Noise impact factor in the performance of interference-limited diversity combining antenna arrays

There is an abundant literature on the fully-analytical performance assessment of diversity combining arrays in the presence of interference, where the combining method is anything from scanning and selection diversity through optimum (MMSE) combining. However, in most of the literature and for the sake of analytic tractability, the noise is often assumed to be zero (high SNR assumption) in some portion of the derivation. The practical justification is that if the SNR is high enough and the system is interference-limited, then the impact of noise is negligible. This paper considers the case of a diversity combiner applying the zero-forcing criterion and operating under overloaded conditions, i.e. there are more impinging signals (desired plus interferers) than antenna elements. In this context, it is shown analytically that the output SINR can be factored into two components, namely the ideal SINR (whose distribution is already known) and the noise impact factor, whose distribution is derived herein. Furthermore, it is shown that the impact of the noise can be surprisingly significant in terms of BER in such scenarios.