DOA Estimation Resolution Research Articles

Direction‐of‐arrival estimation for wideband linear frequency modulated signals with weighted l1‐norm in the fractional Fourier domain

AbstractDirection‐of‐arrival (DOA) estimation methods for wideband linear frequency modulated (LFM) signals based on fractional Fourier transform (FRFT) typically use the single snapshot vector in the fractional Fourier (FRF) domain. However, the low‐rank problem of the second‐order statistics in the single snapshot vector can decrease the DOA estimation resolution and cause issues in DOA estimation for coherent sources. In order to address these problems, a weighted l1‐norm method based on FRFT is proposed. The proposed method utilises the energy aggregation property of FRFT for LFM signals. This allows for obtaining a single snapshot vector in the FRF domain. Subsequently, a sparse representation DOA estimation model is established by taking advantage of the sparsity of the target distribution in the spatial domain. The DOA estimation is then obtained by minimising the l1‐norm. To further enhance the DOA estimation performance, we construct a matrix by rearranging the elements of the eigenvectors corresponding to the nonzero eigenvalue of the covariance matrix in the FRF domain. The rank of this matrix is equal to the number of sources, ensuring the orthogonality of the subspace obtained by the reconstructed matrix. Finally, a weighted matrix is constructed by exploiting the subspace orthogonality principle to adjust the sparsity penalty of the l1 constraint model. Simulation results demonstrate that our method is capable of achieving high angular resolution and accuracy even at low SNR and can process coherent signals directly.

A Two-Dimensional DOA Estimation Method Based on Virtual Extension of Sparse Array

The interelement spacing of a coprime array breaks through the half-wavelength limitation, so that a larger array aperture can be obtained with a fixed number of array elements. In this paper, the symmetry of the noncircular signal is used to virtually expand the L-shaped array into an orthogonal cross array. Furthermore, the virtual received signal of the augmented array is obtained by the second-order statistic of the received data. Decoupling and dimension reduction of elevation and azimuth are realized by a z-axis subarray and y-axis subarray. Finally, the sparse reconstruction of the signal is realized by the minimum absolute convergence and selection operator method. This method can enlarge the aperture and freedom of array and has higher accuracy and resolution of DOA estimation. It has the advantages of automatic parameter pairing without additional pairing operation and is effective for coherent and incoherent signals. The final numerical simulation results prove the effectiveness of the method in this paper.

A Low Computational Complexity SML Estimation Algorithm of DOA for Wireless Sensor Networks

We address the problem of DOA estimation in positioning of nodes in wireless sensor networks. The Stochastic Maximum Likelihood (SML) algorithm is adopted in this paper. The SML algorithm is well-known for its high resolution of DOA estimation. However, its computational complexity is very high because multidimensional nonlinear optimization problem is usually involved. To reduce the computational complexity of SML estimation, we do the following work. (1) We point out the problems of conventional SML criterion and explain why and how these problems happen. (2) A local AM search method is proposed which could be used to find the local solution near/around the initial value. (3) We propose an algorithm which uses the local AM search method together with the estimation of DML or MUSIC as initial value to find the solution of SML. Simulation results are shown to demonstrate the effectiveness and efficiency of the proposed algorithms. In particular, the algorithm which uses the local AM method and estimation of MUSIC as initial value has much higher resolution and comparable computational complexity to MUSIC.