On the Distribution of SINR for Widely Linear MMSE MIMO Systems with Rectilinear or Quasi-Rectilinear Signals

TL;DR

This paper derives the statistical distribution of SINR for WLMMSE MIMO systems with rectilinear signals, providing insights into performance metrics like outage probability and diversity gain, and compares it to conventional LMMSE.

Contribution

It offers the first analytical PDF of SINR for WLMMSE MIMO systems with arbitrary antennas, including approximate forms for larger systems, and quantifies the diversity gain improvement.

Findings

Derived exact SINR PDF for small antenna systems.

Provided approximate SINR PDF for larger systems.

Quantified diversity gain and improvement over LMMSE.

Abstract

Although the widely linear least mean square error (WLMMSE) receiver has been an appealing option for multiple-input-multiple-output (MIMO) wireless systems, a statistical understanding on its pose-detection signal-to-interference-plus-noise ratio (SINR) in detail is still missing. To this end, we consider a WLMMSE MIMO transmission system with rectilinear or quasi-rectilinear (QR) signals over the uncorrelated Rayleigh fading channel and investigate the statistical properties of its SINR for an arbitrary antenna configuration with $N_t$ transmit antennas and $N_r$ receive ones. We first derive an analytic probability density function (PDF) of the SINR in terms of the confluent hypergeometric function of the second kind, for WLMMSE MIMO systems with an arbitrary $N_r$ and $N_t=2, 3$. For a more general case in practice, i.e., $N_t>3$, we resort to the moment generating function to obtain an approximate but closed form PDF under some mild conditions, which, as expected, is more Gaussian-like as $2N_r-N_t$ increases. The so-derived PDFs are able to provide key insights into the WLMMSE MIMO receiver in terms of the outage probability, the symbol error rate, and the diversity gain, all presented in closed form. In particular, its diversity gain and the gain improvement over the conventional LMMSE one are explicitly quantified as $N_r-(N_t-1)/2$ and $(N_t-1)/2$, respectively. Finally, Monte Carlo simulations support the analysis.