A Riemannian Manifold Approach to Constrained Resource Allocation in ISAC

This paper introduces a new resource allocation framework for integrated sensing and communication (ISAC) systems, which are expected to be fundamental aspects of sixth-generation networks. In particular, we develop an augmented Lagrangian manifold optimization (ALMO) framework designed to maximize communication sum rate while satisfying sensing beampattern gain targets and base station (BS) transmit power limits. ALMO applies the principles of Riemannian manifold optimization (MO) to navigate the complex, non-convex landscape of the resource allocation problem. It efficiently leverages the augmented Lagrangian method to ensure adherence to constraints. We present comprehensive numerical results to validate our framework, which illustrates the ALMO 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 ALMO algorithm delivers a 10.1 gain over a benchmark optimization-based algorithm. This work demonstrates significant improvements in system performance and contributes a new algorithmic perspective to ISAC resource management.