Dictionary Learning for Phase-Less Beam Alignment Codebook Design in Multipath Channels

Abstract

Large antenna arrays are critical for reliability and high data rates in wireless networks at millimeter-wave and sub-terahertz bands. While traditional methods for initial beam alignment for analog phased arrays scale beam alignment overhead linearly with the array size, compressive sensing (CS) and machine learning (ML) algorithms can scale logarithmically. CS and ML methods typically utilize pseudo-random or heuristic beam designs as compressive codebooks. However, these codebooks may not be optimal for scenarios with uncertain array impairments or multipath, particularly when measurements are phase-less or power-based. In this work, we propose a novel dictionary learning method to design codebooks for phase-less beam alignment given multipath and unknown impairment statistics. This codebook learning algorithm uses an alternating optimization with block coordinate descent to update the codebooks and Monte Carlo trials over multipath and impairments to incorporate a-priori knowledge of the hardware and environment. Additionally, we discuss engineering considerations for the codebook design algorithm, including a comparison of three proposed loss functions and three proposed beam alignment algorithms used for codebook learning. As one of the three beam alignment methods, we propose transfer learning for ML-based beam alignment to reduce the training time of both the ML model and codebook learning. We demonstrate that codebook learning and our ML-based beam alignment algorithms can significantly reduce the beam alignment overhead in terms of number of measurements required.