Maximum-SNR Antenna Selection Among a Large Number of Transmit Antennas

The recent increased interest in large-scale multiple-input multiple-output systems, combined with the cost of analog radio-frequency (RF) chains, necessitates the use of efficient antenna selection (AS) schemes. Capacity or signal-to-noise ratio (SNR) optimal AS has been considered to require an exhaustive search among all possible antenna subsets. In this work, we prove that, under a total power constraint on the beamformer, the maximum-SNR joint beamforming transmit AS problem with two receive antennas and an arbitrary number of transmit antennas is polynomially solvable and develop an algorithm that solves it with quartic complexity, independently of the number of selected antennas. The algorithm identifies with complexity a cubic-size collection of antenna subsets that contains the one that maximizes the post-processing receiver SNR. From a different perspective, for any given two-row complex matrix, our algorithm computes with quartic complexity its two-row submatrix with the maximum principal singular value, for any number of selected columns. In addition, our method also applies to receive AS with two transmit antennas. Finally, if we enforce a per-antenna-element power constraint on the beamformer (i.e., constant-envelope transmission), then the set of transmit AS subsets that contains the optimal one is the same as in the total power constraint case. Therefore, our algorithm offers a practical solution to the maximum-SNR antenna selection problem when either the transmitter or the receiver consists of a large number of antennas.