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42
CHAPTER 3
MULTIUSER DETECTION
3.1 INTRODUCTION
The Multiuser Detector (MUD) operates directly on the received
signal, sampled once or several times during each chip period. Such a
receiver is relatively insensitive to errors in the estimate of the propagation
delay and other system parameters. Another advantage is that, it can be
implemented in such a way that only signals that are of interest need to be
detected.
Instead of tuning the receiver directly from the received signal, a
linear filter model of the DS CDMA system is also derived. This
multivariable model has the symbols transmitted by all users as input and
the received chip sampled signal as output. This model is then used as a
basis for the detector design. Both synchronization errors and multi-path
propagation is incorporated in this model and unknown parameters can be
estimated with relative ease. The filter model will be time invariant or
slowly time varying in a system with short codes. When long codes are
used, the filter model will change abruptly from symbol to symbol, when
the multipath channel is time invariant. Multiuser detection deals with the
development and application of joint demodulation and interference
cancellation techniques for improved detection of a desired set of digital
signals.
43
A differential matched filter which is used the differential
information in the FIR filter coefficients mitigates the complexity. This
complexity reduction is important for the multistage detector. The SNR is
still maximized but the detector is not Maximum Likelihood (ML) due to
the presence of Multiple Access Interference (MAI). The effectiveness of
the conventional receiver is limited because it disregards the structure of
MAI and is susceptible to disparities in the received powers of the different
user’s signals. MUD jointly detecting the signal from different users has
been under intense research as a potential method to improve the system
performance of CDMA systems during the last ten years.
The DS/CDMA receivers are divided into Single user and
Multiuser detectors. A single user receiver detects the data of one user at a
time whereas a multiuser receiver jointly detects several users information.
Single user and multiuser receivers are also sometimes called as
decentralized and centralized receivers respectively. In DS-CDMA systems
all users concurrently share the same bandwidth. The users are
distinguished by assigning to each user a unique code or signature
sequence, whose bandwidth is much larger than that of the transmitted
information. This code sequence is used to modulate the data stream.
3.2 LITERATURE REVIEW
In the linear multiuser detector for synchronous CDMA systems,
the received signal is demodulated using an orthogonal multiuser receiver
that is matched to a set of orthogonal vectors that are closest in a least
squares sense to the signature vectors. This approach is equivalent to
optimally whitening the noise component in the output of the decorrelator
prior to detection reported by Eldar and Oppenheim (2002).
44
In an asynchronous CDMA environment, receiver has
knowledge of the signature waveforms of all the users with white Gaussian
noise. The received energies of the users are unknown to the receiver and
whose BER is independent of the energy of the interfering users discussed
by Lupas and Verdu (1990). A new real time, digital adaptive multiuser
receiver structure over white Gaussian noise was designed. This receiver
efficiently implements the decorrelating detector and adapted to incorporate
decision feedback detector to further improvement in their detector
performance (Dao Sheng Chen Roy 1994).
The adaptive receiver has no knowledge of the signature
waveforms and timing of other users. The receiver is trained by a known
training sequence prior to data transmission and continuously adjusted by
an adaptive algorithm during data transmission. The linear receiver is a
standard single user detector receiver consisting of a matched filter with
constant coefficients discussed by Rapajic and Vucetic (1994). Several
multiuser detectors such as decorrelator, the two stage detector and the
decision feedback detector for the Raleigh flat fading synchronous CDMA
channel was compared. In the presence of channel mismatch, the
decorrelator offers better performance than more complex decision
feedback and two stage detectors performed by Duel-Hallen et al (1995).
The performance analysis of the minimum mean square error
linear multiuser detector is considered in an environment of nonorthogonal
signaling and additive white Gaussian noise. The probability of error of this
detector is better than the decorrelating linear detector for all values of
normalized cross correlations dealt by Poor and Verdu (1997). Adaptive
receivers depend on number of users, their received powers, spreading
45
codes and time delays. Two adaptive receiver architectures such as the
sampled received signals are filtered and another in which the spreading
codes of users is filtered considered by Teng joon lim and Sumit roy
(1998).
The adaptive Multiuser Detector which converges to the
minimum mean square error detector without training sequences and which
requires less information discussed by Howard C. Huang and Verdu (1998).
The signal detection based on additive colored non Gaussian noise, and
attention is focused on one-shot structures where detection of each symbol
is based only on the received process during its corresponding interval by
Poor and Verdu (1998). Lupas and Verdu (1989) proposed the performance
achieved by linear Multiuser Detectors whose linear memory
transformation is a generalized inverse of the matrix of signature waveform
cross correlations.
