An emerging alliance: higher order statistics should partner conventional statistics in digital signal processing applications

The conjecture of the paper is that higher order statistics are best used in combination with conventional second order statistics; not in isolation. This is demonstrated by showing some established and new examples where this proposal has been utilised. A conventional, second order, spectral estimator stabilises the statistical performance of higher order spectral estimation techniques. The performance of an adaptation algorithm based upon a higher order error norm is regularised by the inclusion of a second order moment. The statistical properties of AR parameter estimates are improved through a combination of second and third order statistics. Finally, a two-stage adaptive equalisation algorithm uses conventional statistics to remove amplitude distortion and higher order statistics to overcome a non-minimum phase channel each working with preferred signals. Simulation studies are included to support the assertion