Interference Constrained Beam Alignment for Time-Varying Channels via Kernelized Bandits

TL;DR

This paper introduces a kernelized bandit algorithm for beam alignment in mmWave channels, effectively handling time-varying environments and interference constraints without prior channel knowledge.

Contribution

It formulates beam alignment as a non-stationary online learning problem and proposes a constrained kernelized bandit algorithm with theoretical guarantees.

Findings

The algorithm achieves sublinear regret and constraint violation bounds.

It adapts effectively to time-varying channels without prior knowledge.

Simulations demonstrate its practical effectiveness.

Abstract

To fully utilize the abundant spectrum resources in millimeter wave (mmWave), Beam Alignment (BA) is necessary for large antenna arrays to achieve large array gains. In practical dynamic wireless environments, channel modeling is challenging due to time-varying and multipath effects. In this paper, we formulate the beam alignment problem as a non-stationary online learning problem with the objective to maximize the received signal strength under interference constraint. In particular, we employ the non-stationary kernelized bandit to leverage the correlation among beams and model the complex beamforming and multipath channel functions. Furthermore, to mitigate interference to other user equipment, we leverage the primal-dual method to design a constrained UCB-type kernelized bandit algorithm. Our theoretical analysis indicates that the proposed algorithm can adaptively adjust the beam in time-varying environments, such that both the cumulative regret of the received signal and constraint violations have sublinear bounds with respect to time. This result is of independent interest for applications such as adaptive pricing and news ranking. In addition, the algorithm assumes the channel is a black-box function and does not require any prior knowledge for dynamic channel modeling, and thus is applicable in a variety of scenarios. We further show that if the information about the channel variation is known, the algorithm will have better theoretical guarantees and performance. Finally, we conduct simulations to highlight the effectiveness of the proposed algorithm.