This paper proposes two methods for robust Capon beamforming. One is for the doubly constrained robust Capon beamforming problem, where the unit modular constraints on the elements of the steering vector of interest are enforced to circumvent the look direction error or phase perturbations of the signal-of-interest; and another addresses robust beamforming in impulsive noise environment, where we consider the lp-norm minimization (0 < p < 2) of the output while constraining the mainlobe response ripple term. We apply the splitting technique to simplify the resultant nonconvex optimization problem and solve it using alternating direction method of multipliers. The performance of the proposed methods is demonstrated via numerical examples.

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks.

This paper develops a distributed dictionary learning algorithm for sparse representation of the data distributed across nodes of sensor networks, where the sensitive or private data are stored or there is no fusion center or there exists a big data application. The main contributions of this paper are: 1) we decouple the combined dictionary atom update and nonzero coefficient revision procedure into two-stage operations to facilitate distributed computations, first updating the dictionary atom in terms of the eigenvalue decomposition of the sum of the residual (correlation) matrices across the nodes then implementing a local projection operation to obtain the related representation coefficients for each node; 2) we cast the aforementioned atom update problem as a set of decentralized optimization subproblems with consensus constraints. Then, we simplify the multiplier update for the symmetry undirected graphs in sensor networks and minimize the separable subproblems to attain the consistent estimates iteratively; and 3) dictionary atoms are typically constrained to be of unit norm in order to avoid the scaling ambiguity. We efficiently solve the resultant hidden convex subproblems by determining the optimal Lagrange multiplier. Some experiments are given to show that the proposed algorithm is an alternative distributed dictionary learning approach, and is suitable for the sensor network environment.