On the Distribution of SINR for Widely Linear MMSE MIMO Systems With Rectilinear or Quasi-Rectilinear Signals
On the Distribution of SINR for Widely Linear MMSE MIMO Systems With Rectilinear or Quasi-Rectilinear Signals
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DOI：
10.1109/tvt.2021.3132377
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发表时间：
2020-11
影响因子：
6.8
通讯作者：
Wei Deng;Yili Xia;Zhe Li;Wenjiang Pei
中科院分区：
文献类型：
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作者：
Wei Deng;Yili Xia;Zhe Li;Wenjiang Pei
虽然宽线性最小均方误差（WLMMSE）接收机已经成为多输入多输出（MIMO）无线系统的一个有吸引力的选择，但是仍然缺乏对其姿态检测信号与干扰加噪声比（SINR）的详细统计理解。为此，我们考虑了一个WLMMSE MIMO传输系统的直线或准直线（QR）信号在不相关的瑞利衰落信道和调查的统计特性的信干噪比为任意天线配置与$N_t$发送天线和$N_r$接收的。对于任意N_r和N_t=2，3$的WLMMSE MIMO系统，我们首先推导出了基于第二类合流超几何函数的SINR的解析概率密度函数（PDF）。对于实践中更一般的情况，即，$N_t>3$时，利用矩母函数在适当的条件下得到了一个近似的封闭形式的概率密度函数，正如所料，随着$2N_r-N_t$的增加，它更像高斯分布。因此，推导的PDF能够提供关键的见解WLMMSE MIMO接收机的中断概率，符号错误率，和分集增益，都在封闭的形式。特别地，它的分集增益和相对于传统LMMSE的增益改进分别被明确地量化为$N_r-（N_t-1）/2$和$（N_t-1）/2$。最后，蒙特卡洛模拟支持的分析。
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.