Fundamental Asymptotic Behavior of (Two-User) Distributed Massive MIMO

This paper considers the uplink of a distributed Massive MIMO network where $N$ base stations (BSs), each equipped with $M$ antennas, receive data from $K=2$ users. We study the asymptotic spectral efficiency (as $M\to \infty$) with spatial correlated channels, pilot contamination, and different degrees of channel state information (CSI) and statistical knowledge at the BSs. By considering a two-user setup, we can simply derive fundamental asymptotic behaviors and provide novel insights into the structure of the optimal combining schemes. In line with [1], when global CSI is available at all BSs, the optimal minimum-mean squared error combining has an unbounded capacity as $M\to \infty$, if the global channel covariance matrices of the users are asymptotically linearly independent. This result is instrumental to derive a suboptimal combining scheme that provides unbounded capacity as $M\to \infty$ using only local CSI and global channel statistics. The latter scheme is shown to outperform a generalized matched filter scheme, which also achieves asymptotic unbounded capacity by using only local CSI and global channel statistics, but is derived following [2] on the basis of a more conservative capacity bound.