TDE, DOA and related parameter estimation problems in impulsive noise

We address the problem of time-delay estimation (TDE) and direction-of-arrival (DOA) estimation in the presence of symmetric alpha-stable noise. We show that these problems can be handled by conventional correlation or cumulant based techniques, provided that the noisy signals are first passed through a generic zero-memory non-linearity. This pre-processing is also useful in the detection context. We also address the problem of blind linear system identification, where the input is an lid alpha-stable process; we show that consistent estimates of the possibly non-minimum phase ARMA parameters can be obtained by using self-normalized correlations and cumulants. Theoretical arguments are supported by simulations.