Adaptive detection and extraction of sparse signals embedded in colored Gaussian noise using higher order statistics

A cumulant-based adaptive approach for the detection and extraction of sparse signals embedded in colored Gaussian noise is presented. In this approach, the extracted signal is obtained by adaptive FIR filtering of the noisy signal. Coefficients of the adaptive filter are updated using a recursive algorithm based on a sum of cumulants of orders k⩾3 of the input signal. This is to ensure super sufficient detection of different sparse signals and to ensure efficient removal of colored Gaussian noise. It is shown that when the sparse pulse is absent, the coefficients of the adaptive filter converge to zero. However, when the sparse pulse exists the FIR adaptive filter converges to a type of signal-matched filter. Simulation and experimental results are included to show the high efficiency of the presented approach in comparison with the adaptive short-term correlation counterpart