Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part I: Nash Equilibria

In this two-parts paper we propose a decentralized strategy, based on a game-theoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipoint-to-multipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and bandwidth. We assume, as optimality criterion, the achievement of a Nash equilibrium and consider two alternative optimization problems: 1) the competitive maximization of mutual information on each link, given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies; and 2) the competitive maximization of the transmission rate, using finite order constellations, under the same constraints as above, plus a constraint on the average error probability. In Part I of the paper, we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies. Then, we prove that the optimal precoding/multiplexing scheme for both games leads to a channel diagonalizing structure, so that both matrix-valued problems can be recast in a simpler unified vector power control game, with no performance penalty. Thus, we study this simpler game and derive sufficient conditions ensuring the uniqueness of the Nash equilibrium. Interestingly, although derived under stronger constraints, incorporating for example spectral mask constraints, our uniqueness conditions have broader validity than previously known conditions. Finally, we assess the goodness of the proposed decentralized strategy by comparing its performance with the performance of a Pareto-optimal centralized scheme. To reach the Nash equilibria of the game, in Part II, we propose alternative distributed algorithms, along with their convergence conditions.Comment: Paper submitted to IEEE Transactions on Signal Processing, September 22, 2005. Revised March 14, 2007. Accepted June 5, 2007. To be published on IEEE Transactions on Signal Processing, 2007. To appear on IEEE Transactions on Signal Processing, 200

Distributed space-time coding for two-way wireless relay networks

In this paper, we consider distributed space-time coding for two-way wireless relay networks, where communication between two terminals is assisted by relay nodes. Relaying protocols using two, three, and four time slots are proposed. The protocols using four time slots are the traditional amplify-and-forward (AF) and decode-and-forward (DF) protocols, which do not consider the property of the two-way traffic. A new class of relaying protocols, termed as partial decode-and-forward (PDF), is developed for the two time slots transmission, where each relay first removes part of the noise before sending the signal to the two terminals. Protocols using three time slots are proposed to compensate the fact that the two time slots protocols cannot make use of direct transmission between the two terminals. For all protocols, after processing their received signals, the relays encode the resulting signals using a distributed linear dispersion (LD) code. The proposed AF protocols are shown to achieve the diversity order of min{N,K}(1- (log log P/log P)), where N is the number of relays, P is the total power of the network, and K is the number of symbols transmitted during each time slot. When random unitary matrix is used for LD code, the proposed PDF protocols resemble random linear network coding, where the former operates on the unitary group and the latter works on the finite field. Moreover, PDF achieves the diversity order of min{N,K} but the conventional DF can only achieve the diversity order of 1. Finally, we find that two time slots protocols also have advantages over four-time-slot protocols in media access control (MAC) layer

Processing and Transmission of Information

Contains research objectives and reports on three research projects.National Aeronautics and Space Administration (Grant NsG-334)Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E