Distributed stochastic optimization via matrix exponential learning

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.Comment: 31 pages, 3 figure

Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks

The problem of distributed rate maximization in multi-channel ALOHA networks is considered. First, we study the problem of constrained distributed rate maximization, where user rates are subject to total transmission probability constraints. We propose a best-response algorithm, where each user updates its strategy to increase its rate according to the channel state information and the current channel utilization. We prove the convergence of the algorithm to a Nash equilibrium in both homogeneous and heterogeneous networks using the theory of potential games. The performance of the best-response dynamic is analyzed and compared to a simple transmission scheme, where users transmit over the channel with the highest collision-free utility. Then, we consider the case where users are not restricted by transmission probability constraints. Distributed rate maximization under uncertainty is considered to achieve both efficiency and fairness among users. We propose a distributed scheme where users adjust their transmission probability to maximize their rates according to the current network state, while maintaining the desired load on the channels. We show that our approach plays an important role in achieving the Nash bargaining solution among users. Sequential and parallel algorithms are proposed to achieve the target solution in a distributed manner. The efficiencies of the algorithms are demonstrated through both theoretical and simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM Transactions on Networking, part of this work was presented at IEEE CAMSAP 201

Reconfigurable Intelligent Surfaces for Energy Efficiency in Wireless Communication

The adoption of a Reconfigurable Intelligent Surface (RIS) for downlink multi-user communication from a multi-antenna base station is investigated in this paper. We develop energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements, subject to individual link budget guarantees for the mobile users. This leads to non-convex design optimization problems for which to tackle we propose two computationally affordable approaches, capitalizing on alternating maximization, gradient descent search, and sequential fractional programming. Specifically, one algorithm employs gradient descent for obtaining the RIS phase coefficients, and fractional programming for optimal transmit power allocation. Instead, the second algorithm employs sequential fractional programming for the optimization of the RIS phase shifts. In addition, a realistic power consumption model for RIS-based systems is presented, and the performance of the proposed methods is analyzed in a realistic outdoor environment. In particular, our results show that the proposed RIS-based resource allocation methods are able to provide up to $300\%$ higher energy efficiency, in comparison with the use of regular multi-antenna amplify-and-forward relaying.Comment: Accepted by IEEE TWC; additional materials on the topic are included in the 2018 conference publications at ICASSP (https://ieeexplore.ieee.org/abstract/document/8461496) and GLOBECOM 2018 (arXiv:1809.05397

Spectrum Coordination in Energy Efficient Cognitive Radio Networks

Device coordination in open spectrum systems is a challenging problem, particularly since users experience varying spectrum availability over time and location. In this paper, we propose a game theoretical approach that allows cognitive radio pairs, namely the primary user (PU) and the secondary user (SU), to update their transmission powers and frequencies simultaneously. Specifically, we address a Stackelberg game model in which individual users attempt to hierarchically access to the wireless spectrum while maximizing their energy efficiency. A thorough analysis of the existence, uniqueness and characterization of the Stackelberg equilibrium is conducted. In particular, we show that a spectrum coordination naturally occurs when both actors in the system decide sequentially about their powers and their transmitting carriers. As a result, spectrum sensing in such a situation turns out to be a simple detection of the presence/absence of a transmission on each sub-band. We also show that when users experience very different channel gains on their two carriers, they may choose to transmit on the same carrier at the Stackelberg equilibrium as this contributes enough energy efficiency to outweigh the interference degradation caused by the mutual transmission. Then, we provide an algorithmic analysis on how the PU and the SU can reach such a spectrum coordination using an appropriate learning process. We validate our results through extensive simulations and compare the proposed algorithm to some typical scenarios including the non-cooperative case and the throughput-based-utility systems. Typically, it is shown that the proposed Stackelberg decision approach optimizes the energy efficiency while still maximizing the throughput at the equilibrium.Comment: 12 pages, 10 figures, to appear in IEEE Transactions on Vehicular Technolog

Energy-Efficient Power Control: A Look at 5G Wireless Technologies

This work develops power control algorithms for energy efficiency (EE) maximization (measured in bit/Joule) in wireless networks. Unlike previous related works, minimum-rate constraints are imposed and the signal-to-interference-plus-noise ratio takes a more general expression, which allows one to encompass some of the most promising 5G candidate technologies. Both network-centric and user-centric EE maximizations are considered. In the network-centric scenario, the maximization of the global EE and the minimum EE of the network are performed. Unlike previous contributions, we develop centralized algorithms that are guaranteed to converge, with affordable computational complexity, to a Karush-Kuhn-Tucker point of the considered non-convex optimization problems. Moreover, closed-form feasibility conditions are derived. In the user-centric scenario, game theory is used to study the equilibria of the network and to derive convergent power control algorithms, which can be implemented in a fully decentralized fashion. Both scenarios above are studied under the assumption that single or multiple resource blocks are employed for data transmission. Numerical results assess the performance of the proposed solutions, analyzing the impact of minimum-rate constraints, and comparing the network-centric and user-centric approaches.Comment: Accepted for Publication in the IEEE Transactions on Signal Processin