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.

翻译：虽然广为线性最小的平方误差(NLMMSE)接收器对于多投入-多输出(MIMO)无线系统来说是一个吸引多投入-多输出(MIMO)无线系统的选项,但对于其配置的显示信号到干涉+噪声比率(SINR)的详细统计理解仍然缺乏。为此,我们认为在与无C关系的RayLayle 淡化频道(QR)上安装了WLMMSE MIMS(QR)的直线性或准正反线(QR)信号的传输系统,并调查其SINR的统计特性,用于使用$Nt传输天线和$r美元接收的任意天线性天线配置。我们首先从SIMR(PDF)配置的配置的配置的显示显示显示显示感知性概率(PDFFS),对于具有任意的WMMSE(r) r r 和 $t=2, 3美元 。对于实践中,所有一般的支持,即改进值,我们利用瞬间生成的功能获得大约但关闭式的计算结果的计算结果,在一定的硬值中,其硬值中,在硬值中,在硬值中,在某种硬值中,其精度值中,其精确值的计算中,其直值中,在某种硬值中,其计算值中,其直值中,在某种直值中,其直值中,在某种直值中,在某种直值中,在某种直值中,在某种直值中,其计算值中,其直值中,以正值中,在某种硬值中,其直值的计算值的计算值的计算中,在某种直值的计算中,在某种直值中,则提供。