Accelerated Fractional Programming for Multi-User ISAC Beamforming Optimization with Per-Group Power Constraints

This letter presents an efficient beamforming solution for a multi-user integrated sensing and communication (ISAC) system. The problem of optimizing ISAC beamforming vectors is formulated to maximize a weighted sum of communication sum-rate and radar sensing signal-to-interference-plus-noise ratio (SINR), subject to arbitrary per-group power constraints (PGPCs). To address the non-convexity, we employ fractional programming (FP) approach, transforming the original problem into a series of convex subproblems with fixed auxiliary variables. To avoid dependence on convex optimization tools, we propose an accelerated FP (A-FP) scheme that partitions the beamforming vectors into block variables, which are sequentially optimized with closed-form solutions for each block. Numerical results demonstrate that the A-FP scheme achieves almost identical performance to the FP scheme, while significantly reducing computational complexity.