To reduce mutual coupling of a two-level nested array (TLNA) with an even number of sensors, we propose an improved array configuration that exhibits all the good properties of the prototype optimal configuration under the constraint of a fixed number of sensors N and achieves reduction of mutual coupling. Compared with the prototype optimal TLNA (POTLNA), which inner level and outer level both have N/2 sensors, those of the improved optimal TLNA (IOTLNA) are N/2-1 and N/2+1. It is proved that the physical aperture and uniform degrees of freedom (uDOFs) of IOTLNA are the same as those of POTLNA, and the number of sensor pairs with small separations of IOTLNA is reduced. We also construct an improved optimal second-order super nested array (SNA) by using the IOTLNA as the parent nested array, termed IOTLNA-SNA, which has the same physical aperture and the same uDOFs, as well as the IOTLNA. Numerical simulations demonstrate the better performance of the improved array configurations.

A novel matrix completion ESPRIT (MC-ESPRIT) algorithm is proposed to estimate the direction of arrival (DOA) with nonuniform linear arrays (NLA). By exploiting the matrix completion theory and the characters of Hankel matrix, the received data matrix of an NLA is tranformed into a two-fold Hankel matrix, which is a treatable for matrix completion. Then the decision variable can be reconstructed by the inexact augmented Lagrange multiplier method. This approach yields a completed data matrix, which is the same as the data matrix of uniform linear array (ULA). Thus the ESPRIT-type algorithm can be used to estimate the DOA. The MC-ESPRIT could resolve more signals than the MUSIC-type algorithms with NLA. Furthermore, the proposed algorithm does not need to divide the field of view of the array compared to the existing virtual interpolated array ESPRIT (VIA-ESPRIT). Simulation results confirm the effectiveness of MC-ESPRIT.

Direction of arrival (DOA) estimation as a fundamental issue in array signal processing has been extensively studied for many applications in military and civilian fields. Many DOA estimation algorithms have been developed for different application scenarios such as low signal-to-noise ratio (SNR), limited snapshots, etc. However, there are still some practical problems that make DOA estimation very difficult. One of them is the correlation between sources. In this paper, we develop a sparsity-based method to estimate the DOA of coherent signals with sparse linear array (SLA). We adopt the off-grid signal model and solve the DOA estimation problem in the sparse Bayesian learning (SBL) framework. By considering the SLA as a ‘missing sensor’ ULA, our proposed method treats the output of the SLA as a partial output of the corresponding virtual uniform linear array (ULA) to make full use of the expanded aperture character of the SLA. Then we employ the expectation-maximization (EM) method to update the hyper-parameters and the output of the virtual ULA in an iterative manner. Numerical results demonstrate that the proposed method has a better performance in correlated signal scenarios than the reference methods in comparison, confirming the advantage of exploiting the extended aperture feature of the SLA.

An underdetermined direction of arrival estimation method based on signal sparsity is proposed when independent and coherent signals coexist. Firstly, the estimate of the mixing matrix of the impinging signals is obtained by clustering the single source points which are detected by the ratio of time-frequency transforms of the received signals. Then, each column vector of the mixing matrix is processed by exploiting the forward and backward vectors in turn to obtain the directions of arrival of all signals. The number of independent signals and coherent signal groups that can be estimated by the proposed method can be greater than the number of sensors. The validity of the method is demonstrated by simulations.