Generalized rotation measurement matrix and its application in underwater echo signals

According to the properties and requirements of the measurement matrix in compressed sensing, a generalized rotation measurement matrix based on the rotation deterministic measurement matrix is proposed by adjusting the coefficients of each column element of the measurement matrix to enhance the correlation between columns, and it is applied to compressed sensing observations of underwater echo signals. By observing the variations of the matching degree and relative error with compression ratio in the condition of noise free, and the variations of the matching degree and output SNR with compression ratio in the condition of input SNR=4, 0 and -3 dB, the performances of different measurement matrices in underwater echo signals processing are compared. Simulation results show that compared with some deterministic measurement matrices such as Hadamard and the random measurement matrices represented by Gaussian, the generalized rotation measurement matrices have a great improvement in output signal-to-noise ratio, matching degree and relative error. Also the generalized rotation matrix is a deterministic measurement matrix, which is convenient for engineering implementation.