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

Abstract

The generation of binary sequences that exhibit the characteristics of higher order white noise signals is considered in this paper. Maximal length sequences fail to approximate higher order white noise signals due to the existence of peaks in their higher order statistics. Three classes of binary sequences are examined in detail: dual-BCH sequences, Gold sequences, and sequences generated by the term-by-term modulo 2 addition of two maximal length (and/or Gold) sequences whose least periods are relatively prime. The second and third-order moments of each construction are mainly investigated and useful results are obtained. It is shown that in all of the cases the spectra of the moments of order two (autocorrelation) and three are determined by the crosscorrelation function of the component sequences used in each construction. The number of peaks appearing in third-order moments is significantly reduced or vanished in all classes. These results can be readily generalized to higher order (greater than three) moments. Finally, the quality and efficiency of sequences from each class in simulating higher order white noise signals is demonstrated by providing simulation results in the context of bilinear input–output system identification.