Convergence analysis of performance-measure expressions for MIMO ZF under Rician fading

The performance of multiple-input/multiple-output (MIMO) communications systems employing spatial multiplexing and zero-forcing detection (ZF) has yet to be analyzed for several cases of practically-relevant Rician fading. For the special case of Rician-Rayleigh fading, we have recently derived a set of expressions for important MIMO ZF performance measures. They were obtained from the moment generating function of the signal-to-noise ratio (SNR) expressed in terms of the confluent hypergeometric function, i.e., an infinite-series. Herein, the prove the convergence of the ensuing infinite-series expressions obtained for the SNR probability density function, as well as for the ZF outage probability, average error probability, and ergodic capacity. For the ergodic-capacity infinite-series, we describe a computation method and discuss its numerical instability issues.