Polynomial Solvers for mmWave Radio Beamforming

Millimeter (mmWave) beamforming is an integral component of fifth-generation (5G) and beyond radio commu-nications. 5G beamforming involves the initial beam selection procedure using a codebook with multiple radio beam directions. Conventional codebook-based alignment schemes involve exhaustive sweeping over the predefined beam directions, the number of which increases significantly with large numbers of antennas resulting in undesirable latency and communications signal overhead. In this paper, we propose a novel algebraic-based codebook using Gröbner basis polynomial solvers to reduce the signal overhead during beam alignment. We also analyze the complexity-performance tradeoff between the proposed algebraic-based codebook and the exhaustive-based beam alignment across different monomial thresholds, multiple antenna configurations and radio contextual location information. Our results show that the proposed approach reduces the beam-search overhead at an average complexity reduction ratio of 73.95% with a performance tradeoff error of 32.25%.