Optimal linear quadratic detector for deterministic signals in impulsive noise

The detection of a known signal in additive noise consisting of a Poisson impulse process and an independent white Gaussian noise (WGN) is considered. Expressions for the fourth order cumulant of the Poisson impulse process is obtained in terms of the rate of the process and fourth moment of the impulse amplitudes. The linear quadratic detector (LQD) that maximizes the deflection is determined by the higher order moments of the combined noise. It is shown that the LQD consists of a matched filter and a quadratic filter which depends on the weighted signal correlation matrix, ss^T. The performance of the LQD is evaluated by simulation.