SIS-BAM Algorithm for Angular Parameter Estimation of 2-D Incoherently Distributed Sources

For two-dimensional (2-D) incoherently distributed sources, this paper presents an effective angular parameter estimation method based on shift invariant structure (SIS) of the beamspace array manifold (BAM), named as SIS-BAM algorithm. In the proposed method, a shift invariance structure (SIS) of the observed vectors is firstly established utilizing a generalized array manifold of an uniform linear orthogonal array (ULOA). Secondly, based on Fourier basis vectors and the SIS, a beamspace transformation matrix can be performed. It projects received signals into the corresponding beamspace, so as to carry out dimension reduction of observed signals in beamspace domain. Finally, according to the SIS of beamspace observed vectors, the closed form solutions of the nominal azimuth and elevation are derived. Compared with the previous works, the presented SIS-BAM method provides better estimation performance, for example: 1) the computational complexity is reduced due to dealing with low-dimension beamspace signals and avoiding spectral search; 2) it can not only improve the angular parameter estimation accuracy but also have excellent robustness to the change of signal-to-noise ratio (SNR) and snapshot number. The theoretical analysis and simulation results confirm the effectiveness of the proposed method.

Estimation for Two-Dimensional Incoherently Distributed Source in Double L-Shape Arrays

Distributed sources can be regarded as an assembly of point sources within a spatial distribution. In this paper, we explore the estimation of the two-dimensional incoherently distributed sources using double L-shape arrays. The rotational invariance properties of the nominal elevation and nominal elevation are firstly obtained by taking first-order Taylor series expansions with regard to the generalized steering vectors of two pairs of parallel subarrays. The rotation operators can be solved based on signal subspace. Then the nominal elevation and nominal elevation can be obtained from parameters matching method. Estimation of direction of arrival can be used in multi-source scenario and needn't peak-finding search. Lastly the angular spreads can be solved through two-dimensional Capon search based on nominal angles. The simulation experiments show that the proposed method has good performance on the estimation of two-dimensional incoherently distributed sources. Investigating different experimental conditions, sources with different angular spreads, simulations are conducted to validate better estimation accuracy of the proposed method.

A 2D Nested Array Based DOA Estimator for Incoherently Distributed Sources via Sparse Representation Utilizing L1-Norm

Nested arrays are sparse arrays composed of subarrays with nonuniform sensor spacing. Compared with traditional uniform arrays, nested arrays have more degree of freedoms (DOFs) and larger apertures. In this paper, a nested array has been proposed as well as a direction-of-arrival (DOA) estimation method for two-dimensional (2D) incoherently distributed (ID) sources. A virtual array is firstly obtained through vectorization of the cross-correlation matrix of subarrays. Sensor positions of the virtual array and the optimal configuration of the nested array are derived next. Then rotational invariance relationship for generalized steering matrix of the virtual array with respect to nominal azimuth is deduced. According to the rotational invariance relationship, sparse representation model under l1-norm constraint is established, which is resolved by transferring the objective function to second-order cone constraints and combining a estimation residual error constraint for receive vector of the virtual array. Simulations are conducted to investigate the effectiveness of the proposed method in underdetermined situation and examine different experiment factors including SNR, snapshots, and angular spreads as well as sensor number of subarrays. Results show that the proposed method has better performance than uniform parallel arrays with the same number of sensors.