Spatial evolutionary spectrum for DOA estimation and blind signal separation

In this paper, we combine the concepts of evolutionary spectrum and array processing.We present a cross-power evolutionary periodogram for both direction-of-arrival (DOA) estimation and blind separation of nonstationary signals. We model nonstationary signals received by each array sensor as a sum of complex sinusoids with time-varying amplitudes. These amplitudes carry information about the DOA that may also be time varying. We first estimate the time-varying amplitudes using linear estimators obtained by minimizing the mean-squared error. Then, using the estimated time-varying amplitudes, we estimate the evolutionary cross-power distributions of the sensor data. Next, using cross-power estimates at time–frequency points of interest, we estimate the DOA’s using one of the existing estimation methods. If the directions are time varying, we choose the time–frequency points around the time of interest to estimate instantaneous source locations. If the sources are stationary, all time–frequency points of interest can be combined for the estimation of fixed directions. Whitening and subspace methods are used to find the mixing matrix and separate nonstationary signals received by the array.We present examples illustrating the performances of the proposed algorithms.