Diversity Combining over Rayleigh Fading Channels with Symmetric Alpha-Stable Noise

This paper addresses the bit error rate performance of diversity combining schemes for a single-user communication system operating over Rayleigh flat fading channels subject to impulsive alpha-stable noise, which is known to arise due to network interference from a Poisson field of interference sources. Under this setting, a theoretical benchmark receiver is analyzed, the maximum possible diversity order attainable is derived to be Lα/2, where L is the number of antennas and α is the characteristic exponent of the noise. Moreover, trade-offs between the diversity gain and the array gain have been identified. The conventional linear matched filter receiver (also known as maximum ratio combining in the Gaussian case) has been shown to have a diversity order of α/2, thereby not benefiting from spatial diversity. Closed form expressions for the diversity gain and array gain of post-detection combining have been derived. As an improvement to conventional combining schemes, the optimum maximum likelihood detector is derived. A simpler high SNR approximation of the detector is shown to not depend on the noise parameters, and is compared to the generalized Cauchy detector under stable noise. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of the detectors.