The multiuser receiver is quite effective in increasing capacity of
users with higher data rate and lower target bit error rate for multirate
CDMA system described by Guo and Aazhang (1999). The front-end
Recursive Least Square-minimum mean square error filters can be
implemented using systolic arrays to exploit massively parallel signal
processing computation, and to achieve energy efficiency by Xiaodong
wang and Poor (1998).
Moshavi (1996) discussed with multiuser detection, where
information about multiple users is used to improve detection of each
individual user. The optimum receiver to detect the bits of multiple CDMA
users has an exponential complexity in the number of active users using
nonlinear programming relaxations define by Yener et al (2002).
46
Komninakis et al (2002) dealt with algorithm offers good
tracking behavior for multiuser fading ISI channels at higher complexity
than conventional adaptive algorithms. Fuxjaeger and Iitis (2004) proposed
the receiver consisting of a parallel bank of extended Kalman filters extracts
estimates of the timing, and the multipath coefficients. The cross coupled
decision feedback detector is suggested to reduce both inter symbol
interference and multiple access interference for an asynchronous
multicarrier CDMA scheme suggested by Liu et al (2004).
The partial cancellation technique and minimum mean square
error multiuser detection techniques are used for interference cancellation
and the performance of this receiver is evaluated in Rayleigh multipath
fading channel by Kumpoopong et al (2005). Mitsuhiro Tomita
et al (2005) concentrated on sequential detection technique for a multiuser
receiver that is constructed over a CDMA system. In this system, the
transmitter transmits a symbol made by spreading the spectrum with an
enveloped sequence protected by guard sequences, and a receiver
demodulates the core sequence part of the received symbol with either a
decorrelating detector.
The adaptive multiuser detector has two major disadvantages.
First, it cannot be applied in systems with long codes. Second, in some
cases the rate of convergence may be too slow. However, these two issues
are used in tuning procedure.
The other group of detectors is based upon Interference
Cancellation (IC). The idea is to cancel the interference generated by users
other than the desired user. The lower computation demand and hardware
related structures are the major advantages of this strategy. This category
includes Serial Interference Cancellation (SIC) and Parallel Interference
47
Cancellation (PIC). One of the most effective PICs comes from the iterative
multistage method. The inputs of one particular stage are the estimated bits
of the previous stage. After interference cancellation, the new estimations,
which should be closer to the transmitted bits, come out to be fed into the
next stage.
Therefore in last several stages, the multistage detector will
almost compute from the same input to generate the same output. This is a
substantial waste of the computation power and it increases the system
delay.
To overcome these limitations, a modified linear multiuser
receiver has been proposed for synchronous CDMA systems, referred to as
the Orthogonal Multiuser (OMU) receiver. Unlike the linear minimum
mean squared error receiver, the OMU receiver depends only on the
signature vectors and does not require knowledge of the received
amplitudes or the channel SNR. Here an optimal set of vectors with a
specified inner product structure is constructed, from a given set of vectors
in a complex Hilbert space. The optimal vectors are chosen to minimize the
sum of the squared norms of the errors between the constructed vectors and
the given vectors.
An algorithm has been developed using the principles of
quantum parameters and some of its axioms and constraints. In place of the
classical Matched Filter (MF) receiver, proposed receiver improves the
accuracy which necessarily results in improved performance. The
simulation results suggest that in certain cases, the OMU receivers can
significantly increase the probability of correct detection with low error rate
over the MF receiver. The OMU receiver achieves lower probability of
48
error compared with other receivers such as decorrelating receiver,
minimum mean squared error receiver, Kalman receiver for SNR values
ranging from 0 dB to 10 dB.
3.3 ORTHOGONALITY AND ORTHONORMALITY
The continuous speech signal can be constructed as a set of
orthonormal and orthogonal vector {hk, 1≤ k≤ N} from a given set of
vectors {Sk, 1 ≤ k≤ N} such that the inner products between vectors in the
set have some specified structure. Specifically, the constructed vectors are
closest in a least squares sense and minimize the sum of the squared norms
of the error vectors between the constructed vectors and the given vectors.
The development considers both the case in which the given
vectors are linearly independent and linearly dependent. The closest
orthonormal vectors refer to as the Orthonormal Least Squares Vectors
(OLSV). Next generalize these results to allow for unequal weighting of the
squared norms of the error vectors referred to as the Weighted Orthonormal
Least Squares Vectors (WOLSV). The problem of constructing orthogonal
vectors that are not constrained to have equal norm and the given vectors
closest in a least squares sense are referred to as the orthogonal least
squares vectors.
