This work develops a Riemannian manifold approach for constrained resource allocation in integrated sensing and communication (ISAC). Rather than optimizing beamforming directly in a difficult non-convex Euclidean space, the method reformulates the beamforming variable on a structured manifold and updates it through geometric operations such as the Riemannian gradient, vector transport, and retraction.
An augmented Lagrangian mechanism is then used to enforce sensing beampattern targets, user SINR constraints, and transmit power limits during the iterative process. The resulting view is both algorithmic and geometric: the iterate moves along tangent directions, retracts back to the manifold, and updates its multipliers until the communication and sensing constraints are satisfied.
Paper: A Riemannian Manifold Approach to Constrained Resource Allocation in ISAC.