Sparse-reconstruction-based direction of arrival, polarisation and power estimation using a cross-dipole array

This study demonstrates how the multiple parameters can be exactly obtained in sparse signal reconstruction framework using a cross-dipole array. Instead of using subspace-based methods, first direction of arrival (DOA) estimation of all sources is obtained, by solving a weighted `group lasso´ problem in second-order statistics domain. Then a truncated ℓ₁-function is utilised to approximate ℓ₀-norm, and an unbiased estimator is successively proposed to obtain the polarisation and power estimation. A statistical technique is introduced to select the regularisation parameter properly. Compared with the estimation of signal parameters via rotational invariance techniques-based algorithm, the proposed algorithm can provide improved resolution and estimation accuracy. Furthermore, the proposed algorithm can identify two sources with the same DOA successfully, provided that the polarisation parameters are different.