Cancellation of polarized impulsive noise using an azimuth-dependent conditional mean estimator

The separation of signals from noisy vector measurements is obtained by taking advantage of the Middleton Class A model of noise amplitude and the correlation of the components of the noise process due to their polarization. The signal is assumed to be white Gaussian. Noise is a superposition of M non-Gaussian processes, each with a fixed azimuth of polarization. Neither the number of processes (M) nor their azimuths are known. The separation of signal from noise is based on the conditional mean estimators. In addition to the optimum estimator, which can be derived from a knowledge of the bivariate density functions, two suboptimum solutions for polarized noise are discussed: the circularly symmetric estimator and the azimuth-dependent one. Circular symmetry is suitable for the nonpolarized noise vector, whereas the azimuth-dependent estimator is tailored to polarized noise. The azimuth-dependent approach consists of two steps: first, the data vector process is discretized into azimuth sectors, and then, in those classified as noisy, the signal is separated from the noise. Statistical model parameters of random processes are estimated by using the optimum classification, based on the likelihood ratio test (decision-directed method). Iterative whitening methods are also discussed for correlated vector signals. Numerical examples show the effectiveness of the above technique in canceling polarized noise.