c(l)sk_, + v(k) = Hs(k) + v(k) , (1)
r=0
where x(k) is an Mxl vector representing the output
from the antennas, H is an MxL matrix containing the channel
response for the antenna array, s(k) is an Lxl vector for
the corresponding symbols transmitted, and v(k) is an Mxl
vector including the AWGN and the interference. The space-
time extension for formula (1) can be obtained by stacking N
time-delayed versions of x(k) into a taller MNxl vector i(k)
as follows:
x(k) = [xT (k), xT (k -1), = = =, xT (k - N + 1)t = Hs(k) + v(k) , (2)
where H an MNx(L+N-1) matrix is the block Toeplitz
version of H and s(k)=[sk, sk-1, ..., Sk-L-N+2]T. The samples
that correspond to the training sequence can be collected,
X=[x(k),x(k+l), ,x(k+p-1)]=HS+V, (3)
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where p = P- L- N+ 2, P is the number of symbols of
the training sequence, X is an MNxp matrix, and S=
[ s( k) , s( k+1) , ..., s( k+p-1) ] is an (L+N-1) xp convolution
matrix of the training symbols. The joint optimization is to
find a non-trivial MNxl weight vector w for a space-time
filter and a non-trivial (L+N-1)xlchannel estimation vector
h after the filter such that the output interference
residual of the filter is minimized, i.e., to solve the
following optimization problem:
mhnIIWTX-hTS142. (4)
It can be found that the optimal weight is:
wop, = RX1RXhopt , (5)
and the optimal channel estimation hoPt is the
eigenvector corresponding to the minimum eigenvalue of the
matrix Rs -Rx Rx'Rxs, where
Rx= X'XT, (MNxMN) (6)
RS = S * ST , ( (L+N-1)x (L+N-1) ) and (7)
RxS =X*ST, ((MN)x (L+N-1) ) . (8)
Given that the noise plus interference component V in
the space-time model of equation (3) is no longer white but
approximately Gaussian distributed with unknown covariance
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matrix R,, the optimal estimation for the channel H is the
maximum-likelihood (ML) estimation, which is a minimization
of the following quantity:
~(H,Rv)=loglR, I+IIX-HSIIRV . (9)
In this non-limiting space-time model, the number of
the independent channels is always less than or equal to M
and H is usually rank deficient, i.e., rank(ii) = r <
min(MN, L+N-1). The rank deficient ML problem can be used
for the rank-1 approximation of the space-time filter.
The JSTOF circuit in one embodiment can use a different
approach to find the joint optimum solutions for the filter
weight and the channel estimation. It is possible to find
the ML estimation of H. The estimation can be decomposed as
H* =HSHH, (10)
where Hs(MNxM) is the estimation of the space matrix of
H and Ht((L+N-1)xM) is the estimation of the time matrix of
H. They can be obtained by:
H~ = Rs1/2VDM . and (11)
Hs = RxsHt , (12)
where Rs =Rs~ZRHiZ is the Cholesky factorization and VDM
consists of the M eigenvectors corresponding to the
top M eigenvalues of the matrix D.
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D _ Rsxi2RS RSiRxS Rsii2 . (13)
In a next step, the optimal weight for the space-time
filter can be obtained by
wop, = Rx'RxSH1 , (MNxM) (14)
and the optimal channel estimation is
hopt =w pt =H H. (Mx (L+N-1) ) (15)
It is then possible to apply the optimal space-time
filter in equation (14) to the samples from the antenna
array 24. Clearly the outputs of the filter 30 still have M
channels, and it is a MIMO system. The optimal channel
estimation in equation (15) can be used for the multi-
channel matched filters 32. The outputs of the matched
filter are then combined (summed up) and rescaled in the
rescaling circuit 34 to the modified desired level. The
final output is a single-channel sample stream and can be
fed into the Viterbi equalizer 38. Note also that the number
of channel taps after the JSTOF has been changed to L+N-1
comparing to L of the modeled channel taps before the JSTOF.
