Person:

Babadi, Behtash

In this paper, we study the problem of distributed spectrum allocation under a vertical spectrum sharing scenario in a cognitive radio network. The secondary users share the spectrum licensed to the primary user by observing the activity statistics of the primary users, and regulate their transmission strategy in order to abide by the spectrum sharing etiquette. When the primary user is inactive in a subset of the available frequency bands, from the perspective of the secondary users the problem reduces to a distributed horizontal spectrum sharing. For a specific class of networks, the latter problem is addressed by the recently proposed GADIA algorithm [1]. In this paper, we present analytical and numerical results on the performance of the GADIA algorithm in conjunction with the above-mentioned vertical spectrum sharing scenario. These results reveal near-optimal performance guarantees for the overall vertical spectrum sharing scenario.

In this paper, we study the problem of anomaly detection in sparse channel tracking applications via the (l_1)-regularized least squares adaptive filter (SPARLS). Anomalies arise due to unexpected adversarial changes in the channel and quick detection of these anomalies is desired. We first prove analytically that the prediction error of the SPARLS algorithm can be substantially lower than that of the widely-used Recursive Least Squares (RLS) algorithm. Furthermore, we present Receiver Operating Characteristic (ROC) curves for the detection/false alarm trade-off of anomaly detection in a sparse multi-path fading channel tracking scenario. These curves reveal the considerable advantage of the SPARLS algorithm over the RLS algorithm.

We develop a recursive ${cal L}_{1}$-regularized least squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight vector output stream and produces its estimate using an expectation-maximization type algorithm. We prove the convergence of the SPARLS algorithm to a near-optimal estimate in a stationary environment and present analytical results for the steady state error. Simulation studies in the context of channel estimation, employing multipath wireless channels, show that the SPARLS algorithm has significant improvement over the conventional widely used recursive least squares (RLS) algorithm in terms of mean squared error (MSE). Moreover, these simulation studies suggest that the SPARLS algorithm (with slight modifications) can operate with lower computational requirements than the RLS algorithm, when applied to tap-weight vectors with fixed support.

Greedy algorithms form an essential tool for compressed sensing. However, their inherent batch mode discourages their use in time-varying environments due to significant complexity and storage requirements. In this paper two existing powerful greedy schemes developed in the literature are converted into an adaptive algorithm which is applied to estimation of a class of nonlinear communication systems. Performance is assessed via computer simulations on a variety of linear and nonlinear channels; all confirm significant improvements over conventional methods.

In this paper, the problem of distributed dynamic frequency allocation is considered for a canonical communication network, which spans several networks such as cognitive radio networks and digital subscriber lines (DSLs). A greedy asynchronous distributed interference avoidance (GADIA) algorithm for horizontal spectrum sharing has been proposed that achieves performance close to that of a centralized optimal algorithm. The convergence of the GADIA algorithm to a near-optimal frequency allocation strategy is proved and several asymptotic performance bounds have been established for various spatial configurations of the network nodes. Furthermore, the near-equilibrium dynamics of the GADIA algorithm has been studied using the Glauber dynamics, by identifying the problem with the antiferromagnetic inhomogeneous long-range Potts model. Using the near-equilibrium dynamics and methods from stochastic analysis, the robustness of the algorithm with respect to time variations in the activity of network nodes is studied. These analytic results along with simulation studies reveal that the performance is close to that of an optimum centralized frequency allocation algorithm. Further simulation studies confirm that our proposed algorithm outperforms the iterative water-filling algorithm in the low signal-to-interference-plus-noise ratio (SINR) regime, in terms of achieved sum rate, complexity, convergence rate, and robustness to time-varying node activities.

In this paper, we consider the estimation of sparse nonlinear communication channels. Transmission over the channels is represented by sparse Volterra models that incorporate the effect of Power Amplifiers. Channel estimation is performed by compressive sensing methods. Efficient algorithms are proposed based on Kalman filtering and Expectation Maximization. Simulation studies confirm that the proposed algorithms achieve significant performance gains in comparison to the conventional non-sparse methods.