Closed-form performance analysis of linear MIMO receivers in general fading scenarios

TL;DR

This paper derives the first closed-form expressions for the SINR distributions of ZF and MMSE linear MIMO receivers across various fading scenarios, including correlated and scattering-rich channels.

Contribution

It provides novel closed-form formulas for the SINR distributions of linear MIMO receivers under general fading conditions, extending beyond the uncorrelated Rayleigh case.

Findings

Closed-form SINR pdfs for ZF and MMSE receivers derived.

Applicable to a wide range of fading models, including correlated channels.

Enhances understanding of MIMO performance in realistic wireless environments.

Abstract

Linear precoding and post-processing schemes are ubiquitous in wireless multi-input-multi-output (MIMO) settings, due to their reduced complexity with respect to optimal strategies. Despite their popularity, the performance analysis of linear MIMO receivers is mostly not available in closed form, apart for the canonical (uncorrelated Rayleigh fading) case, while for more general fading conditions only bounds are provided. This lack of results is motivated by the complex dependence of the output signal-to-interference and noise ratio (SINR) at each branch of the receiving filter on both the squared singular values as well as the (typically right) singular vectors of the channel matrix. While the explicit knowledge of the statistics of the SINR can be circumvented for some fading types in the analysis of the linear Minimum Mean-Squared Error (MMSE) receiver, this does not apply to the less complex and widely adopted Zero-Forcing (ZF) scheme. This work provides the first-to-date closed-form expression of the probability density function (pdf) of the output ZF and MMSE SINR, for a wide range of fading laws, encompassing, in particular, correlations and multiple scattering effects typical of practically relevant channel models.