Minimum Mean Squared Error Holographic Beamforming for Sum-Rate Maximization

This paper studies the problem of hybrid holographic beamforming for sum-rate maximization in a reconfigurable holographic surface (RHS) assisted system. We establish the mathematical relationship between the mean squared error (MSE) and the holographic response of the RHS to enable alternating optimization based on the minimum MSE (MMSE) criterion. Our analysis demonstrates that this relationship exhibits a quadratic dependency on each element of the holographic beamformer. Exploiting this property, we derive closed-form optimal expressions for updating the holographic beamforming weights, resulting in linear complexity in terms of the RHS size, thereby ensuring scalability for large-scale deployments. The presented simulation results validate the effectiveness of our MMSE-based holographic approach, providing useful insights.