Truncated nuclear norm matrix recover algorithm for direction-of-arrival estimation

The received signal may suffer from continuous missing data due to reasons such as antenna damage, which affects the performance of the direction-of-arrival (DOA) estimation. In order to achieve a better DOA estimation performance, this paper presents a matrix recovery DOA estimation method based on the truncated nuclear norm (TrNN) robust principal component analysis (RPCA). Firstly, the received signal recovery and noise reducing problem of a single snapshot is modeled as a low-rank matrix RPCA recovery problem, and the F-norm is used to constrain the noise entries so as to better separate the low-rank received signal from the noise. Secondly, TrNN is introduced into the low-rank matrix RPCA model in order to make better use of the a priori information on the number of signal sources in the received signal. In the process of TrNN optimization, only large singular values are used corresponding to the number of sources for processing, which reduces the computational complexity of the nuclear norm optimization to some extent without losing the target signal information. The proposed algorithm is used to complete the data of all snapshots. Finally, the DOA parameters are estimated by means of subspace theory. Simulation results show that the proposed algorithm achieves better angular parameter estimation performance with associated low-rank matrix recovery at low SNR.