Fast Fractional Programming for Multi-Cell Integrated Sensing and Communications

TL;DR

This paper introduces a fast fractional programming algorithm for multi-cell integrated sensing and communications that avoids costly matrix inversions, enabling efficient beamforming with massive antennas.

Contribution

We develop a novel FP-based beamforming method that eliminates large matrix inversions and accelerates convergence using Nesterov's extrapolation.

Findings

The proposed algorithm significantly reduces computational complexity.

It achieves faster convergence compared to traditional methods.

The method effectively balances data rate and sensing information.

Abstract

This paper concerns the coordinate multi-cell beamforming design for integrated sensing and communications (ISAC). In particular, we assume that each base station (BS) has massive antennas. The optimization objective is to maximize a weighted sum of the data rates (for communications) and the Fisher information (for sensing). We first show that the conventional beamforming method for the multiple-input multiple-output (MIMO) transmission, i.e., the weighted minimum mean square error (WMMSE) algorithm, works for the ISAC problem case from a fractional programming (FP) perspective. However, the WMMSE algorithm frequently requires computing the $N\times N$ matrix inverse, where $N$ is the number of transmit or receive antennas, so the algorithm becomes quite costly when antennas are massively deployed. To address this issue, we develop a nonhomogeneous bound and use it in conjunction with the FP technique to solve the ISAC beamforming problem without the need to invert any large matrices. It is further shown that the resulting new FP algorithm has an intimate connection with gradient projection, based on which we can accelerate the convergence via Nesterov's gradient extrapolation.