We have studied the performance of the adaptive receiver for cases where the noise and fading coefficient estimates obtained by the receiver are different from the true noise and fading parameters. The main result is that the detector is robust to impulses as long as the estimated noise parameters correspond to a pdf that is at least slightly impulsive. In this case large observations are limited, as described in the previous subsections. Note that Gaussian noise is a special case of the Gaussian mixture pdf, so our receiver is capable of adapting to Gaussian noise and performing the linear processing that is optimum. Preliminary simulations have also been performed to investigate other types of mismatch between the true noise and the noise model in the receiver. For example, when the number of mixture terms L is mismatched, the EM algorithm still yields reasonable estimates and the detector performance is only slightly degraded.
The mixture model we have considered is known to be useful for representing a large number of noise pdfs which occur in practical situations [18]. The relationship to the GMBFN with its universal approximation capabilities further justifies using the mixture model to characterize unknown noise.
We have investigated mismatch cases in which the non-Gaussian noise is outside the mixture class. The results have been quite good. For noise with in-phase and quadrature components that are circularly symmetric with Cauchy marginal pdfs [19], the simulated BER performance results are presented in Table 1. The optimum detector is a likelihood ratio test using the true noise pdf, and the other detectors in Table 1 are the maximal ratio combiner and our new adaptive diversity combiner using L=2, 3, and 4 terms in the Gaussian mixture pdf to model the noise. The EM algorithm is used to estimate the mixture pdf parameters from 100 training symbols for each value of L. For N=1 antenna, all methods perform poorly due to fading. However, the adaptive receiver with L=3 and L=4 performs very close to the optimum receiver, indicating that very few terms in the Gaussian mixture pdf provide a good approximation to the optimum detector.
Table 1:
BER performance of optimum, maximum ratio, and
adaptive combiner in narrowband
noise with Cauchy in-phase and quadrature components.
The adaptive combiner results are presented for the cases of L=2,3,
and 4 terms in the Gaussian mixture pdf.