Robustness of Massive MIMO to Location and Phase Errors

The impact of random errors in element locations and beamforming phases on the performance of massive multipleinput multiple-output (MIMO) systems and their ability to cancel inter-user interference (IUI) are studied. For an arbitrary array geometry, user orthogonality, also known as “favorable propagation” (FP), is shown to hold asymptotically for the perturbed array as long as it holds for the unperturbed one, for independent (possibly non-Gaussian) errors. This means that small errors do not have catastrophic impact on the FP, even for a large number of antennas, and IUI can be reduced to any desired level. 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 IUI as without errors. Practical design guidelines are given as to what implementation accuracy is needed to make the impact of random errors negligible and a closed-form estimate of IUI under random errors is presented. The analytical results are validated via numerical simulations and are in agreement with measurement-based studies.