Interpretation of cumulants for array processing

Cumulants can increase the effective aperture of an array, and they suppress non-Gaussian noise. Our earlier works showed these properties to be true for fourth-order cumulants. Here we show these properties are also true for third-order cumulants. We have done this because it is usually good practice to work with as lower an order cumulant as possible, if possible, in order to reduce cumulant estimation errors and to work with shorter data lengths. Our Virtual Cross-Correlation Computer (VC³), which lets us compute cross-correlations and autocorrelations for all the sensors in an array, as well as for “virtual” sensors, using cumulants, is applicable to third- and fourth-order cumulants. It leads to increased aperture (much greater for fourth-order cumulants than for third-order cumulants), a virtual ESPRIT algorithm, and non-Gaussian noise suppression