Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks

The problem of distributed rate maximization in multi-channel ALOHA networks is considered. First, we study the problem of constrained distributed rate maximization, where user rates are subject to total transmission probability constraints. We propose a best-response algorithm, where each user updates its strategy to increase its rate according to the channel state information and the current channel utilization. We prove the convergence of the algorithm to a Nash equilibrium in both homogeneous and heterogeneous networks using the theory of potential games. The performance of the best-response dynamic is analyzed and compared to a simple transmission scheme, where users transmit over the channel with the highest collision-free utility. Then, we consider the case where users are not restricted by transmission probability constraints. Distributed rate maximization under uncertainty is considered to achieve both efficiency and fairness among users. We propose a distributed scheme where users adjust their transmission probability to maximize their rates according to the current network state, while maintaining the desired load on the channels. We show that our approach plays an important role in achieving the Nash bargaining solution among users. Sequential and parallel algorithms are proposed to achieve the target solution in a distributed manner. The efficiencies of the algorithms are demonstrated through both theoretical and simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM Transactions on Networking, part of this work was presented at IEEE CAMSAP 201

Collaborative Spectrum Sensing from Sparse Observations in Cognitive Radio Networks

Spectrum sensing, which aims at detecting spectrum holes, is the precondition for the implementation of cognitive radio (CR). Collaborative spectrum sensing among the cognitive radio nodes is expected to improve the ability of checking complete spectrum usage. Due to hardware limitations, each cognitive radio node can only sense a relatively narrow band of radio spectrum. Consequently, the available channel sensing information is far from being sufficient for precisely recognizing the wide range of unoccupied channels. Aiming at breaking this bottleneck, we propose to apply matrix completion and joint sparsity recovery to reduce sensing and transmitting requirements and improve sensing results. Specifically, equipped with a frequency selective filter, each cognitive radio node senses linear combinations of multiple channel information and reports them to the fusion center, where occupied channels are then decoded from the reports by using novel matrix completion and joint sparsity recovery algorithms. As a result, the number of reports sent from the CRs to the fusion center is significantly reduced. We propose two decoding approaches, one based on matrix completion and the other based on joint sparsity recovery, both of which allow exact recovery from incomplete reports. The numerical results validate the effectiveness and robustness of our approaches. In particular, in small-scale networks, the matrix completion approach achieves exact channel detection with a number of samples no more than 50% of the number of channels in the network, while joint sparsity recovery achieves similar performance in large-scale networks.Comment: 12 pages, 11 figure

Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View

Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin

An Online Parallel and Distributed Algorithm for Recursive Estimation of Sparse Signals

In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel estimation scheme that consists in solving a sequence of $\ell_{1}$-regularized least-square problems approximately. The proposed scheme is novel in three aspects: i) all elements of the unknown vector variable are updated in parallel at each time instance, and convergence speed is much faster than state-of-the-art schemes which update the elements sequentially; ii) both the update direction and stepsize of each element have simple closed-form expressions, so the algorithm is suitable for online (real-time) implementation; and iii) the stepsize is designed to accelerate the convergence but it does not suffer from the common trouble of parameter tuning in literature. Both centralized and distributed implementation schemes are discussed. The attractive features of the proposed algorithm are also numerically consolidated.Comment: Part of this work has been presented at The Asilomar Conference on Signals, Systems, and Computers, Nov. 201

Affine Projection Algorithm Based Decision Fusion for Cooperative Spectrum Sensing In Cognitive Radio Networks

Spectrum sensing is a main function in cognitive radio networks to detect the spectrum holes or unused spectrum. Cooperative spectrum sensing schemes are recently suggested and they provide fast and accurate results. In this paper, we suggested a new adaptive and cooperative spectrum sensing technique based on the affine projection algorithm (APA). In this method, each secondary user (SU) takes a binary decision by its local sensing of the spectrum using energy detector. Local decisions are then forward to the fusion center (FC), where definitive decision is taken on the status of the spectrum using adaptive filters. In our suggested technique, APA updates the weights of the adaptive filter by using the current and the 1 delayed input signal vectors. Simulation results indicate that the suggested approach provides faster convergence speed and less steady state mean square error than the existing methods that are based on the normalized least mean square (NLMS) or the so-called kernel least mean square (KLMS) algorithm