It was observed by simulations that the JSTOF receiver
incurred more that 1 dB loss in the pure AWGN cases compared
to the conventional receiver using the conventional filter.
To reduce the loss, a strategy of automatic switching
between the JSTOF and conventional receivers was developed.
The switching is based on the measurement of the difference
of the input and output SINR's of the JSTOF. When the
difference is below a predefined threshold the JSTOF
receiver is turned off and the conventional receiver is
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turned on. The input SINR can be easily computed once the
estimation of H is done in equation (10)
1114S'1z tr(H'R HT)
SINR _ = S , (16)
inp - HS1IZ tr(Rx +H'RsHT -2Re{RXSHT})
and the output SINR can be computed from equations (14)
and (15):
Iz = T
IIhop1SI ~(haPtRshop,)
SINRout Ilw ptX-hop,SllZ tr(w p,Rxw+hop1RSh Ft -2Re{w ptRxsh Pt}) (17)
On the mobile side, a virtual antenna array can be set
up by the combination of oversampling and the separation of
the real and imaginary parts as shown in FIG. 1.
In accordance with various embodiments, the joint
optimum MIMO space-time filter and channel estimation set
forth in equations (14) and (15) enhances interference
suppression performance. The MISO multi-channel matched
filters 32, which are based on the channel estimation in
equation (15), improve the error rate performance while
reducing the complexity of the Viterbi equalizer 38. A
strategy of automatic switching between JSTOF and
conventional receivers reduces the loss in pure AWGN cases.
The JSTOF defined by equations (6)-(17) can be
implemented in different ways in terms of numerical
stability and computational complexity. The major
differences are the way in which the inverse of the
autocorrelation matrix RX is calculated and the way in which
the channel H is estimated with reduced rank.
One such implementation is a Cholesky decomposition-
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based matrix inversion of Rx and the eigenvalue
decomposition of matrix D in equation (13) . Specifically,
since RX is symmetric positive definite, the Cholesky
decomposition exists:
Rx = LxLX (18)
D can be rewritten as
D=DID~ , (19)
where
D, =LSTR SLx (20)
It should be noted that the inverse is actually
performed with the square-root of Rx, and the explicit
computation of the inverse may be avoided by the back-
substitution. Also, D is numerically stable because of its
structure of mutual cancellations. This was verified by
simulations that showed the condition number of D is seldom
greater than 300. This implies the eigenvalue decomposition
on D would not require unduly sophisticated algorithms for
typical applications, as will be appreciated by those
skilled in the art. In fact, this approach may potentially
have the least computational complexity of the approaches
outlined herein.
One potential numerical concern is the Cholesky
decomposition on Rx, as its condition number may potentially
be relatively high, and its positive definite property may
be offset to some degree by round-off errors. Simulations
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showed, however, that the condition number of Rx is less
than 107 even in some extreme scenarios such as very high and
very low carrier-to-interference (C/I) ratios.
In accordance with an alternate embodiment, the QR
decomposition in the sample domain may be used to avoid the
direct calculation of the inverse of R. Since the XT in
equation (3) has full column rank, it has the unique QR
decomposition
XT =QR, (21)
where Qis a pxMN matrix with orthogonal columns and R
is a full rank MNxMN upper triangular matrix. It can be
shown that
RXl _ R-1R-r ~ (22)
and the D in equation (13) can be written in the form
of equation (19) with the D, re-defined by
D, =LsTSQ . (23)
The reduced rank channel estimation may be performed
with the eigenvalue decomposition on D as in the previous
approach, and the optimum filter weight matrix of (14) can
be reduced as
wopr =R-1DiVDM = (24)
This approach is basically an equivalent version of
Cholesky decomposition in the sample domain since one can
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show that R= LX. It has improved numerical stability at the
expense of the QR decomposition's greater complexity
(requiring approximately twice as many operations for a
matrix of given size) and larger sample matrix (having
approximately 3 times as many rows in an example case where
M=4, N=2 and L=5).
