Research on the Measurement Matrix Apply to Estimate the Angle Using Compressed Sensing

A DOA estimation algorithm based on global information’s compression projection is proposed to solve the problem that the estimated accuracy of the DOA is low after compressing the received data. Firstly, the vandermonde matrix which is sparse in the space has been proposed and it is used to get the Gram matrix of the model, and then the non-diagonal elements of the Gram matrix are compressed to obtain the target matrix. In order to optimize the Gram matrix, Gradient descent method with Wolfson condition is used to reduce the difference between the target matrix and the Gram matrix. The measurement matrix corresponds to the resulting Gram matrix can retain more global information. Finally, the received data is compressed by this matrix, and projected into the space of the measurement matrix. The angle estimation result is obtained by sparse reconstruction. Simulation results show that the accuracy of the proposed algorithm is higher than the direct reconstruction results of the source signal under the same conditions, when the signal-to-noise ratio is greater than -6dB, the estimated success rate of the data compression projection is 100%, and the performance is superior.