Exact Performance Analysis of MIMO Zero Forcing Detection for Transmit Correlated Rician Rayleigh Fading

This paper reveals a previously-unknown infinite linear combination of Gamma distributions with simple coefficients for the symbol-detection signal-to-noise ratio (SNR) in multiple-input/multiple-output (MIMO) communications employing spatial multiplexing and zero-forcing detection (ZF), whereby the intended (detected) and interfering symbol streams experience correlated Rician and Rayleigh fading, respectively. Our derivation of the exact moment generating function (m.g.f.) of the ZF SNR for the Rician-fading stream bypasses the noncentral-Wishart distribution, whose intractability has required previously approximation with a central-Wishart distribution of equal mean. We also express exactly the ZF SNR moments and probability density function, as well as the ZF average error probability, outage probability, and ergodic capacity. Numerical results from analysis and Monte Carlo simulations confirm the accuracy of our new expressions and reveal that the symbol-detection performance for the Rician-fading stream is: 1) unaffected by the ‘direction’ of the channel-vector mean, 2) unaffected by transmit-correlation, at realistic K values (unlike for Rayleigh–Rayleigh fading), 3) seriously degraded by Rayleigh-fading interference even for large K, which is of concern in heterogeneous networks.