Low-rank matrix completion for array signal processing

In this paper, we propose the application of low-rank matrix completion techniques for array signal processing. Specifically, under the assumption that the number of targets is generally much smaller than the number of antennas, the received signals can form a low-rank matrix with noise. According to the recently proposed matrix completion theory, only a subset of the entries are enough to recover the whole matrix as long as certain conditions are met, thus the implementation cost of obtaining a matrix could be reduced. We prove that the matrix formed by the received signals satisfies the condition for matrix recovery. Moreover, a uniform spatial sampling (USS) method is proposed, which is easy for hardware implementation and also could take advantage of the available number of front-end elements to achieve a better performance. We analytically prove that the probability of matrix recovery failure under the USS model is asymptotically equal to that under the Bernoulli model. Simulation results demonstrate that the matrix recovery performance under the USS model is very close to that using the uniform model.