The Statistical Mechanics of Multi-antenna communications: Replicas and Correlations∗

The use of multi-antenna arrays has been predicted to provide substantial throughput gains for wireless communication systems. However, these predictions have to be assessed in realistic situations, such as correlated channels and in the presence of interference. In this review, we show results obtained using methods borrowed from statistical physics of random media for the average and the variance of the distribution of the mutual information of multi-antenna systems with arbitrary correlations and interferers. Even though the methods are asymptotic in the sense they are valid in the limit of large antenna numbers, the results are extremely accurate results even for small arrays. We also optimize over the input signal covariance with channel covariance feedback and calculate closed-loop capacities. This method provides a simple tool to analyze the statistics of throughput for arrays of any size.