CHAPTER 2 ITERATIVE INTERFERENCE CANCELLATION RECEIVERS Single user detectors are not optimal for CDMA because they process other user interference as unstructured channel noise. Better CDMA receivers can be designed if the specific structure of multiple access interference (MAI) is fully exploited. To realize this, novel receiver structures have been proposed over the years that take advantage of the knowledge of MA1 signal parameters [144-1481. Such receivers termed as multi-user receivers are more complex than conventional ones because of their capability of using MA1 signal information to help recover the desired user. A general multi-user detector depicted in Figure 2.1, is composed of an initial correlation stage followed by a set of additional stages where a multi-user detection algorithm is implemented. It is shown by Verdu that the set of correlator outputs for each user forms a set of sufficient statistics which, if processed properly, can lead to an optimal multi-user detection. The most commonly analyzed multi-user detectors are presented in this section. 2.1.1 Optimal Detector The optimal structure shown in Figure 2.2 consists of a bank of matched filters providing first order user amplitude estimates to a Viterbi decision algorithm. Verdu [I491 has shown that the optimal structure afforded significant performance improvement over the conventional structures and is insensitive to the near-far problem. The extraordinary performance enhancements however come at a price. The optimal receiver assumes apriori knowledge of the received signal amplitudes as well as delays; in practice, such ideals are usually not attainable. In addition to that the use of Viterbi decision algorithm makes the receiver complex and more burdensome.
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CHAPTER 2
ITERATIVE INTERFERENCE CANCELLATION RECEIVERS
Single user detectors are not optimal for CDMA because they process other
user interference as unstructured channel noise. Better CDMA receivers can be
designed if the specific structure of multiple access interference (MAI) is fully
exploited. To realize this, novel receiver structures have been proposed over the years
that take advantage of the knowledge of MA1 signal parameters [144-1481. Such
receivers termed as multi-user receivers are more complex than conventional ones
because of their capability of using MA1 signal information to help recover the
desired user. A general multi-user detector depicted in Figure 2.1, is composed of an
initial correlation stage followed by a set of additional stages where a multi-user
detection algorithm is implemented. It is shown by Verdu that the set of correlator
outputs for each user forms a set of sufficient statistics which, if processed properly,
can lead to an optimal multi-user detection. The most commonly analyzed multi-user
detectors are presented in this section.
2.1.1 Optimal Detector
The optimal structure shown in Figure 2.2 consists of a bank of matched filters
providing first order user amplitude estimates to a Viterbi decision algorithm. Verdu
[I491 has shown that the optimal structure afforded significant performance
improvement over the conventional structures and is insensitive to the near-far
problem. The extraordinary performance enhancements however come at a price. The
optimal receiver assumes apriori knowledge of the received signal amplitudes as well
as delays; in practice, such ideals are usually not attainable. In addition to that the use
of Viterbi decision algorithm makes the receiver complex and more burdensome.
Fig. 2.1 General multi user receiver structure
f 3 Zl
Fig33 BPSK based optlmrl CDMA reeeiver
+
-+ I I I
I
: I I I
---*
/
L 1
Further processing/ Multiuser detection algorithm
' Correlator ' 21
\ J
First stage Processing/ Correlation
I I I
; ; ;
!
----+ f \
b
2 2
+ I I I I I I I I I I I I
zk b
user 1 - b,
r(t) - Viterbi Decision Algorithm
\ J
I, - b2 ; I I I I I I I I - 4
i J
' orr relator ' ' 2
+ L 1
I I I I I I I
z, + -----b UserK
user2 b '
The Viterbi decision algorithm performs maximal likelihood sequence
estimation over the entire sequence of received message bits, thereby decoding the
whole message sequence in a trellis with 2' states. The computational complexity per
bit decision then becomes exponential in the number of users, clearly rendering the
optimal receiver impractical for implementation. Due to its prohibitively expensive
complexity, the role of the optimal receiver has bem relegated to that of a benchmark
against which sub-optimal CDMA detectors exhibiting more reasonable
computational complexity are compared. Some important sub-optimal multi-user
receivers are discwed here.
2.1.2 Decorrelator
The Decorrelator [150-1521 is a linear multi-- detector with K' as upper
bound on complexity. It functions by applying a linear transformation to the set of
matched-filter outputs obtained from the first stage. As its name implies, the receiver
seeks to undo the various inter-user correlations so as to isolate users from one
another. This decorrelation attempt is canied out by computing PN code waveform
cross correlation values and storing these in a k x k matrix, and multiplying the
inverse of this matrix by the vector of matched-filter outputs from the first stage. The
decorrelator does not require knowledge of signal amplitudes and is completely
insensitive to the near-far effect. Its k2 complexity stems from the k x k matrix storage
requirement; and while not exponential, such complexity is formidable nonetheless.
This matrix is time varying as users come on and drop off of the system, thereby
making updates on such a large matrix expensive. Further, this correlation matrix
needs to be inverted, bringing about the issue of singularity. The decorrelator relies
upon accurate PN code correlation values, and if the inverse correlation matrix
becomes unstable or undefined even, then the detector ceases to function adequately.
Of concern as well is a noise enhancement produced by the decorrelation operation,
rendering decision statistics noisier.
In general, the decorrelator provides substantial performance and capacity
gains over the conventional receiver, however, it has many drawbacks and hence it is
not widely used.
2.1.3 Mldmum Mean Square Error Detector
The MMSE detector [ I S ] , like the decornlator, operates by applying a linear
transformation to the set of first stage matched-filter outputs. It seeks to minimize the
averaged square error between actual data and the sot? outputs from the first stage. In
this case, linear transformation TR=R" used in de-cornlator is replaced by
( T R = R + N ~ ~ ~ Y ' . The performance of MMSE approaches that of de-cornlator as the
noise level drops to zero i.e. No+O, but as No increases, the performance deteriorates
to that of conventional receiver. At low Ed No MMSE receiver outperfoms the de-
correlator while at high E d , , the de-correlator's performance approaches to that of a
MMSE receiver. MMSE receiver rectifies the decorrelator's shortcoming of
enhancing noise, but at the cost of requiring knowledge of signal amplitudes. Even
though near far resistance of MMSE is slightly better than that of decorrelator, both
MMSE and decorrelator has the same computational complexity due to the necessity
of computing the inverse of a matrix. Owing to the complexity of these suboptimal
detectors researchers concentrated on the less complex linear interference cancellation
receivers.
2.2 INTERFERENCE CANCELLATION RECEIVERS
Interference cancellation has received a great deal of attention in the literature
and the premier objective of this thesis is to design a Hybrid Interference Cancellation
scheme. Interference cancellation detectors seek to remove interference by actually
subtracting estimates of interfering signals from the received signal. A general
interference cancellation receiver is depicted in Figure 2.3. It comprises of an initial
stage of matched-filters, like the other multi-user receivers, followed by stages of
interference cancellation. Interference cancellation receivers typically come in two
forms: parallel and successive. In parallel interference cancellation, all interfering
users are cancelled (subtracted) concurrently (in parallel) from the received signal. In
the successive approach proposed by Patel and Holtzman [lo], users are cancelled
serially in the descending order of estimated received power, from strongest to
weakest. These two interference cancellation receivers are completely analyzed in the
next section based on which the hybrid interference cancellation receiver is designed.
Fig.2.3 BPSK based interference cancellation CDMA receiver