A Riemannian Manifold Approach to Constrained Resource Allocation in ISAC

This paper introduces a universal optimization framework for integrated sensing and communication (ISAC) systems, which are expected to be fundamental aspects of sixth-generation networks. In particular, we develop an iterative augmented Lagrangian manifold optimization (IALMO) framework designed to maximize communication sum rate while satisfying sensing beampattern gain targets, users’ minimum rate requirements, and base station (BS) transmit power limits. IALMO applies the principles of Riemannian manifold optimization to navigate the complex, non-convex landscape of the resource allocation problem. It efficiently leverages the augmented Lagrangian method to ensure adherence to constraints. Comprehensive numerical results are presented to validate our framework, which illustrates the IALMO method’s superior capability to enhance the dual functionalities of communication and sensing in ISAC systems. For instance, with 12 antennas and 30 dBm BS transmit power, our proposed IALMO algorithm delivers a 4.2% sum rate gain over a benchmark optimization-based algorithm. Remarkably, the suggested method performs better in complexity and execution time. For instance, the proposed IALMO algorithm reduces average algorithm execution time by 89.5% with 20 BS transmit antennas compared to the standard optimization-based benchmark. This work demonstrates significant improvements in system performance and contributes a new algorithmic perspective to ISAC resource management.