Suppression of Gaussian noise using cumulants: a quantitative analysis

Higher-order-statistics (HOS) are being used in many areas of digital signal processing, e.g. in the field of array processing. The main aim is often to suppress Gaussian noise. Mostly, the corresponding algorithms are applied to short data blocks, because only then the stationarity of the data needed for cumulant estimation is given. In many cases, not enough attention is paid to the fact that for short data blocks the suppression of Gaussian noise is small compared to the estimation error made because of the higher order of the cumulants. The property of cumulants used to suppress Gaussian noise is studied in detail. With an algorithm for direction-of-arrival (DOA) estimation in the field of array processing, the estimation errors that occur when using HOS are compared with the estimation errors that occur when using 2nd order statistics. A quantitative result is given to show that for short data blocks the suppression of Gaussian noise with HOS doesn't lead to a better result than using 2nd order statistics.