To address the low estimation accuracy of existing direction of arrival (DOA) algorithms under Alpha-stable distributed noise, an off-grid approximate \(l_0\) -norm algorithm based on bounded nonlinear function (BNF) and phased fractional lower order moment (PFLOM) is proposed. First, the array data is preprocessed using BNF, and its PFLOM matrix is computed to mitigate the impact of Alpha-stable distributed noise. Next, an exponential family distribution (EFD) function is constructed, and its smoothness and steepness are analyzed to select the optimal smooth function. An EFD-based approximate \(l_0\) -norm algorithm is then proposed to obtain the initial support set and sparse solution. Subsequently, the initial support set is expanded forward and backward, with the support set minimizing the residual error selected as the optimal set. The on-grid DOA estimates are determined based on the positions of the atoms in the optimal support set within the steering vector matrix. Finally, to further address the grid mismatch effects, the off-grid deviation is introduced into the sparse DOA model using the first-order Taylor expansion of the steering vector. This leads to the construction of an off-grid sparse DOA model, which is solved iteratively to estimate the coarse DOA and off-grid deviation, ultimately yielding the off-grid DOA estimate. Lastly, computer simulations confirm that the proposed algorithm achieves high estimation accuracy and success rates under Alpha-stable distributed noise.
