Direction of arrival estimation with missing data via matrix completion

In this paper, we consider the problem of direction of arrival (DOA) estimation on a large sensor array, in the case of missing data resulting from chain failure or employed sub-sampling schemes. Since the missing measurements impair the performance of DOA estimation, we propose to recover the missing entries from the available ones, by applying matrix completion (MC) techniques. We use three well-known MC algorithms SVT, LMaFit, and OptSpace for imputation of the missing entries and then employing MUSIC algorithm to estimate the angles of impinging signals. In addition, we improve the performance of MC techniques, by employing the information theoretic based source enumeration methods, such as MDL and AIC, instead of the heuristic and imprecise rank estimator in current methods. The mean-square error (MSE) of DOA estimation is taken as an assessment criterion for comparing the performance of the aforementioned MC algorithms. Simulation results are conducted to show that in addition to performance improvement achieved by imputation of the missing measurements, the LMaFit algorithm with the proposed rank estimator has the lowest runtime and DOA MSE comparing to the other well-known MC algorithms.