Construction of deterministic sensing matrix and its application to DOA estimation

Compressive sensing (CS) has emerged as a novel sampling framework which enables sparse signal acquisition and reconstruction with fewer measurements below the Nyquist rate. An important issue for CS is the construction of measurement matrix or sensing matrix. A new deterministic sensing matrix, named as OOC-B, is proposed by exploiting optical orthogonal codes (OOCs), Bernoulli matrix and Singer structure, which has the entries of 0, +1 and-1 before normalization. We have proven that the designed deterministic matrix is asymptotically optimal. In addition, the proposed deterministic sensing matrix is applied to direction of arrival (DOA) estimation of narrowband signals by CS arrays (CSA) processing and CS recovery. Theoretical analysis and simulation results show that the proposed sensing matrix has good performance for DOA estimation. It is very effective for simplifying hardware structure and decreasing computational complexity in DOA estimation by CSA processing. Besides, lower root mean square error (RMSE) and bias are obtained in DOA estimation by CS recovery.