Mobile Beamforming & Spatially Controlled Relay Communications

TL;DR

This paper develops a stochastic optimization framework for relay placement in robotic networks using beamforming, proposing a tractable relaxation that results in a spatial control policy favoring the best relay's movement.

Contribution

It introduces a novel 2-stage stochastic programming approach for relay positioning in stochastic media, with a tractable relaxation leading to a simple, effective control policy.

Findings

The relaxed problem yields a purely selective control policy.

Optimal relay movement involves only the best relay at each step.

The approach maximizes the expected reciprocal of total beamforming power.

Abstract

We consider stochastic motion planning in single-source single-destination robotic relay networks, under a cooperative beamforming framework. Assuming that the communication medium constitutes a spatiotemporal stochastic field, we propose a 2-stage stochastic programming formulation of the problem of specifying the positions of the relays, such that the expected reciprocal of their total beamforming power is maximized. Stochastic decision making is made on the basis of random causal CSI. Recognizing the intractability of the original problem, we propose a lower bound relaxation, resulting to a nontrivial optimization problem with respect to the relay locations, which is equivalent to a small set of simple, tractable subproblems. Our formulation results in spatial controllers with a predictive character; at each time slot, the new relay positions should be such that the expected power reciprocal at the next time slot is maximized. Quite interestingly, the optimal control policy to the relaxed problem is purely selective; under a certain sense, only the best relay should move.