The Robustness of Favorable Propagation in Massive MIMO to Location and Phase Errors

The impact of random errors (implementation inaccuracies) in element locations and beamforming phases on favorable propagation (FP) in massive multiple-input multiple-output (MIMO) line-of-sight (LOS) channels is studied. For arbitrary array geometry and under independent (possibly non-Gaussian) errors, the FP property is shown to hold for the perturbed array as long as it holds for the unperturbed one. This means that small errors do not have catastrophic impact on the FP, even for a large number of antennas. The negative impact of random errors is to slow down the convergence to the asymptotic value so that more antennas are needed under random errors to achieve the same low inter-user interference as without errors. For large but finite number of antennas, the distribution and an analytically-tractable approximation of the inter-user interference power are obtained. Practical design guidelines are given that quantify the accuracy level needed to make the impact of random errors negligible. The analytical results are validated via numerical simulations and are in agreement with measurement-based studies.