The two approaches described above still require the
computation of the triangular matrix inverse, although this
may be done by back-substitutions. Turning now to yet
another alternate approach, i.e., the singular value
decomposition (SVD) approach, the matrix inversion may be
avoided and the numerical stability may be further improved
in some applications. This approach starts with the SVD on
the sample matrix in equation (3):
T =UxExVx (25)
where Ux is a pxMN matrix with orthogonal columns, Vx
is an MNxMN orthogonal matrix and EX is an MNxMN diagonal
matrix, Ex =diag(61,===,ffMN), with the singular values on its
diagonal. It can be shown that
Rx' = y'Zx-2VT (26)
The D in equation (13) still has the form of equation
(19) with D, defined by:
D, =L_STSUx . (27)
The channel estimation may be obtained by the SVD on D,
and the filter weight matrix may be written as
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Wopt = VxEx lD T, VDM , (28)
where VDM contains the top M right singular vectors of
Di . The SVD in this approach may require more computations
than the Cholesky and QR decompositions used in the previous
two approaches.
As a comparison of the three approaches outlined above
(i.e., Cholesky, QR, and SVD), the table in FIG. 9 lists the
computations step by step for an example where M=4, N=2 and
L=5. To find the best timing of the burst, the JSTOF
searches a number of timing hypotheses and the one
corresponding to the minimum output residual is chosen as
the best timing. The output residual is defined by:
e 'Ilw p,X-h Ptsllz, (29)
The search process basically repeats the operations
listed in the table for each hypothesis, but the input
sample matrices from the consecutive timing hypotheses
change slightly by appending and deleting a column. The
updating and the downdating algorithms are potentially
applicable to some of the operations, and the overall
computation load may potentially be reduced.
Let X(k) represent the sample matrix at time instant k.
It may be partitioned from equation (3) to
X(k) = [x(k), X(k + 1)] , (30)
where
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X(k+l)=[x(k+l), 'x(k+p-1)] (31)
The sample matrix at time k+1 may be expressed as
X(k + 1) =[X(k + 1), x(k + p)] . (32)
The autocorrelation matrix at time k+1 has the form
RX (k + 1) = Rx (k) - x(k)xT (k) + x(k + p)xT (k + p) (33)
This is a combination of a rank-1 downdate and a rank-i
update. One hyperbolic rotation-based algorithm for
updating/downdating the Cholesky factorization is set forth
in Matrix Computations by Golub et al., 3rd edition, 1996.
Another applicable update/downdate algorithm disclosed
in Golub et al. text is for QR decomposition, which is based
on the Givens rotation. Of course, the given approach that
should be used in a particular application will depend on
factors such as available processing resources,
computational complexity, etc., as will be appreciated by
those skilled in the art. Other approaches may also be used,
as will also be appreciated by those skilled in the art.
The performance of the JSTOF based receiver has been
evaluated by Matlab simulations using an extended BLER
simulation engine. The parameters for the JSTOF based
receiver can be set with different aspects. Examples of
values follow:
1) The oversampling ratio (OSR) of 2 can be
selected, which maps to the number of virtual antennas
(M) of 4 in this non-limiting example, and simulation
shows that reducing the OSR to 1 causes significant
performance degradations;
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2) A number of temporal delayed samples (N) can
be selected as 2. Increasing the number, however, does
not always improve the performance;
3) A reduced rank for the channel response
matrix can be selected as M. Increasing or decreasing
the rank does not necessarily improve the performance.
4) An auto-switch threshold can be 4.75 dB.
5) A soft decision output can be quantized in 5
bits width. Increasing the width to 8 bits can improve
the performance marginally for DTS-5. Soft decision
correction can be enabled.
The AMR speech channel, TCH-AFS12.2 can be used to
evaluate the performance of the JSTOF in terms of FER. The
propagation condition TU50km/h-1950MHz can be assumed
throughout the simulations. A simulation ran 1000 trials
(blocks) for each case.
