Asymptotic Performance of MMSE Receivers for Large Systems Using Random Matrix Theory

Random matrix theory is used to derive the limit and asymptotic distribution of signal-to-interference-plus-noise ratio (SIR) for a class of suboptimal minimum mean-square-error (MMSE) receivers applied to large random systems with unequal-power users. We prove that the limiting SIR converges to a deterministic value when K and N go to infinity with lim K/N = y being a positive constant, where K is the number of users and N is the number of degrees of freedom. We also prove that the SIR of each particular user is asymptotically Gaussian for large N and derive the closed-form expressions of the variance for the SIR variable under real-spreading and complex-spreading channel environments. It is revealed that for a given (K,N) pair, under certain mild conditions, the variance of the SIR for complex-spreading channels is half of that for the corresponding real-spreading channels. Since the suboptimal MMSE receiver becomes optimal for the case when the users are equally powered, our results show that the conjecture made by Tse and Zeitouni for the complex-spreading case is not affirmative. We also derive the asymptotic distribution for SIR in decibels which provides better description when N is small. Numerical results and computer simulations are provided to evaluate the accuracy of various limiting and asymptotic results obtained in this paper.