3.3.1 Least Square Orthonormalization
The set of orthonormal vectors { hk, 1 ≤ k ≤ N } with set
transformation H, that minimize E = ||S –H||2F subject to <hm, hK> = δmk, or
H*H = I. Thus H is constrained to be a partial isometry. The least squares
orthonormalization problem reduces to find the partial isometry H that
49
minimizes E = ||S –H||2F. The optimal H denoted as H׀ is well known and it
is partial isometry in the polar decomposition of S.
Let S have a Singular Value Decomposition defined as S =
UΣV*, where U is an n × N partial isometry, Σ is an N × N diagonal matrix
and V is an N × N unitary matrix. Then H׀ = UΣV*. A partial isometry is a
transformation T that satisfies T*T = I. If the vectors Sk are linearly
independent, then the results obtained from H׀ = S(S*S)-1/2. The OLSV can
also be obtained as the solution to an orthogonal problem.
3.3.2 Least Square Orthogonalization
Consider the problem of constructing an optimal orthogonal
vector {hk, 1≤ k≤ N} from the given vectors {sk, 1≤ k≤ N} and the vectors
are constrained to have some specified norm. Next constructing a set of
orthogonal vectors {hk, 1≤ k≤ N} that minimize E = ||S –H||2F. F subject to
the constraint <hm, hk > = ck2 δmk, where the scalars ck ≤ 0 are specified. The
assumption without loss of generality that ck > 0 for 1 ≤ k ≤ P and the error
E can be written as E = N≤ k ≤1, < hk - hk, Sk – hk > =N≤ k. If the vectors Sk
are linearly independent and ck > 0 for all k, then the results are obtained as
H׀ = S*C (CS*SC)-1/2.
3.4 GENERAL LINEAR RECEIVER
New classes of receivers consisting of a bank of correlators with
correlating signals matched to a set of signals with a specified inner product
structure R and are closest in an LS sense to the transmitted signals shown
in Figure 3.1. These receivers depend only on the transmitted signals, so
that they do not require knowledge of the noise distribution refer to as MF
50
X1
X2
Xm
b1
b2
bm
r
receivers. In the special case in which R=I(identity), the receiver consists of
a bank of correlators with orthogonal correlating signals that are closest in
an LS sense to the transmitted signals referred to as the Orthogonal
Matched Filter (OMF) receiver.
Figure 3.1 General Linear Receiver
Multiuser receivers include the optimal multiuser receiver, the
linear minimum mean squared error receiver, the decorrelator, and the
Matched Filter (MF) receiver for CDMA signals. Both the optimal receiver
and the linear minimum mean square error receiver require knowledge of
the channel parameters, namely, the noise level and the received amplitudes
of the user’s signals.
The MF and the decorrelator receivers are linear receivers that only
require knowledge of the signature vectors. The MF optimally compensates
for the white noise, but does not exploit the structure of the MAI. The
decorrelator optimally rejects the MAI for linearly independent signature
vectors, but does not consider the white noise.
q1
:
q2
qm
51
X1
X2
Xm
b1
b2
bm
r
a1
a2
am
3.4.1 Decorrelator Receiver
The receiver shown in Figure 3.2 consists of a decorrelator
demodulator followed by an optimal minimum mean square error whitening
transformation on a space formed by the signature vectors. This whitening
transformation is designed to optimally decorrelate the outputs of the
decorrelator prior to detection. Specifically, it minimizes the Mean Square
Error (MSE) between the vector output of the decorrelator and the output of
the whitening transformation, so that distortion to the output vector is
minimized under the whitening constraint.
Figure 3.2 Decorrelator Receiver
The demodulator consists of a bank of correlators with
correlating vectors that are projections of a set of orthogonal vectors, and
are closest in a least squares sense to the decorrelator vectors and also
closest in a least squares sense to the signature vectors.
v1
:
v2
vm
Whitening W
52
3.4.2 Minimum Mean Square Error Receiver
Here the receiver consists of an MF demodulator followed by an
optimal minimum mean square error whitening transformation on a space
formed by the signature vectors, which minimizes the MSE between the
vector output of the MF and the output of the whitening transformation.
3.4.3 Orthogonal Multiuser Receiver
The whitening approach proposed in this chapter is different
from previous whitening approaches to multiuser detection. In the
decorrelating decision feedback detector, the components of the output
vector of the feed forward filter are indeed whitened, but not according to
the criterion used by the OMU demodulator. Rather, the whitening
transformation is chosen in anticipation of a nonlinear feedback loop. A
noise whitening approach is also used, where the whitening has a different
context.
