A computationally efficient blind estimator of polynomial phase signals observed by a sensor array

Consider estimating the parameters of polynomial phase signals observed by an antenna array given that the array manifold is unknown (e.g., uncalibrated array). To date, only an approximated maximum likelihood estimator (AMLE) was suggested, however, it involves a multidimensional search over the entire coefficient space. Instead, we propose a two-step estimation approach, termed as SEparate-EStimate (SEES): First, the signals are separated with a blind source separation technique by exploiting the constant modulus property; Then, the coefficients of each polynomial are estimated using a least squares method from the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces and its computational complexity increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulations show that the proposed estimator achieves the Cramér-Rao lower bound (CRLB) at moderate or high signal to noise ratio (SNR).