Spatially Controlled Relay Beamforming

We consider the problem of enhancing Quality-of-Service (QoS) in mobile relay beamforming networks, by optimally controlling relay motion, in the presence of a dynamic channel. We assume a time-slotted system, where the relays update their positions before the beginning of each slot. Modeling the wireless channel as a Gaussian spatiotemporal field, we propose a novel 2-stage stochastic programming approach for optimally specifying relay positions and beamforming weights, such that the expected QoS of the network is maximized, based on causal channel state information and under a total relay power budget. This results in a scheme where, at each time slot, apart from optimally beamforming to the destination, the relays also optimally decide their positions at the next slot, based on causal experience. The stochastic program considered is shown to be equivalent to a set of simple subproblems, which may be solved in a naturally distributed fashion, one at each relay. However, exact evaluation of the objective of each subproblem is impossible. To mitigate this issue, we propose three efficient, theoretically grounded surrogates to the original subproblems, which rely on the Sample Average Approximation method, the Gauss-Hermite Quadrature, and the Method of Statistical Differentials, respectively. The efficacy and several properties of the proposed approach are demonstrated via simulations. In particular, we report a substantial improvement of about 80% on the average network QoS at steady state, compared to randomized relay motion. This shows that strategic relay motion control can result in substantial performance gains, as far as QoS maximization is concerned.