Non-Asymptotic Analysis of Random Vector Channels

The analysis of large random vector channels, particularly multiple-input-multiple-output (MIMO) channels, has primarily been established in the asymptotic regime, due to the intractability of characterizing the exact distribution of the objective performance metrics. This paper advocates a non-asymptotic approach that often results in more refined estimates on the statistical uncertainty of various performance metrics. Specifically, we present a general template that characterizes various performance metrics in a narrow confidence interval rather than the asymptotic value, while ensuring that the metric of interest falls within the obtained interval with high probability. The effectiveness of our general framework is illustrated through three simple examples derived from it, including the MIMO channel capacity and power offset, the minimum mean squared estimation error for linear Gaussian processes, and the capacity loss under random sub-sampling. Our analysis is based on the pervasive concentration of spectral measure phenomenon, which arises in a variety of random matrix ensembles irrespective of the precise entry distributions.