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

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 WLMMSE MIMO transmission system with rectilinear or quasi-rectilinear (QR) signals over uncorrelated Rayleigh fading channel and investigate properties of SINR arbitrary antenna configuration $N_t$ transmit antennas notation="LaTeX">$N_r$ receive ones. We first derive analytic probability density function (PDF) terms confluent hypergeometric second kind, systems notation="LaTeX">$N_t=2, 3$ . For more general case practice, i.e., notation="LaTeX">$N_t>3$ , resort to moment generating obtain approximate but closed form PDF under some mild conditions, which, as expected, Gaussian-like notation="LaTeX">$2N_r-N_t$ increases. The so-derived PDFs are able provide key insights into outage probability, symbol rate, diversity gain, all presented form. In particular, gain improvement conventional LMMSE one explicitly quantified notation="LaTeX">$N_r-(N_t-1)/2$ notation="LaTeX">$(N_t-1)/2$ respectively. Finally, Monte Carlo simulations support analysis.