Tensor Decomposition-based Beamspace Esprit Algorithm for Multidimensional Harmonic Retrieval

Beamspace processing is an efficient and commonly used approach in harmonic retrieval (HR). In the beamspace, measurements are obtained by linearly transforming the sensing data, thereby achieving a compromise between estimation accuracy and system complexity. Meanwhile, the widespread use of multi-sensor technology in HR has highlighted the necessity to move from a matrix (two-way) to tensor (multi-way) analysis. In this paper, we propose a beamspace tensor-ESPRIT for multidimensional HR. In our algorithm, parameter estimation and association are achieved simultaneously

Sparse Bayesian Learning Approach for Discrete Signal Reconstruction

This study addresses the problem of discrete signal reconstruction from the perspective of sparse Bayesian learning (SBL). Generally, it is intractable to perform the Bayesian inference with the ideal discretization prior under the SBL framework. To overcome this challenge, we introduce a novel discretization enforcing prior to exploit the knowledge of the discrete nature of the signal-of-interest. By integrating the discretization enforcing prior into the SBL framework and applying the variational Bayesian inference (VBI) methodology, we devise an alternating update algorithm to jointly characterize the finite alphabet feature and reconstruct the unknown signal. When the measurement matrix is i.i.d. Gaussian per component, we further embed the generalized approximate message passing (GAMP) into the VBI-based method, so as to directly adopt the ideal prior and significantly reduce the computational burden. Simulation results demonstrate substantial performance improvement of the two proposed methods over existing schemes. Moreover, the GAMP-based variant outperforms the VBI-based method with an i.i.d. Gaussian measurement matrix but it fails to work for non i.i.d. Gaussian matrices.Comment: 13 pages, 7 figure

Convergence Analysis of Consensus-ADMM for General QCQP

We analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the augmented Lagrangian function value is monotonically non-increasing as long as the augmented Lagrangian parameter is chosen to be sufficiently large. Simulation results show that the augmented Lagrangian function is bounded from below when the matrix in the quadratic term of the objective function is positive definite. In such a case, the consensus-ADMM is convergent.Comment: 13 pages, 5 figure

Sparse Array Beamformer Design via ADMM

In this paper, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method utilizes the alternating direction method of multipliers (ADMM), and admits closed-form solutions at each ADMM iteration. The algorithm convergence properties are analyzed by showing the monotonicity and boundedness of the augmented Lagrangian function. In addition, we prove that the proposed algorithm converges to the set of Karush-Kuhn-Tucker stationary points. Numerical results exhibit its excellent performance, which is comparable to that of the exhaustive search approach, slightly better than those of the state-of-the-art solvers, including the semidefinite relaxation (SDR), its variant (SDR-V), and the successive convex approximation (SCA) approaches, and significantly outperforms several other sparse array design strategies, in terms of output SINR. Moreover, the proposed ADMM algorithm outperforms the SDR, SDR-V, and SCA methods, in terms of computational complexity.Comment: Accepted by IEEE Transactions on Signal Processin