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

Abstract

Direction‐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.