Backing off from Infinity: Tight Performance Bounds for Large 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 exposes a non-asymptotic analysis framework that allows the characterization of various system performance metrics to within a narrow confidence interval with high probability, provided that these metrics can be expressed as a separable function of matrix singular values. The effectiveness of our framework is illustrated through three canonical examples derived from it, including the capacity and power offset of random MIMO channels, the minimum mean squared estimation in Gaussian MIMO channels, and the channel capacity loss under random sub-sampling. Our analysis is based on the concentration of spectral measure phenomenon, which arises in a variety of random matrix ensembles irrespective of the precise entry distributions.