Maximum-SNR transmit antenna selection with two receive antennas is polynomially solvable

The recent increased interest in massive multiple-input multiple-output systems, combined with the cost of the analog RF chains, necessitates the use of efficient antenna selection (AS) schemes. Capacity or SNR optimal AS has been considered to require an exhaustive search among all possible antenna subsets. In this work, we prove that the maximum-SNR transmit AS problem with two receive antennas is polynomially solvable and develop an algorithm that solves it with quartic complexity, independently of the number of selected antennas. Our method also applies to receive AS with two transmit antennas.