Fast Fractional Programming for Multi-Cell Integrated Sensing and Communications

This paper concerns the coordinate multi-cell beamforming design for integrated sensing and communications (ISAC). The optimization objective is to maximize a weighted sum of the communication rates and the sensing Fisher information. The conventional beamforming method for massive multiple-input multiple-output transmission, i.e., the weighted minimum mean square error (WMMSE) algorithm, has a natural extension to the ISAC problem scenario from a fractional programming (FP) perspective. However, the extended WMMSE algorithm requires computing the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N \times N$</tex> matrix inverse extensively, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> is proportional to the antenna array size, 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 the convergence can be accelerated.