22 research outputs found
Stochastic Differential Games and Energy-Efficient Power Control
One of the contributions of this work is to formulate the problem of
energy-efficient power control in multiple access channels (namely, channels
which comprise several transmitters and one receiver) as a stochastic
differential game. The players are the transmitters who adapt their power level
to the quality of their time-varying link with the receiver, their battery
level, and the strategy updates of the others. The proposed model not only
allows one to take into account long-term strategic interactions but also
long-term energy constraints. A simple sufficient condition for the existence
of a Nash equilibrium in this game is provided and shown to be verified in a
typical scenario. As the uniqueness and determination of equilibria are
difficult issues in general, especially when the number of players goes large,
we move to two special cases: the single player case which gives us some useful
insights of practical interest and allows one to make connections with the case
of large number of players. The latter case is treated with a mean-field game
approach for which reasonable sufficient conditions for convergence and
uniqueness are provided. Remarkably, this recent approach for large system
analysis shows how scalability can be dealt with in large games and only relies
on the individual state information assumption.Comment: The final publication is available at
http://www.springerlink.com/openurl.asp?genre=article\&id=doi:10.1007/s13235-012-0068-
Information Design for Strategic Coordination of Autonomous Devices with Non-Aligned Utilities
In this paper, we investigate the coordination of autonomous devices with
non-aligned utility functions. Both encoder and decoder are considered as
players, that choose the encoding and the decoding in order to maximize their
long-run utility functions. The topology of the point-to-point network under
investigation, suggests that the decoder implements a strategy, knowing in
advance the strategy of the encoder. We characterize the encoding and decoding
functions that form an equilibrium, by using empirical coordination. The
equilibrium solution is related to an auxiliary game in which both players
choose some conditional distributions in order to maximize their expected
utilities. This problem is closely related to the literature on "Information
Design" in Game Theory. We also characterize the set of posterior distributions
that are compatible with a rate-limited channel between the encoder and the
decoder. Finally, we provide an example of non-aligned utility functions
corresponding to parallel fading multiple access channels.Comment: IEEE Proc. of the Fifty-fourth Annual Allerton Conference Allerton
House, UIUC, Illinois, USA September 27 - 30, 201
Dynamic Power Allocation Games in Parallel Multiple Access Channels
We analyze the distributed power allocation problem in parallel multiple
access channels (MAC) by studying an associated non-cooperative game which
admits an exact potential. Even though games of this type have been the subject
of considerable study in the literature, we find that the sufficient conditions
which ensure uniqueness of Nash equilibrium points typically do not hold in
this context. Nonetheless, we show that the parallel MAC game admits a unique
equilibrium almost surely, thus establishing an important class of
counterexamples where these sufficient conditions are not necessary.
Furthermore, if the network's users employ a distributed learning scheme based
on the replicator dynamics, we show that they converge to equilibrium from
almost any initial condition, even though users only have local information at
their disposal.Comment: 18 pages, 4 figures, submitted to Valuetools '1
A Repeated Game Formulation of Energy-Efficient Decentralized Power Control
Decentralized multiple access channels where each transmitter wants to
selfishly maximize his transmission energy-efficiency are considered.
Transmitters are assumed to choose freely their power control policy and
interact (through multiuser interference) several times. It is shown that the
corresponding conflict of interest can have a predictable outcome, namely a
finitely or discounted repeated game equilibrium. Remarkably, it is shown that
this equilibrium is Pareto-efficient under reasonable sufficient conditions and
the corresponding decentralized power control policies can be implemented under
realistic information assumptions: only individual channel state information
and a public signal are required to implement the equilibrium strategies.
