On Robust and Efficient Design of Optimally-Weighted Linear Arrays for mMIMO

Robust and efficient design of uniform linear arrays (ULA) with non-uniform weights for multi-user massive MIMO systems is formulated as a constrained min-max optimization problem to minimize the number of antennas while meeting performance target. Chebyshev beamforming weights are shown to be optimal for this problem in line-of-sight (LoS) channels when precise channel state information (CSI) of interfering users is not available. Based on this, explicit closed-form solutions are obtained for sum as well as per-user interference constraints, which reveal the scaling of the minimal number of antennas with target signal-to-interference plus noise ratio and the number of interfering users. Comparison with widely-used uniformweighting arrays highlights the superior scalability and efficiency of the proposed Chebyshev-based design, particularly in complex interference environments.