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Register a new userSpatially Controlled Relay Beamforming: $2$-Stage Optimal Policies
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Added by
Dionysios Kalogerias
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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The problem of enhancing Quality-of-Service (QoS) in power constrained, mobile relay beamforming networks, by optimally and dynamically controlling the motion of the relaying nodes, is considered, in a dynamic channel environment. We assume a time slotted system, where the relays update their positions before the beginning of each time slot. Modeling the wireless channel as a Gaussian spatiotemporal stochastic field, we propose a novel $2$-stage stochastic programming problem formulation for optimally specifying the positions of the relays at each time slot, such that the expected QoS of the network is maximized, based on causal Channel State Information (CSI) and under a total relay transmit power budget. This results in a schema where, at each time slot, the relays, apart from optimally beamforming to the destination, also optimally, predictively decide their positions at the next time slot, based on causally accumulated experience. Exploiting either the Method of Statistical Differentials, or the multidimensional Gauss-Hermite Quadrature Rule, the stochastic program considered is shown to be approximately equivalent to a set of simple subproblems, which are solved in a distributed fashion, one at each relay. Optimality and performance of the proposed spatially controlled system are also effectively assessed, under a rigorous technical framework; strict optimality is rigorously demonstrated via the development of a version of the Fundamental Lemma of Stochastic Control, and, performance-wise, it is shown that, quite interestingly, the optimal average network QoS exhibits an increasing trend across time slots, despite our myopic problem formulation. Numerical simulations are presented, experimentally corroborating the success of the proposed approach and the validity of our theoretical predictions.
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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.
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