A Direct Coarray Interpolation Approach for Direction Finding

Joint Estimation Method of DOD and DOA of Bistatic Coprime Array MIMO Radar for Coherent Targets Based on Low-Rank Matrix Reconstruction

Based on low-rank matrix reconstruction theory, this paper proposes a joint DOD and DOA estimation method for coherent targets with bistatic coprime array MIMO radar. Unlike the conventional vectorization, the proposed method processed the coprime array with virtual sensor interpolation, which obtained a uniform linear array to generate the covariance matrix. Then, we reconstructed the Toeplitz matrix and established a matrix optimization recovery model according to the kernel norm minimization theory. Finally, the reduced dimension multiple signal classification algorithm was applied to estimate the angle of the coherent targets, with which the automatic pairing of DOD and DOA could be realized. With the same number of physical sensors, the proposed method expanded the array aperture effectively, so that the degree of freedom and angular resolution could be improved significantly for coherent signals. However, the effectiveness of the method was largely limited by the signal-to-noise ratio. The superiority and effectiveness of the method were proved using simulation experiments.

Multi-Frequency Based Direction-of-Arrival Estimation for 2q-Level Nested Radar & Sonar Arrays

Direction finding is a hot research area in radar and sonar systems. In the case of q ≥ 2, the 2qth-order cumulant based direction of arrival (DOA) estimation algorithm for the 2q-level nested array can achieve high resolution performance. A virtual 2qth-order difference co-array, which contains O(N2q) virtual sensors in the form of a uniform linear array (ULA), is yielded and the Gaussian noise is eliminated. However, some virtual elements are separated by the holes among the 2qth-order difference co-array and cannot be fully used. Even though the application of the multi-frequency method for minimum frequency separation (MFMFS) can fill the holes with low computation complexity, it requires that the number of frequencies must increase with the number of holes. In addition, the signal spectra have to be proportional for all frequencies, which is hard to satisfy when the number of holes is large. Aiming at this, we further propose a multi-frequency method for a minimum number of frequencies (MFMNF) and discuss the best frequency choice under two specific situations. Simulation results verify that, compared with the MFMFS method, the proposed MFMNF method can use only one frequency to fill all the holes while achieving a longer virtual array and the DOA estimation performance is, therefore, improved.

DOA Estimation for Coprime Linear Array Based on MI-ESPRIT and Lookup Table

In order to improve the angle measurement performance of a coprime linear array, this paper proposes a novel direction-of-arrival (DOA) estimation algorithm for a coprime linear array based on the multiple invariance estimation of signal parameters via rotational invariance techniques (MI-ESPRIT) and a lookup table method. The proposed algorithm does not require a spatial spectrum search and uses a lookup table to solve ambiguity, which reduces the computational complexity. To fully use the subarray elements, the DOA estimation precision is higher compared with existing algorithms. Moreover, the algorithm avoids the matching error when multiple signals exist by using the relationship between the signal subspace of two subarrays. Simulation results verify the effectiveness of the proposed algorithm.

Two-Dimensional DOA Estimation for Three-Parallel Nested Subarrays via Sparse Representation

Nested arrays are considered attractive due to their hole-free performance, and have the ability to resolve O(N2) sources with O(N) physical sensors. Inspired by nested arrays, two kinds of three-parallel nested subarrays (TPNAs), which are composed of three parallel sparse linear subarrays with different inter-element spacings, are proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation in this paper. We construct two cross-correlation matrices and combine them as one augmented matrix in the first step. Then, by vectorizing the augmented matrix, a hole-free difference coarray with larger degrees of freedom (DOFs) is achieved. Meanwhile, sparse representation and the total least squares technique are presented to transform the problem of 2-D DOA searching into 1-D searching. Accordingly, we can obtain the paired 2-D angles automatically and improve the 2-D DOA estimation performance. In addition, we derive closed form expressions of sensor positions, as well as number of sensors for different subarrays of two kinds of TPNA to maximize the DOFs. In the end, the simulation results verify the superiority of the proposed TPNAs and 2-D DOA estimation method.

Two-Dimensional Direction-of-Arrival Fast Estimation of Multiple Signals with Matrix Completion Theory in Coprime Planar Array

In estimating the two-dimensional (2D) direction-of-arrival (DOA) using a coprime planar array, the main issues are the high complexity of spectral peak search and the limited degree of freedom imposed by the number of sensors. In this paper, we present an algorithm based on the matrix completion theory in coprime planar array that reduces the computational complexity and obtains a high degree of freedom. The algorithm first analyzes the covariance matrix of received signals to estimate the covariance matrix of a virtual uniform rectangular array, which has the same aperture as the coprime planar array. Matrix completion theory is then applied to estimate the missing elements of the virtual array covariance matrix. Finally, a closed-form DOA solution is obtained using the unitary estimation signal parameters via rotational invariance techniques (Unitary-ESPRIT). Simulation results show that the proposed algorithm has a high degree of freedom, enabling the estimation of more signal DOAs than the number of sensors. The proposed algorithm has reduced computational complexity because the spectral peak search is replaced by Unitary-ESPRIT, but attains similarly high levels accuracy to those of the 2D multiple signal classification algorithm.

Improved Coarray Interpolation Algorithms with Additional Orthogonal Constraint for Cyclostationary Signals

Many modulated signals exhibit a cyclostationarity property, which can be exploited in direction-of-arrival (DOA) estimation to effectively eliminate interference and noise. In this paper, our aim is to integrate the cyclostationarity with the spatial domain and enable the algorithm to estimate more sources than sensors. However, DOA estimation with a sparse array is performed in the coarray domain and the holes within the coarray limit the usage of the complete coarray information. In order to use the complete coarray information to increase the degrees-of-freedom (DOFs), sparsity-aware-based methods and the difference coarray interpolation methods have been proposed. In this paper, the coarray interpolation technique is further explored with cyclostationary signals. Besides the difference coarray model and its corresponding Toeplitz completion formulation, we build up a sum coarray model and formulate a Hankel completion problem. In order to further improve the performance of the structured matrix completion, we define the spatial spectrum sampling operations and the derivative (conjugate) correlation subspaces, which can be exploited to construct orthogonal constraints for the autocorrelation vectors in the coarray interpolation problem. Prior knowledge of the source interval can also be incorporated into the problem. Simulation results demonstrate that the additional constraints contribute to a remarkable performance improvement.