两个独立复高斯随机变量乘积的相位精确分布

Exact phase distribution for the product of two independent complex Gaussian random variables

摘要:

针对两个高斯随机变量相乘经常出现在雷达和通信系统信号处理中的情况,研究了两个独立的具有任意均值和方差的复高斯随机变量乘积的相位分布。将该相位的概率密度函数表达为一个包含Kummer函数的无穷级数,分析了该概率密度函数的收敛性及收敛速度。利用所得结果分析信道状态信息不完美情况下单天线多进制相移键控通信系统的性能,推导了该系统的符号错误率,并通过数值实验对所得结果进行了验证。

Abstract:

In view of fact that the product of two Gaussian random variables appears frequently in radar and communication signal processing systems, the phase distribution for the product of two independent complex Gaussian random variables with arbitrary means and variances was investigated. The probability density function (PDF) of the phase was determined in terms of an infinite summation of Kummer functions, and the convergence and convergence rate of the PDF were studied. The derived PDF was used to analyze the performance of a single-antenna M-ary phase-shift-keying(MPSK) communication system with imperfect channel state information. The resulting symbol error probability (SEP) was derived, and finally the derived expressions were verified through numerical experiments.