Non-convex power allocation games in MIMO cognitive radio networks

Consideramos un escenario de reparto del espectro, basado en la detección, en una red de radio cognitiva MIMO donde el objetivo general es maximizar el rendimiento total de cada usuario de radio cognitiva optimizando conjuntamente la operación de detección y la asignación de potencia en todos los canales, bajo una restricción de interferencia para los usuarios primarios. Los problemas de optimización resultantes conducen a un juego no convexo, que presenta un nuevo desafío a la hora de analizar los equilibrios de este juego. Con el fin de hacer frente a la no convexidad del juego, utilizamos un nuevo concepto relajado de equilibrio, el equilibrio cuasi-Nash (QNE). Se demuestran las condiciones suficientes para la existencia y la unicidad de un QNE. El trabajo también presenta un método de optimización de punto interior primal-dual que converge a un QNE. Los resultados de la simulación muestran que el juego propuesto puede lograr una considerable mejora del rendimiento con respecto a un juego determinista.TEC2010- 19545-C04-04 “COSIMA”,CONSOLIDER-INGENIO 2010 CSD2008-00010 “COMONSENS”“HYDROBIONETS” FP7 Grant no. 287613 FP7We consider a sensing-based spectrum sharing scenario in a MIMO cognitive radio network where the overall objective is to maximize the total throughput of each cognitive radio user by jointly optimizing both the detection operation and the power allocation over all the channels, under a interference constraint bound to primary users. The resulting optimization problems lead to a non-convex game, which presents a new challenge when analyzing the equilibria of this game. In order to deal with the non-convexity of the game, we use a new relaxed equilibria concept, namely, quasi-Nash equilibrium (QNE). We show the sufficient conditions for the existence and the uniqueness of a QNE. A primal-dual interior point optimization method that converges to a QNE is also discussed in this paper. Simulation results show that the proposed game can achieve a considerable performance improvement with respect to a deterministic game

Transmit without regrets: Online optimization in MIMO-OFDM cognitive radio systems

In this paper, we examine cognitive radio systems that evolve dynamically over time due to changing user and environmental conditions. To combine the advantages of orthogonal frequency division multiplexing (OFDM) and multiple-input, multiple-output (MIMO) technologies, we consider a MIMO-OFDM cognitive radio network where wireless users with multiple antennas communicate over several non-interfering frequency bands. As the network's primary users (PUs) come and go in the system, the communication environment changes constantly (and, in many cases, randomly). Accordingly, the network's unlicensed, secondary users (SUs) must adapt their transmit profiles "on the fly" in order to maximize their data rate in a rapidly evolving environment over which they have no control. In this dynamic setting, static solution concepts (such as Nash equilibrium) are no longer relevant, so we focus on dynamic transmit policies that lead to no regret: specifically, we consider policies that perform at least as well as (and typically outperform) even the best fixed transmit profile in hindsight. Drawing on the method of matrix exponential learning and online mirror descent techniques, we derive a no-regret transmit policy for the system's SUs which relies only on local channel state information (CSI). Using this method, the system's SUs are able to track their individually evolving optimum transmit profiles remarkably well, even under rapidly (and randomly) changing conditions. Importantly, the proposed augmented exponential learning (AXL) policy leads to no regret even if the SUs' channel measurements are subject to arbitrarily large observation errors (the imperfect CSI case), thus ensuring the method's robustness in the presence of uncertainties.Comment: 25 pages, 3 figures, to appear in the IEEE Journal on Selected Areas in Communication

Energy Efficiency in MIMO Underlay and Overlay Device-to-Device Communications and Cognitive Radio Systems

This paper addresses the problem of resource allocation for systems in which a primary and a secondary link share the available spectrum by an underlay or overlay approach. After observing that such a scenario models both cognitive radio and D2D communications, we formulate the problem as the maximization of the secondary energy efficiency subject to a minimum rate requirement for the primary user. This leads to challenging non-convex, fractional problems. In the underlay scenario, we obtain the global solution by means of a suitable reformulation. In the overlay scenario, two algorithms are proposed. The first one yields a resource allocation fulfilling the first-order optimality conditions of the resource allocation problem, by solving a sequence of easier fractional problems. The second one enjoys a weaker optimality claim, but an even lower computational complexity. Numerical results demonstrate the merits of the proposed algorithms both in terms of energy-efficient performance and complexity, also showing that the two proposed algorithms for the overlay scenario perform very similarly, despite the different complexity.Comment: to appear in IEEE Transactions on Signal Processin

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201

Distributed Learning Policies for Power Allocation in Multiple Access Channels

We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a continuous non-cooperative game whose strategy space represents the users' distribution of transmission power over the network's channels. When the channels are static, we find that this game admits an exact potential function and this allows us to show that it has a unique equilibrium almost surely. Furthermore, using the game's potential property, we derive a modified version of the replicator dynamics of evolutionary game theory which applies to this continuous game, and we show that if the network's users employ a distributed learning scheme based on these dynamics, then they converge to equilibrium exponentially quickly. On the other hand, a major challenge occurs if the channels do not remain static but fluctuate stochastically over time, following a stationary ergodic process. In that case, the associated ergodic game still admits a unique equilibrium, but the learning analysis becomes much more complicated because the replicator dynamics are no longer deterministic. Nonetheless, by employing results from the theory of stochastic approximation, we show that users still converge to the game's unique equilibrium. Our analysis hinges on a game-theoretical result which is of independent interest: in finite player games which admit a (possibly nonlinear) convex potential function, the replicator dynamics (suitably modified to account for nonlinear payoffs) converge to an eps-neighborhood of an equilibrium at time of order O(log(1/eps)).Comment: 11 pages, 8 figures. Revised manuscript structure and added more material and figures for the case of stochastically fluctuating channels. This version will appear in the IEEE Journal on Selected Areas in Communication, Special Issue on Game Theory in Wireless Communication