Explicit equilibrium conditions are derived in terms of minimum number of game
stages or maximum discount factor. Both analytical and simulation results are
provided to compare the performance of the proposed power control policies with
those already existing and exploiting the same information assumptions namely,
those derived for the one-shot and Stackelberg games.Comment: 25 pages, 5 figures, accepted for publication in IEEE Transaction on
Wireless Communicatio
A Stochastic Game Formulation of Energy-Efficient Power Control: Equilibrium Utilities and Practical Strategies
Frequency non-selective time-selective multiple access channels in which
transmitters can freely choose their power control policy are considered. The
individual objective of the transmitters is to maximize their averaged
energy-efficiency. For this purpose, a transmitter has to choose a power
control policy that is, a sequence of power levels adapted to the channel
variations. This problem can be formulated as a stochastic game with
discounting for which there exists a theorem characterizing all the equilibrium
utilities (equilibrium utility region). As in its general formulation, this
theorem relies on global channel state information (CSI), it is shown that some
points of the utility region can be reached with individual CSI. Interestingly,
time-sharing based solutions, which are usually considered for centralized
policies, appear to be part of the equilibrium solutions. This analysis is
illustrated by numerical results providing further insights to the problem
under investigation.Comment: DSP 2011: 17th International Conference on Digital Signal Processing,
July 2011, Corfu, Greec
Adaptive Power Allocation and Control in Time-Varying Multi-Carrier MIMO Networks
In this paper, we examine the fundamental trade-off between radiated power
and achieved throughput in wireless multi-carrier, multiple-input and
multiple-output (MIMO) systems that vary with time in an unpredictable fashion
(e.g. due to changes in the wireless medium or the users' QoS requirements).
Contrary to the static/stationary channel regime, there is no optimal power
allocation profile to target (either static or in the mean), so the system's
users must adapt to changes in the environment "on the fly", without being able
to predict the system's evolution ahead of time. In this dynamic context, we
formulate the users' power/throughput trade-off as an online optimization
problem and we provide a matrix exponential learning algorithm that leads to no
regret - i.e. the proposed transmit policy is asymptotically optimal in
hindsight, irrespective of how the system evolves over time. Furthermore, we
also examine the robustness of the proposed algorithm under imperfect channel
state information (CSI) and we show that it retains its regret minimization
properties under very mild conditions on the measurement noise statistics. As a
result, users are able to track the evolution of their individually optimum
transmit profiles remarkably well, even under rapidly changing network
conditions and high uncertainty. Our theoretical analysis is validated by
extensive numerical simulations corresponding to a realistic network deployment
and providing further insights in the practical implementation aspects of the
proposed algorithm.Comment: 25 pages, 4 figure
Outage Probability and Outage-Based Robust Beamforming for MIMO Interference Channels with Imperfect Channel State Information
In this paper, the outage probability and outage-based beam design for
multiple-input multiple-output (MIMO) interference channels are considered.
First, closed-form expressions for the outage probability in MIMO interference
channels are derived under the assumption of Gaussian-distributed channel state
information (CSI) error, and the asymptotic behavior of the outage probability
as a function of several system parameters is examined by using the Chernoff
bound. It is shown that the outage probability decreases exponentially with
respect to the quality of CSI measured by the inverse of the mean square error
of CSI. Second, based on the derived outage probability expressions, an
iterative beam design algorithm for maximizing the sum outage rate is proposed.
Numerical results show that the proposed beam design algorithm yields better
sum outage rate performance than conventional algorithms such as interference
alignment developed under the assumption of perfect CSI.Comment: 41 pages, 14 figures. accepted to IEEE Transactions on Wireless
Communication
Methodologies for Analyzing Equilibria in Wireless Games
Under certain assumptions in terms of information and models, equilibria
correspond to possible stable outcomes in conflicting or cooperative scenarios
where rational entities interact. For wireless engineers, it is of paramount
importance to be able to predict and even ensure such states at which the
network will effectively operate. In this article, we provide non-exhaustive
methodologies for characterizing equilibria in wireless games in terms of
existence, uniqueness, selection, and efficiency.Comment: To appear in IEEE Signal Processing Magazine, Sep. 200