From Sparse Probes to Sum-Rate Maximization: Electromagnetic Twin Beamforming

Probing every candidate location at each wireless-map update is costly. This letter develops electromagnetic-twin (ET) beamforming that converts sparse spatial probes into a sum-rate decision. The ET stores a location-dependent angular power spectrum, updates its innovation through graph-regularized estimation, and queries user covariances for projected beam optimization. A rate-sensitivity bound selects subsequent probes by query-weighted posterior-variance reduction. With 1% random probes, ET beamforming achieves $2.69$ bit/s/Hz versus $1.12$ for a static channel knowledge map; with 7% query-aware probes, it reaches $3.03$ bit/s/Hz, within 3.4% of perfect-covariance beamforming.