Wireless Network Stability in the SINR Model

We study the stability of wireless networks under stochastic arrival processes of packets, and design efficient, distributed algorithms that achieve stability in the SINR (Signal to Interference and Noise Ratio) interference model. Specifically, we make the following contributions. We give a distributed algorithm that achieves $\Omega(\frac{1}{\log^2 n})$-efficiency on all networks (where $n$ is the number of links in the network), for all length monotone, sub-linear power assignments. For the power control version of the problem, we give a distributed algorithm with $\Omega(\frac{1}{\log n(\log n + \log \log \Delta)})$-efficiency (where $\Delta$ is the length diversity of the link set).Comment: 10 pages, appeared in SIROCCO'1

Beyond Geometry : Towards Fully Realistic Wireless Models

Signal-strength models of wireless communications capture the gradual fading of signals and the additivity of interference. As such, they are closer to reality than other models. However, nearly all theoretic work in the SINR model depends on the assumption of smooth geometric decay, one that is true in free space but is far off in actual environments. The challenge is to model realistic environments, including walls, obstacles, reflections and anisotropic antennas, without making the models algorithmically impractical or analytically intractable. We present a simple solution that allows the modeling of arbitrary static situations by moving from geometry to arbitrary decay spaces. The complexity of a setting is captured by a metricity parameter Z that indicates how far the decay space is from satisfying the triangular inequality. All results that hold in the SINR model in general metrics carry over to decay spaces, with the resulting time complexity and approximation depending on Z in the same way that the original results depends on the path loss term alpha. For distributed algorithms, that to date have appeared to necessarily depend on the planarity, we indicate how they can be adapted to arbitrary decay spaces. Finally, we explore the dependence on Z in the approximability of core problems. In particular, we observe that the capacity maximization problem has exponential upper and lower bounds in terms of Z in general decay spaces. In Euclidean metrics and related growth-bounded decay spaces, the performance depends on the exact metricity definition, with a polynomial upper bound in terms of Z, but an exponential lower bound in terms of a variant parameter phi. On the plane, the upper bound result actually yields the first approximation of a capacity-type SINR problem that is subexponential in alpha

Jamming-Resistant Learning in Wireless Networks

We consider capacity maximization in wireless networks under adversarial interference conditions. There are n links, each consisting of a sender and a receiver, which repeatedly try to perform a successful transmission. In each time step, the success of attempted transmissions depends on interference conditions, which are captured by an interference model (e.g. the SINR model). Additionally, an adversarial jammer can render a (1-delta)-fraction of time steps unsuccessful. For this scenario, we analyze a framework for distributed learning algorithms to maximize the number of successful transmissions. Our main result is an algorithm based on no-regret learning converging to an O(1/delta)-approximation. It provides even a constant-factor approximation when the jammer exactly blocks a (1-delta)-fraction of time steps. In addition, we consider a stochastic jammer, for which we obtain a constant-factor approximation after a polynomial number of time steps. We also consider more general settings, in which links arrive and depart dynamically, and where each sender tries to reach multiple receivers. Our algorithms perform favorably in simulations.Comment: 22 pages, 2 figures, typos remove

Convex Relaxation Algorithms for Energy-Infeasibility Tradeoff in Cognitive Radio Networks

In cognitive radio networks, uncontrolled access of secondary users degrades the performance of primary users and can even lead to system infeasibility, as the secondary users are allowed to transmit simultaneously on a shared spectrum. We study the feasibility of the total energy consumption minimization problem subjecting to power budget and Signal-to-Interference-plus-Noise Ratio (SINR) constraints. Finding the largest set of secondary users (i.e., the system capacity) that can be supported in the system is hard to solve due to the nonconvexity of the cardinality objective. We formulate this problem as a vector-cardinality optimization problem, and propose a convex relaxation that replaces the objective with a continuous and convex function. Motivated by the sum-of-infeasibilities heuristic, a joint power and admission control algorithm is proposed to compute the maximum number of secondary users that can be supported. Numerical results are presented to show that our algorithm is theoretically sound and practically implementable