Exact MIMO Zero-Forcing Detection Analysis for Transmit-Correlated Rician Fading

TL;DR

This paper provides an exact analysis of MIMO zero-forcing detection performance under Rician and Rayleigh fading with transmit correlation, deriving new series expressions for key performance metrics.

Contribution

It introduces a novel exact analysis method for ZF SNR distribution considering Rician fading and correlation, overcoming previous approximation limitations.

Findings

Exact ZF SNR distribution derived for Rician-Rayleigh fading.

Gamma distribution result for Rayleigh-Rician fading.

New series expressions for error probability, outage, and capacity.

Abstract

We analyze the performance of multiple input/multiple output (MIMO) communications systems employing spatial multiplexing and zero-forcing detection (ZF). The distribution of the ZF signal-to-noise ratio (SNR) is characterized when either the intended stream or interfering streams experience Rician fading, and when the fading may be correlated on the transmit side. Previously, exact ZF analysis based on a well-known SNR expression has been hindered by the noncentrality of the Wishart distribution involved. In addition, approximation with a central-Wishart distribution has not proved consistently accurate. In contrast, the following exact ZF study proceeds from a lesser-known SNR expression that separates the intended and interfering channel-gain vectors. By first conditioning on, and then averaging over the interference, the ZF SNR distribution for Rician-Rayleigh fading is shown to be an infinite linear combination of gamma distributions. On the other hand, for Rayleigh-Rician fading, the ZF SNR is shown to be gamma-distributed. Based on the SNR distribution, we derive new series expressions for the ZF average error probability, outage probability, and ergodic capacity. Numerical results confirm the accuracy of our new expressions, and reveal effects of interference and channel statistics on performance.