Adaptive Discrete Motion Control for Mobile Relay Networks

Abstract

We consider the problem of joint beamforming and discrete motion control for mobile relaying networks in dynamic channel environments. We assume a single source-destination communication pair. We adopt a general time slotted approach where, during each slot, every relay implements optimal beamforming and estimates its optimal position for the subsequent slot. We assume that the relays move in a 2D compact square region that has been discretized into a fine grid. The goal is to derive discrete motion policies for the relays, in an adaptive fashion, so that they accommodate the dynamic changes of the channel and, therefore, maximize the Signal-to-Interference + Noise Ratio (SINR) at the destination. We present two different approaches for constructing the motion policies. The first approach assumes that the channel evolves as a Gaussian process and exhibits correlation with respect to both time and space. A stochastic programming method is proposed for estimating the relay positions (and the beamforming weights) based on causal information. The stochastic program is equivalent to a set of simple subproblems and the exact evaluation of the objective of each subproblem is impossible. To tackle this we propose a surrogate of the original subproblem that pertains to the Sample Average Approximation method. We denote this approach as model-based because it adopts the assumption that the underlying correlation structure of the channels is completely known. The second method is denoted as model-free, because it adopts no assumption for the channel statistics. For the scope of this approach, we set the problem of discrete relay motion control in a dynamic programming framework. Finally we employ deep Q learning to derive the motion policies. We provide implementation details that are crucial for achieving good performance in terms of the collective SINR at the destination.