Matrix Factorization for Blind Beam Alignment in Massive mmWave MIMO

This paper proposes a new approach for Machine Learning (ML)-based beam alignment, for a single radiofrequency chain millimeter-wave (mmW) MIMO transmitter (Tx) and receiver (Rx), with massive antennas. Assuming (massive) codebooks of possible beams at Tx and Rx, we propose to sound a very small subset of beams from the Tx/Rx codebooks. We then use the SNR of the (subset of) sounded beams, to learn two ML models: Matrix Factorization (MF), and Nonnegative MF. Furthermore, we derive the update eqts for two optimization methods to solve the MF/Nonnegative MF optimization problems. While the first optimization method is shown to converge (and exhibits medium complexity), the second optimization method has negligible complexity (but lacks a convergence guarantee). Our extensive numerical results suggest that by sounding just 10% of the beams from the (large) Tx and Rx codebooks, MF and Nonnegative MF are able to predict the SNR of the remaining beams, with extremely high accuracy. This observation holds as the Tx/Rx codebook sizes vary from 64x64 to 1024x1024