Unlike the decorrelating decision feedback detector and the
OMU detector, where the whitening is performed across users in the same
symbol period, the detector performs whitening of the power spectrum of
the received chip waveform followed by MF detection of the desired user as
shown in Figure 3.3. The results are inferior performance than typical
multiuser detectors, it can be applied to a broader set of circumstances and
the spreading codes of interferers are not required to be known.
53
X1
X2
Xm
b1
b2
bm
r
Figure 3.3.Orthogonal Multiuser Receiver
Here the OMU demodulator maximizes both the total Signal to
Interference Ratio (SIR) and the total Signal to Noise Ratio (SNR) at the
output subject to the whitening constraint. The OMU demodulator also
approximately maximizes both the total output SIR and the total output
SNR for nearly orthogonal signature vectors. This provides some additional
justification for this receiver. The performance of the OMU receiver
depends on the probability of error and the exact expressions for the
probability of error also derived. To analyze the asymptotic performance of
the receiver in the large system limit when random Gaussian signatures and
accurate power control are used. Specifically, the output Signal to
Interference Noise Ratio (SINR) of the output of the OMU receiver
converges to a deterministic limit. This method of proof can be easily
modified to characterize the performance of other Multiuser Detectors in
the large system limit.
h1
:
h2
hm
54
3.4.4 Coloured Noise OMU Receiver
A noise signal, v (k) being uniformly distributed random signal
is generated. Thus, v is white noise, which means it varies randomly
between the samples. This signal is sent to the discrete time signal filter
denoted as shaping filter.
)(*)1(*)( kvkkxakx (3.1)
where ‘a’ is a filter parameter and K is a gain. With ‘a’ = 0, the filter output
signal(x) is also white noise. The value of ‘a’ is in between 0 to 1, x
becomes coloured noise, which means it does not vary randomly between
the samples.
The white noise and coloured noise are important signals in
stochastic systems. In the case of white noise, the set parameter ‘a’ is equal
to 0, causing x to be white noise. Also the gain K is set with 1. In the case
of coloured noise, initially ‘a’ is set to be 0 and also set the gain K with 1.
The parameter ‘a’ is continuously increased and the shape of the signal x
changes also observed. If the noise is coloured, it can be regarded as the
output of a dynamic signal filter typically called a shaping filter.
3.4.5 Kalman Filter Receiver
The Kalman Filter (KF) is one of the most widely used methods
for tracking and estimating due to its simplicity, optimality, tractability and
robustness. However, the application of the KF to nonlinear systems can be
difficult. The most common approach is to use the Extended Kalman Filter
(EKF) which simply linearises all nonlinear models so that the traditional
linear Kalman Filter can be applied. Using this principle, a set of discrete
sampled points can be used to parameterize mean and covariance, the
55
estimator yields performance is equivalent to the KF for linear systems.
Whenever the state of a system must be estimated from noisy sensor
information, some kind of state estimator is employed to fuse the data from
different sensors together to produce an accurate estimate of the true system
state. When the system dynamics and observation models are linear, the
minimum mean squared error estimate can be computed using the Kalman
Filter.
3.5 RESULTS AND DISCUSSION
The performance of OMU receiver is compared with other
receivers such as decorrelating receiver, minimum mean square receiver,
Kalman receiver. The speech signal is opted as an input of the all receivers.
The OMU receiver has achieved low MSE than others.
Figure 3.4 Block diagram representation for Feature Vector Generation
Most useful parameters in speech processing are found in the
frequency domain. There are several ways to extract spectral information of
speech. When the audio file contains two channels (stereo), the block's
output is an M-by-2 matrix containing one frame (M consecutive samples)
Buffer Periodo gram
Selector dB converter
Buffer 1
Transpose Matrix Viewer
Input Speech Signal Vector Scope
56
of audio data from each of the two channels. When the audio file contains a
single channel (mono), the block's output is an M-by-1 matrix containing
one frame (M consecutive samples) of mono audio data. The simulink must
read a continuous stream of data from the device throughout the simulation
shown in Figure 3.4. Delays in reading data from the audio hardware can
result in hardware errors or distortion of the signal.
