Optimal Quantization is a concept in information theory and signal processing that involves the process of mapping a continuous set of values (analog data) to a discrete set of levels (quantized values) in a way that minimizes the overall distortion or error. The goal is to represent the original data using a reduced number of discrete values while preserving its essential characteristics.


On Optimal Multi-user Beam Alignment in Millimeter Wave Wireless Systems

Directional transmission patterns (a.k.a. narrow beams) are the key to wireless communications in millimeter wave (mmWave) frequency bands which suffer from high path loss and severe shadowing. In addition, the propagation channel in mmWave frequencies incorporates only a few number of spatial clusters requiring a procedure to align the corresponding narrow beams with the angle of departure (AoD) of the channel clusters. The objective of this procedure, called beam alignment (BA) is to increase the beamforming gain for subsequent data communication. Several prior studies consider optimizing BA procedure to achieve various objectives such as reducing the BA overhead, increasing throughput, and reducing power consumption. While these studies mostly provide optimized BA schemes for scenarios with a single active user, there are often multiple active users in practical networks. Consequently, it is more efficient in terms of BA overhead and delay to design multi-user BA schemes which can perform beam management for multiple users collectively. This paper considers a class of multi-user BA schemes where the base station performs a one shot scan of the angular domain to simultaneously localize multiple users. The objective is to minimize the average of expected width of remaining uncertainty regions (UR) on the AoDs after receiving users’ feedbacks. Fundamental bounds on the optimal performance are analyzed using information theoretic tools. Furthermore, a BA optimization problem is formulated and a practical BA scheme, which provides significant gains compared to the beam sweeping used in 5G standard, is proposed.