Favorable Propagation with User Cluster Sharing

We examine the favorable propagation (FP) behavior of a massive multi-user multiple-input-multiple-output (MU-MIMO) system equipped with a uniform linear array (ULA), horizontal uniform rectangular array (HURA) or uniform circular array (UCA) using a ray-based channel model with user cluster sharing. We demonstrate FP for these systems and provide analytical expressions for the mean-squared distance (MSD) of the FP metric from its large-system limit for each of the aforementioned topologies. We use these results to examine the detrimental effects of user cluster sharing on FP behavior, and demonstrate the superior performance of the ULA as compared to the UCA and the HURA with equal inter-element spacing. Although cluster sharing has a negative impact on FP for finite arrays, we additionally examine the asymptotic rate of convergence to FP as a function of array size and show that this rate is unchanged with or without user cluster sharing.