On the generation of sequences simulating higher order white noise for system identification

In this paper, we study the generation of binary sequences that exhibit the characteristics of higher order white noise signals. Three classes of binary sequences are examined: Gold sequences, dual-BCH sequences, and sequences generated by the term-by-term modulo 2 addition of two maximal length sequences whose least periods are relatively prime. It is shown that in all of the cases the autocorrelation and the higher order moment spectra are determined by the cross-correlation function of the component sequences used in each construction. The number of peaks appearing in higher order moments is significantly reduced or vanished in all classes. The quality and efficiency of sequences from each class in simulating higher order white noise signals is demonstrated by simulations in the context of bilinear input-output system identification.