Table 3.1 Extraction of vectors arranged in Square Matrix
x= [ 7.1039 7.8186 8.5370 9.2648; 7.1634 7.8803 8.5986 9.3243;
7.1053 7.8222 8.5406 9.2662; 7.1655 7.8832 8.6023 9.3279;
7.1075 7.8251 8.5442 9.2698; 7.1692 7.8839 8.6030 9.3315;
7.1111 7.8259 8.5449 9.2735; 7.1728 7.8875 8.6059 9.3344;
7.1147 7.8295 8.5478 9.2764; 7.1750 7.8912 8.6095 9.3351;
7.1169 7.8331 8.5515 9.2771; 7.1764 7.8948 8.6132 9.3388;
7.1184 7.8367 8.5551 9.2807; 7.1800 7.8984 8.6146 9.3424;
7.1220 7.8404 8.5566 9.2844; 7.1837 7.9020 8.6168 9.3460;
7.1256 7.8440 8.5587 9.2880; 7.1866 7.9057 8.6204 9.3497;
7.1285 7.8476 8.5624 9.2916; 7.1873 7.9064 8.6240 9.3533;
7.1293 7.8483 8.5660 9.2952; 7.1909 7.9093 8.6262 9.3569;
7.1329 7.8512 8.5682 9.2989; 7.1946 7.9129 8.6277 9.3576;
7.1365 7.8549 8.5696 9.2996; 7.1982 7.9166 8.6313 9.3605;
7.1401 7.8585 8.5732 9.3025; 7.2018 7.9180 8.6349 9.3642;
7.1438 7.8600 8.5769 9.3061; 7.2054 7.9202 8.6378 9.3678;
7.1474 7.8621 8.5798 9.3098; 7.2091 7.9238 8.6385 9.3693;
7.1510 7.8658 8.5805 9.3112; 7.2098 7.9274 8.6422 9.3714;
7.1517 7.8694 8.5841 9.3134; 7.2127 7.9296 8.6458 9.3751;
7.1546 7.8716 8.5878 9.3170; 7.2163 7.9311 8.6494 9.3787;
7.1583 7.8730 8.5914 9.3206; 7.2200 7.9347 8.6531 9.3809;
7.1619 7.8766 8.5950 9.3228; 7.2214 7.9383 8.6567 9.3823;
57
At the start of the simulation, the audio device begins writing the
input data to a (hardware) buffer with a capacity of Tb seconds. The Wave
Device block immediately begins pulling the earliest samples off the buffer
(first in, first out) and collecting them in length-M frames for output. As the
audio device continues to append inputs to the bottom of the buffer, the
Wave Device block continues to pull inputs off the top of the buffer at the
best possible rate. Here scalar samples are converted into frame output.
Using the Periodogram block a nonparametric estimate of the power
spectrum of the speech signal is computed. With the use of transpose the
vector input signals are treated as (Mx1) matrices shown in Table 3.1.
For the specified inner product structure another constraint that
can be applied for consistency is the least square inner product constraint.
Here, the obtained optimal vectors must be orthogonal and orthonormal.
The optimal vectors are used to minimize the sum of the mean squared
norms of the errors between constructed and the given vectors. For that
singular value decomposition and other set transformations also satisfy the
condition that the inner product of the resultant matrices will be a identity
matrix, the probability value must be one for all type of vectors. The vectors
are identified for linear dependent and linear independent.
The exact and approximate expressions for the probability of
error, as well as the asymptotic Signal to Interference and Noise Ratio
(SINR) in the small system limit are derived. The analysis suggests that
over a wide range of channel parameters the OMU receiver can outperform
both the decorrelator and the single user MF and perform similarly to the
linear minimum mean square error receiver, despite not knowing the
channel parameters.
58
Figure 3.5 Feature Vector Generation
There are many ways to choose whitening transformation. Here,
to choose the whitening transformation with Eigen decomposition that
results in output that is as close as possible in an MSE sense to the output of
the decorrelator so that minimize the distortion. This whitening
transformation is designed to optimally decorrelate the outputs of the
decorrelator prior to detection, and in that way compensate for the noise
enhancement of the decorrelator receiver.
When the signature vectors are linearly independent, it
decorrelate the outputs of the decorrelator (K<M). If the signature vectors
are linearly dependent, then the noise components in the outputs are linearly
dependent, i.e., they satisfy a deterministic linear relation (K=M). Thus, the
vector noise output of the decorrelator lies in a subspace with probability
one. The same condition can be related with coloured noise components.
The kalman filter is an estimator for linear quadratic Gaussian problem
estimating the instantaneous state of linear system perturbed by white noise
and coloured noise.
