Deterministic and Stochastic Optimization for Robust Beamfocusing Against Positioning Errors

We consider robust hybrid beamfocusing schemes against statistical and norm-bounded positioning errors in order to improve a total system data rate in near-field communications. To this end, baseband and analog beamfocusing designs are formulated as an ergodic sum rate maximization, which is solved via deterministic and stochastic optimization. In particular, a closed-form expression of the erdodic sum rate is introduced, which makes the problem tractable by deterministic optimization. In turn, a new stochastic optimization algorithm is proposed for further data rate improvements, which incorporates matrix fractional programming (FP) and element-wise phase derivatives into stochastic learning frameworks by penalize methods. The proposed stochastic algorithm theoretically guarantees convergence to stationary points of the original problem. Numerical results confirm that the proposed approaches achieve higher data rates than non-robust approaches and a singular value decomposition (SVD) beamfocusing with perfect position information.