Hybrid Beamforming Design on Riemannian Manifolds for Wideband MIMO Systems

This paper proposes a novel, unified approach to design both radio frequency (RF) and baseband beamforming (BF) solutions for wideband hybrid multiple-input multiple-output (MIMO) systems using the Riemannian manifold optimization. The proposed two-stage optimization framework effectively addresses various power constraints of the wideband hybrid MIMO systems, including total sum power, per-RF-chain, and per-antenna power constraints. By transforming constrained optimization problems into unconstrained ones on Riemannian submanifolds, we achieve notable improvements in spectral efficiency (SE) and power consumption. In addition, we account for the log-determinant structure of the objective function, which forms an unconstrained solution subspace. This allows for a more efficient retraction process towards the manifold, representing the set of solutions that satisfy the constraints. This unified design approach provides a more accurate and efficient solution to non-convex optimization problems with complex constraints. Simulation results demonstrate the superior performance of the proposed approach over conventional approaches.