59
Figure 3.6 Probability of Error for Decorrelator Receiver (For linear Dependent and Independent vectors)
Figure 3.7 Probability of Error for Minimum Mean Square Error Receiver (For linear Dependent and Independent vectors)
60
Figure 3.8 Probability of Error for Orthogonal Multiuser Receiver (For linear Dependent and Independent vectors)
Figure 3.9 Probability of Error for Coloured Orthogonal Multiuser Receiver (For linear Dependent and Independent vectors)
61
SNR (dB)
Probability of Error for linearly Dependent vectors
Orthogonal Multiuser Receiver
MMSE Receiver
Decorrelator Receiver
Coloured Orthogonal Multiuser Receiver
Kalman Filter
Receiver
0 0 0 0 0 0 1 0.0005 0.145 0.052 0.005 0.069 2 0.0011 0.267 0.113 0.011 0.151 3 0.0018 0.265 0.184 0.018 0.246 4 0.0018 0.355 0.189 0.018 0.252 5 0.0026 0.452 0.260 0.026 0.346 6 0.0034 0.565 0.340 0.034 0.454 7 0.0043 0.643 0.431 0.043 0.575 8 0.0037 0.724 0.378 0.037 0.504 9 0.0046 0.856 0.468 0.046 0.624
10 0.0056 0.900 0.568 0.056 0.757
Figure 3.10 Probability of Error for Kalman Filter Receiver (For linear Dependent and Independent vectors)
Table 3.2 Comparison of different types of Receivers in terms of Probability of Error (Dependent)
62
In the case of OMU receiver, the error is very low for SNR
values between 0 dB to 10 dB compared with other receivers such as
decorrelating receiver, minimum mean square receiver, and Kalman
receiver. The colored OMU receiver achieved low probability of error for
SNR between 0 dB to 10 dB compared with other receivers such as
decorrelating receiver, minimum mean square receiver, Kalman receiver.
For decorrelator receiver with low SNR values ranging from 0
dB to 5 dB, the probability of error will be less than 0.5. The SNR values
ranging from 5 dB to 10 dB the probability of error will be greater than 0.5.
The probability of error can be calculated for both linearly independent and
dependent vectors.
SNR (dB)
Probability of Error for Linearly independent vectors
Orthogonal Multiuser Receiver
MMSE Receiver
Decorrelator Receiver
Coloured Orthogonal Multiuser Receiver
Kalman Filter
Receiver
0 0 0.1 0 0 0 1 0.0006 0.245 0.046 0.006 0.046 2 0.0015 0.267 0.102 0.015 0.102 3 0.0024 0.465 0.166 0.024 0.166 4 0.0025 0.505 0.170 0.025 0.170 5 0.0037 0.520 0.234 0.034 0.234 6 0.0045 0.650 0.307 0.045 0.307 7 0.0057 0.743 0.389 0.057 0.389 8 0.0050 0.824 0.341 0.050 0.341 9 0.0062 0.956 0.422 0.062 0.422 10 0.0075 0.934 0.512 0.075 0.512
Table 3.3 Comparison of different types of Receivers in terms of Probability of Error (Independent)
63
The corresponding curves for decorrelator receiver, minimum
mean squared error receiver and Kalman receiver is obtained for
comparison with OMU receiver shown in Figure 3.6 to Figure 3.10. The
OMU receiver performs similarly to minimum mean squared error receiver
at all SNR and better than decorrelator receiver and Kalman receiver.
Moreover OMU receiver performs slightly better than minimum mean
squared error receiver at high SNR (although the linear minimum mean
squared error receiver minimizes the MSE, it does not necessarily minimize
the probability of error, especially when the MAI is not approximately
Gaussian).
3.6 CONCLUSION
The multiuser receiver for CDMA channels, referred to as the
OMU receiver has been developed which relies on knowledge of only the
signature vectors to mitigate the effect of both MAI and additive noise.
First, the receiver can be interpreted as a decorrelator receiver followed by a
minimum mean squared error receiver that compensates for the noise
enhancement without reintroducing too much MAI. Second, OMU receiver
for both white Gaussian noise and coloured noise has been demonstrated
and it is equivalent to an MF receiver. The corresponding curves for the
decorrelator receiver, linear minimum mean squared error receiver, OMU
receiver for coloured noise and also to the nonstationary filter like Kalman
Filter receiver are plotted for comparisons. The OMU receiver achieved
minimum probability of error at all SNR (0 dB to 10 dB) and better than the
decorrelator receiver, minimum mean square error receiver and Kalman
Filter receivers.