The FER's of the receiver, against the carrier-to-
interference (C/I) ratio, are shown in the graph of FIG. 3.
The margins against the reference performance specified are
listed in the table below.
Test JSTOF Spec. Margin of
case performance: performance: JSTOF against
C/I at FER = C/I at FER = Spec., dB
1%, dB 1%, dB
DTS-1 -2.6 4 6.6
DTS-2 7.3 9 1.7
DTS-3 7.6 10 2.4
DTS-4 -0.9 6 6.9
DTS-5 7.4 9 1.6
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The performance of the receiver under pure AWGN and
DTS-5 cases with and without the auto-switching strategy is
shown in the graphs of FIG. 4 and FIG. 5, respectively. The
strategy reduced the loss in AWGN by about 1 dB (at FER =
10%) and incurred little loss for DTS-5.
The JSTOF receiver can include multiple Viterbi
equalizers, followed by a multi-channel match filter, which
combines the soft decisions after the equalizers. A result
is shown and compared with the original in the graph of FIG.
6.
Performance can be evaluated with a modified test case
DTS-5R, where the delay of the asynchronous interferer can
be configured. The performance at 0, 1-4, '-~ and U4 of the burst
length is shown in the graph of FIG. 7. The results indicate
that the performance of JSTOF receiver degrades "slowly"
with severe delay of the interferer.
The above-described receiver may advantageously be used
in mobile wireless devices (e.g., cellular devices) as well
as cellular base stations, for example. An example of a
mobile wireless communications device 1000 that may be used
is further described in the example below with reference to
FIG. 8. The device 1000 illustratively includes a housing
1200, a keypad 1400 and an output device 1600. The output
device shown is a display 1600, which is preferably a full
graphic LCD. Other types of output devices may alternatively
be utilized. A processing device 1800 is contained within
the housing 1200 and is coupled between the keypad 1400 and
the display 1600. The processing device 1800 controls the
operation of the display 1600, as well as the overall
operation of the mobile device 1000, in response to
actuation of keys on the keypad 1400 by the user.
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The housing 1200 may be elongated vertically, or may
take on other sizes and shapes (including clamshell housing
structures) . The keypad may include a mode selection key, or
other hardware or software for switching between text entry
and telephony entry.
In addition to the processing device 1800, other parts
of the mobile device 1000 are shown schematically in FIG. 8.
These include a communications subsystem 1001; a short-range
communications subsystem 1020; the keypad 1400 and the
display 1600, along with other input/output devices 1060,
1080, 1100 and 1120; as well as memory devices 1160, 1180
and various other device subsystems 1201. The mobile device
1000 is preferably a two-way RF communications device having
voice and data communications capabilities. In addition, the
mobile device 1000 preferably has the capability to
communicate with other computer systems via the Internet.
Operating system software executed by the processing
device 1800 is preferably stored in a persistent store, such
as the flash memory 1160, but may be stored in other types
of memory devices, such as a read only memory (ROM) or
similar storage element. In addition, system software,
specific device applications, or parts thereof, may be
temporarily loaded into a volatile store, such as the random
access memory (RAM) 1180. Communications signals received by
the mobile device may also be stored in the RAM 1180.
The processing device 1800, in addition to its
operating system functions, enables execution of software
applications 1300A-1300N on the device 1000. A predetermined
set of applications that control basic device operations,
such as data and voice communications 1300A and 1300B, may
be installed on the device 1000 during manufacture. In
addition, a personal information manager (PIM) application
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may be installed during manufacture. The PIM is preferably
capable of organizing and managing data items, such as e-
mail, calendar events, voice mails, appointments, and task
items. The PIM application is also preferably capable of
sending and receiving data items via a wireless network
1401. Preferably, the PIM data items are seamlessly
integrated, synchronized and updated via the wireless
network 1401 with the device user's corresponding data items
stored or associated with a host computer system.
