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.

翻译：本文研究集成感知与通信（ISAC）中的协作多小区波束成形设计。特别地，我们假设每个基站（BS）配备大规模天线阵列。优化目标为最大化数据速率（用于通信）与费舍尔信息（用于感知）的加权和。我们首先证明，从分式规划（FP）的视角来看，传统多输入多输出（MIMO）传输的波束成形方法——即加权最小均方误差（WMMSE）算法——适用于ISAC问题。然而，WMMSE算法频繁需要计算$N\times N$矩阵的逆（其中$N$为发射或接收天线数量），当天线大规模部署时，该算法的计算代价将变得极高。为解决此问题，我们提出一种非齐次界，并将其与FP技术结合以求解ISAC波束成形问题，从而避免任何大规模矩阵求逆。进一步研究表明，所得的新FP算法与梯度投影法存在内在关联，基于此关联，我们可通过涅斯捷罗夫梯度外推法加速算法收敛。