Structural Design of Non-Uniform Linear Arrays for Favorable Propagation in Massive MIMO

Favorable propagation (FP) for massive multiple-input multiple-output (MIMO) systems with uniform and non-uniform linear arrays is considered. A gap in the existing FP studies of uniform linear arrays is identified, which is related to the existence of grating lobes in the array pattern and which results in the FP condition being violated, even under distinct angles of arrival. A novel analysis and design of $\mathit{\text{non-uniform}}$ linear arrays are proposed to cancel grating lobes and to restore favorable propagation for $\mathit{\text{all}}$ distinct angles of arrival. This design is consistent with the popular hybrid beamforming paradigm and extends to multipath channels and arrays of directional elements.