3,144 research outputs found
Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part II: Algorithms
In this two-part paper, we address the problem of finding the optimal
precoding/multiplexing scheme for a set of non-cooperative links sharing the
same physical resources, e.g., time and bandwidth. We consider two alternative
optimization problems: P.1) the maximization of mutual information on each
link, given constraints on the transmit power and spectral mask; and P.2) the
maximization of the transmission rate on each link, using finite order
constellations, under the same constraints as in P.1, plus a constraint on the
maximum average error probability on each link. Aiming at finding decentralized
strategies, we adopted as optimality criterion the achievement of a Nash
equilibrium and thus we formulated both problems P.1 and P.2 as strategic
noncooperative (matrix-valued) games. In Part I of this two-part paper, after
deriving the optimal structure of the linear transceivers for both games, we
provided a unified set of sufficient conditions that guarantee the uniqueness
of the Nash equilibrium. In this Part II, we focus on the achievement of the
equilibrium and propose alternative distributed iterative algorithms that solve
both games. Specifically, the new proposed algorithms are the following: 1) the
sequential and simultaneous iterative waterfilling based algorithms,
incorporating spectral mask constraints; 2) the sequential and simultaneous
gradient projection based algorithms, establishing an interesting link with
variational inequality problems. Our main contribution is to provide sufficient
conditions for the global convergence of all the proposed algorithms which,
although derived under stronger constraints, incorporating for example spectral
mask constraints, have a broader validity than the convergence conditions known
in the current literature for the sequential iterative waterfilling algorithm.Comment: Paper submitted to IEEE Transactions on Signal Processing, February
22, 2006. Revised March 26, 2007. Accepted June 5, 2007. To appear on IEEE
Transactions on Signal Processing, 200
Learning Equilibria with Partial Information in Decentralized Wireless Networks
In this article, a survey of several important equilibrium concepts for
decentralized networks is presented. The term decentralized is used here to
refer to scenarios where decisions (e.g., choosing a power allocation policy)
are taken autonomously by devices interacting with each other (e.g., through
mutual interference). The iterative long-term interaction is characterized by
stable points of the wireless network called equilibria. The interest in these
equilibria stems from the relevance of network stability and the fact that they
can be achieved by letting radio devices to repeatedly interact over time. To
achieve these equilibria, several learning techniques, namely, the best
response dynamics, fictitious play, smoothed fictitious play, reinforcement
learning algorithms, and regret matching, are discussed in terms of information
requirements and convergence properties. Most of the notions introduced here,
for both equilibria and learning schemes, are illustrated by a simple case
study, namely, an interference channel with two transmitter-receiver pairs.Comment: 16 pages, 5 figures, 1 table. To appear in IEEE Communication
Magazine, special Issue on Game Theor
Energy-Aware Competitive Power Allocation for Heterogeneous Networks Under QoS Constraints
This work proposes a distributed power allocation scheme for maximizing
energy efficiency in the uplink of orthogonal frequency-division multiple
access (OFDMA)-based heterogeneous networks (HetNets). The user equipment (UEs)
in the network are modeled as rational agents that engage in a non-cooperative
game where each UE allocates its available transmit power over the set of
assigned subcarriers so as to maximize its individual utility (defined as the
user's throughput per Watt of transmit power) subject to minimum-rate
constraints. In this framework, the relevant solution concept is that of Debreu
equilibrium, a generalization of Nash equilibrium which accounts for the case
where an agent's set of possible actions depends on the actions of its
opponents. Since the problem at hand might not be feasible, Debreu equilibria
do not always exist. However, using techniques from fractional programming, we
provide a characterization of equilibrial power allocation profiles when they
do exist. In particular, Debreu equilibria are found to be the fixed points of
a water-filling best response operator whose water level is a function of
minimum rate constraints and circuit power. Moreover, we also describe a set of
sufficient conditions for the existence and uniqueness of Debreu equilibria
exploiting the contraction properties of the best response operator. This
analysis provides the necessary tools to derive a power allocation scheme that
steers the network to equilibrium in an iterative and distributed manner
without the need for any centralized processing. Numerical simulations are then
used to validate the analysis and assess the performance of the proposed
algorithm as a function of the system parameters.Comment: 37 pages, 12 figures, to appear IEEE Trans. Wireless Commu
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