In recent years, in telecommunication and military applications, using an array system due to the development in the design and implementation of array antennas on a large scale, has been the main subject of speculation. Although increasing the number of antennas can improve the performance of these systems, however, may be due to the acquisition timing constraints or hardware limitations, it is not possible to collect all the samples, or due to the failure in the acquisition process in some antennas, a part of the data may be lost. In such circumstances, the estimation methods of the signal characteristics are encountered a problem and are not applicable without any pre-processing techniques. Thus, the main question is that whether it is possible to estimate the missing samples from the available ones and extract the sig nal characteristics? In this thesis, we first introduce the matrix completion (MC) theory in order to estimate the unknown entries of underlying low-rank matrix from the available ones. Then, the necessary conditions and several optimization methods provided for matrix completion, which are the basis for the study of the other approaches, will be ex- plained. After that, in the missing data scenario, the applicability of MC in direction of arrival (DOA) estimation via the MUSIC algorithm is evaluated through the simulation results. In addition to comparing the performance of MC algorithms together in term of the runtime and their mean square error (MSE) of DOAs, we also suggest to use an information theoretic criteria as a substitute for the embedded rank estimator of these MC algorithms in order to improve their performance. At last, we review several sampling schemes that are provided to reduce the number of received samples from the array antennas in accordance to the MC conditions, and then propose a new structured sampling method, which in addition to the simple implementation structure, also reduces the sampling rate and the number of required RF-chains. Key Words : Matrix Completion (MC), Low-Rank Matrix, Direction of Arrival (DOA).
