Array Signal Processing via Sparsity-Inducing Representation of the Array Covariance Matrix

A method named covariance matrix sparse representation (CMSR) is developed to detect the number and estimate the directions of multiple, simultaneous sources by decomposing the array output covariance matrix under sparsity constraint. In CMSR the covariance matrix elements are aligned to form a new vector, which is then represented on an overcomplete spatial dictionary, and the signal number and directions are finally derived from the representation result. A hard threshold, which is selected according to the perturbation of the covariance elements, is used to tolerate the fitting error between the actual and assumed models. A computation simplification technique is also presented for CMSR in special array geometries when more than one pair of sensors has equal distances, such as the uniform linear array (ULA). Moreover, CMSR is modified with a blind-calibration process under imperfect array calibration to enhance its adaptation to practical applications. Simulation results demonstrate the performance of CMSR.