101 research outputs found
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
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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