Heuristic noise driven compressed sensing for DOA estimation in phased array radar system

For the classic model in compressed sensing, y= Φ_x + e, the proposed noise driven compressed sensing method tries to build an equivalent system of the classic model as, y = (Φ+p)x = Φ_Ex, provided Px = e. This results in an equivalent sensing matrix Φ_E. Inspired by the idea that low coherence guarantees the reconstruction of the sparse vector with large probability, the equivalent sensing matrix Φ_E is updated iteratively in a Markov Chain Monte Carlo (MCMC) based framework to reduce the large coherence between a set of specific columns. At the same time, the proposed method tries to preserve most of the information of the original sensing matrix Φ via adjusting the noise related matrix P. The proposed method is utilized successfully in a phased array radar system based solely on the existing hardware. Numerical simulations show that the proposed method obtains more precise estimation of direction of arrival (DOA) using one snapshot compared with the traditional estimation methods such as Capon, APES and GLRT based on hundreds of snapshots.