An Empirical Lower Bound on Singular Value Ratios for MIMO LOS Links

We investigate ratios of singular values of wireless multiple input multiple output (MIMO) channel matrices. Under certain practically feasible assumptions, we can find expressions that serve as a lower bound for these singular value ratios (SVRs) for the line of sight (LOS) path. The computation of the lower bounds only requires knowledge of the distance between transmitter and receiver and a summary statistic of the size of the arrays. We empirically show the validity of these lower bounds for general antenna array configurations with simulations and measurements. A possible use case for SVRs and their lower bounds is identifying the LOS path in a channel impulse response, which is a problem in localization.