Communication functions, including data and voice
communications, are performed through the communications
subsystem 1001, and possibly through the short-range
communications subsystem. The communications subsystem 1001
includes a receiver 1500, a transmitter 1520, and one or
more antennas 1540 and 1560. In addition, the communications
subsystem 1001 also includes a processing module, such as a
digital signal processor (DSP) 1580, and local oscillators
(LOs) 1601. The specific design and implementation of the
communications subsystem 1001 is dependent upon the
communications network in which the mobile device 1000 is
intended to operate. For example, a mobile device 1000 may
include a communications subsystem 1001 designed to operate
with the MobitexTM, Data TACTM or General Packet Radio Service
(GPRS) mobile data communications networks, and also
designed to operate with any of a variety of voice
communications networks, such as AMPS, TDMA, CDMA, WCDMA,
PCS, GSM, EDGE, etc. Other types of data and voice networks,
both separate and integrated, may also be utilized with the
mobile device 1000. The mobile device 1000 may also be
compliant with other communications standards such as 3GSM,
3GPP, UMTS, etc.
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Network access requirements vary depending upon the
type of communication system. For example, in the Mobitex
and DataTAC networks, mobile devices are registered on the
network using a unique personal identification number or PIN
associated with each device. In GPRS networks, however,
network access is associated with a subscriber or user of a
device. A GPRS device therefore requires a subscriber
identity module, commonly referred to as a SIM card, in
order to operate on a GPRS network.
When required network registration or activation
procedures have been completed, the mobile device 1000 may
send and receive communications signals over the
communication network 1401. Signals received from the
communications network 1401 by the antenna 1540 are routed
to the receiver 1500, which provides for signal
amplification, frequency down conversion, filtering, channel
selection, etc., and may also provide analog to digital
conversion. Analog-to-digital conversion of the received
signal allows the DSP 1580 to perform more complex
communications functions, such as demodulation and decoding.
In a similar manner, signals to be transmitted to the
network 1401 are processed (e.g. modulated and encoded) by
the DSP 1580 and are then provided to the transmitter 1520
for digital to analog conversion, frequency up conversion,
filtering, amplification and transmission to the
communication network 1401 (or networks) via the antenna
1560.
In addition to processing communications signals, the
DSP 1580 provides for control of the receiver 1500 and the
transmitter 1520. For example, gains applied to
communications signals in the receiver 1500 and transmitter
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1520 may be adaptively controlled through automatic gain
control algorithms implemented in the DSP 1580.
In a data communications mode, a received signal, such
as a text message or web page download, is processed by the
communications subsystem 1001 and is input to the processing
device 1800. The received signal is then further processed
by the processing device 1800 for an output to the display
1600, or alternatively to some other auxiliary I/O device
1060. A device user may also compose data items, such as e-
mail messages, using the keypad 1400 and/or some other
auxiliary I/0 device 1060, such as a touchpad, a rocker
switch, a thumb-wheel, or some other type of input device.
The composed data items may then be transmitted over the
communications network 1401 via the communications subsystem
1001.
In a voice communications mode, overall operation of
the device is substantially similar to the data
communications mode, except that received signals are output
to a speaker 1100, and signals for transmission are
generated by a microphone 1120. Alternative voice or audio
I/0 subsystems, such as a voice message recording subsystem,
may also be implemented on the device 1000. In addition, the
display 1600 may also be utilized in voice communications
mode, for example to display the identity of a calling
party, the duration of a voice call, or other voice call
related information.
The short-range communications subsystem enables
communication between the mobile device 1000 and other
proximate systems or devices, which need not necessarily be
similar devices. For example, the short-range communications
subsystem may include an infrared device and associated
circuits and components, or a BluetoothTM communications
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module to provide for communication with similarly-enabled
systems and devices.
Many modifications and other embodiments of the
invention will come to the mind of one skilled in the art
having the benefit of the teachings presented in the
foregoing descriptions and the associated drawings.
Therefore, it is understood that the invention is not to be
limited to the specific embodiments disclosed, and that
modifications and embodiments are intended to be included
within the scope of the invention.
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