Joint Position and Beamforming Control via Alternating Nonlinear Least-Squares with a Hierarchical Gamma Prior

Abstract

We consider the problem of controlling antennae gains and positions among a set collection of mobile beamforming agents. Existing approaches predominately fall into two categories: solvers based upon convex relaxations of subset selection, and Monte Carlo sampling approaches that seek close-to-exact solutions, whose consistency requires the number of samples to approach infinity. In this work, we adopt an approach that improves upon the accuracy of prevailing convex relaxation approaches, motivated by their relative computational efficiency. Specifically, for fixed pose, we develop a modified hierarchical prior which is well-known within Bayesian inference to promote sparsity more effectively than the conventional Gaussian-gamma prior. Then, with this specification, we develop a variant of Expectation Maximization (EM) whose updates can be evaluated in closed form to obtain the beamforming gains and set of active agents. Then, when the signal phase and and amplitude are fixed, we propose a projected block descent approach, i.e., alternating nonlinear least-squares, for efficient relocation of the pruned set of agents. The inter-weaved iterative approach presented here better synthesizes the desired beam pattern with the minimum set of active agents and demands less computational load compared to the dense grid search implementations. Preliminary results indicate the proposed approach attains a superior tradeoff of sparsification and accuracy as compared to existing approaches.