43 research outputs found
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
Protecting Secret Key Generation Systems Against Jamming: Energy Harvesting and Channel Hopping Approaches
Jamming attacks represent a critical vulnerability for wireless secret key generation (SKG) systems. In this paper, two counter-jamming approaches are investigated for SKG systems: first, the employment of energy harvesting (EH) at the legitimate nodes to turn part of the jamming power into useful communication power, and, second, the use of channel hopping or power spreading in block fading channels to reduce the impact of jamming. In both cases, the adversarial interaction between the pair of legitimate nodes and the jammer is formulated as a two-player zero-sum game and the Nash and Stackelberg equilibria are characterized analytically and in closed form. In particular, in the case of EH receivers, the existence of a critical transmission power for the legitimate nodes allows the full characterization of the game's equilibria and also enables the complete neutralization of the jammer. In the case of channel hopping versus power spreading techniques, it is shown that the jammer's optimal strategy is always power spreading while the legitimate nodes should only use power spreading in the high signal-to-interference ratio (SIR) regime. In the low SIR regime, when avoiding the jammer's interference becomes critical, channel hopping is optimal for the legitimate nodes. Numerical results demonstrate the efficiency of both counter-jamming measures
Protecting Secret Key Generation Systems Against Jamming: Energy Harvesting and Channel Hopping Approaches
Jamming attacks represent a critical vulnerability for wireless secret key generation (SKG) systems. In this paper, two counter-jamming approaches are investigated for SKG systems: first, the employment of energy harvesting (EH) at the legitimate nodes to turn part of the jamming power into useful communication power, and, second, the use of channel hopping or power spreading in block fading channels to reduce the impact of jamming. In both cases, the adversarial interaction between the pair of legitimate nodes and the jammer is formulated as a two-player zero-sum game and the Nash and Stackelberg equilibria are characterized analytically and in closed form. In particular, in the case of EH receivers, the existence of a critical transmission power for the legitimate nodes allows the full characterization of the game's equilibria and also enables the complete neutralization of the jammer. In the case of channel hopping versus power spreading techniques, it is shown that the jammer's optimal strategy is always power spreading while the legitimate nodes should only use power spreading in the high signal-to-interference ratio (SIR) regime. In the low SIR regime, when avoiding the jammer's interference becomes critical, channel hopping is optimal for the legitimate nodes. Numerical results demonstrate the efficiency of both counter-jamming measures
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
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
Efficient spectrum scheduling and power management for opportunistic users
International audienceIn this paper, we study the centralized spectrum access and power management for several opportunistic users, secondary users (SUs), without hurting the primary users (PUs). The radio resource manager's objective is to minimize the overall power consumption of the opportunistic system over several orthogonal frequency bands under constraints on the minimum quality of service (QoS) and maximum peak and average interference to the PUs. Given the opposing nature of these constraints, we first study the problem of feasibility, and we provide sufficient conditions and necessary conditions for the existence of a solution. The main challenge lies in the non-convexity of this problem because of the discrete spectrum scheduling: one band can be allocated to at most one SU to avoid interference impairments. To overcome this issue, we use a Lagrangian relaxation technique, and we prove that the discrete solutions of the relaxed problem are the solutions to the initial problem. We propose a projected sub-gradient algorithm to compute the solution, when it exists. Assuming that the channels are drawn randomly from a continuous distribution, this algorithm converges to the optimal solution. We also study a specific symmetric system for which we provide the analytical solution. Our numerical results compare the energy-efficiency of the proposed algorithm with other spectrum allocation solutions and show the optimality of our approach
Fast Optimization with Zeroth-Order Feedback in Distributed, Multi-User MIMO Systems
In this paper, we develop a gradient-free optimization methodology for
efficient resource allocation in Gaussian MIMO multiple access channels. Our
approach combines two main ingredients: (i) an entropic semidefinite
optimization based on matrix exponential learning (MXL); and (ii) a one-shot
gradient estimator which achieves low variance through the reuse of past
information. This novel algorithm, which we call gradient-free MXL algorithm
with callbacks (MXL0), retains the convergence speed of gradient-based
methods while requiring minimal feedback per iterationa single scalar. In
more detail, in a MIMO multiple access channel with users and transmit
antennas per user, the MXL0 algorithm achieves -optimality
within iterations (on average and with high
probability), even when implemented in a fully distributed, asynchronous
manner. For cross-validation, we also perform a series of numerical experiments
in medium- to large-scale MIMO networks under realistic channel conditions.
Throughout our experiments, the performance of MXL0 matchesand
sometimes exceedsthat of gradient-based MXL methods, all the while operating
with a vastly reduced communication overhead. In view of these findings, the
MXL0 algorithm appears to be uniquely suited for distributed massive MIMO
systems where gradient calculations can become prohibitively expensive.Comment: Final version; to appear in IEEE Transactions on Signal Processing;
16 pages, 4 figure
Distributed energy-efficient power optimization in cellular relay networks with minimum rate constraints
In this work, we derive a distributed power control algo- rithm for energy-efficient uplink transmissions in interference- limited cellular networks, equipped with either multiple or shared relays. The proposed solution is derived by model- ing the mobile terminals as utility-driven rational agents that engage in a noncooperative game, under minimum-rate con- straints. The theoretical analysis of the game equilibrium is used to compare the performance of the two different cellular architectures. Extensive simulations show that the shared relay concept outperforms the distributed one in terms of energy efficiency in most network configurations