Low-complexity DCD-based sparse recovery algorithms

Sparse recovery techniques find applications in many areas. Real-time implementation of such techniques has been recently an important area for research. In this paper, we propose computationally efficient techniques based on dichotomous coordinate descent (DCD) iterations for recovery of sparse complex-valued signals. We first consider $\ell_2 \ell_1$ optimization that can incorporate \emph{a priori} information on the solution in the form of a weight vector. We propose a DCD-based algorithm for $\ell_2 \ell_1$ optimization with a fixed $\ell_1$-regularization, and then efficiently incorporate it in reweighting iterations using a \emph{warm start} at each iteration. We then exploit homotopy by sampling the regularization parameter and arrive at an algorithm that, in each homotopy iteration, performs the $\ell_2 \ell_1$ optimization on the current support with a fixed regularization parameter and then updates the support by adding/removing elements. We propose efficient rules for adding and removing the elements. The performance of the homotopy algorithm is further improved with the reweighting. We then propose an algorithm for $\ell_2 \ell_0$ optimization that exploits homotopy for the $\ell_0$ regularization; it alternates between the least-squares (LS) optimization on the support and the support update, for which we also propose an efficient rule. The algorithm complexity is reduced when DCD iterations with a \emph{warm start} are used for the LS optimization, and, as most of the DCD operations are additions and bit-shifts, it is especially suited to real time implementation. The proposed algorithms are investigated in channel estimation scenarios and compared with known sparse recovery techniques such as the matching pursuit (MP) and YALL1 algorithms. The numerical examples show that the proposed techniques achieve a mean-squared error smaller than that of the YALL1 algorithm and complexity comparable to that of the MP algorithm

Multi-Step Knowledge-Aided Iterative ESPRIT for Direction Finding

In this work, we propose a subspace-based algorithm for DOA estimation which iteratively reduces the disturbance factors of the estimated data covariance matrix and incorporates prior knowledge which is gradually obtained on line. An analysis of the MSE of the reshaped data covariance matrix is carried out along with comparisons between computational complexities of the proposed and existing algorithms. Simulations focusing on closely-spaced sources, where they are uncorrelated and correlated, illustrate the improvements achieved.Comment: 7 figures. arXiv admin note: text overlap with arXiv:1703.1052