Optimal Designs of Uniform Linear Arrays for Multi-User Massive MIMO

Multi-user massive MIMO (mMIMO) systems with uniform linear arrays (ULA) are considered in the non-asymptotic regime. To reduce the complexity of implementation, ULA's design is optimized to minimize the number of antennas subject to signal-to-noise plus interference (SINR) constraints. Both per-user and sum interference constraints are considered. While the resulting optimization problems are not convex (so that the standard tools of convex optimization cannot be used), a novel analytical approach is proposed and a number of globally-optimal closed-form solutions/designs are obtained. They reveal the scalings of the optimal number of antennas with the target SINR, the total number of users and their angular separation. The proposed designs are robust, since they do not require a precise knowledge of directions of arrival of interfering users, and allow for distributed implementation.