Performance of Robust Multiuser Detectors in Stable Noise
We consider the performance of the robust multiuser detection
techniques discussed in previous sections in symmetric stable noise. In
particular, we consider the performance of the linear decorrelator, the
maximum-likelihood decorrelator, and the Huber decorrelator, as well as their
improved versions based on local likelihood search. First, the y functions for these three decorrelative detectors are
plotted in Fig. 4.17. For the Huber
decorrelator, the variance s2, the original definition of yH (·) in (4.112), is replaced by the
dispersion parameter g.
Note that since the pdf of the symmetric stable distribution does not have a
closed form, we have to resort to a numerical method to compute yML(x) given by (4.108). In particular, we can
use discrete Fourier transform (DFT) to calculate samples of f(x) and f'(x), as follows.
Recall that the characteristic function is given by
Equation 4.181
The pdf and its derivative are related to the characteristic
function through
Equation 4.182
Equation 4.183
Hence by sampling the characteristic function f(t) and then perform (inverse) DFT, we can get samples
of f(t) and f'(t), which in turns
give yML(x).
First we demonstrate the performance degradation of the linear
decorrelator in symmetric stable noise. The BER performance of the linear
decorrelator in several symmetric stable noise channels is depicted in Fig. 4.18. Here the SNR is defined as 
.
It is seen that the smaller is a (i.e., the more impulsive is the noise), the more
severe is the performance degradation incurred by the linear decorrelator. We
next demonstrate the performance gain achieved by the Huber decorrelator. Figure 4.19 shows the BER performance of the
Huber decorrelator. It is seen that as the noise becomes more impulsive (i.e.,
a becomes smaller), the
Huber deccorrelator offers more performance improvement over the linear
decorrelator. Finally, we depict the BER performance of the linear decorrelator,
the Huber decorrelator, and the ML decorrelator, as well as their their improved
versions based on the slowest-descent search, in Fig. 4.20. It is seen that the performance of the
improved/unimproved linear decorrelator is substantially worse than that of the
Huber decorrelator and the ML decorrelator. The improved Huber decorrelator
performs more closely to the ML decorrelator.
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