Aperiodic properties of generalized binary Rudin-Shapiro sequences and some recent results on sequences with a quadratic phase function

This paper addresses the problem of designing good spreading sequences for CDMA systems that have small-valued auto- and cross-correlation functions. In contrast to the usual mini-max criteria, the l² criteria of goodness axe used to assess correlation properties of spreading sequences. To motivate it, a direct evidence is given to demonstrate the utility of the l² criteria in the context of CDMA performance. Following, these criteria are applied to two types of known unit-magnitude sequences: generalized binary Rudin-Shapiro sequences, and sequences with quadratic phase function. The construction rule of the well-known binary Rudin-Shapiro sequences is based on a recursion formula that starts with the Kronecker sequences. It is shown that the asymptotic limits (N→∞) of l² criteria obtained for original Rudin-Shapiro sequences are also valid in case of two arbitrary sequences obtained by means of the same recursion formula as long as the initial sequences are complementary. As to the sequences with quadratic phase function, the upper and lower bounds on the inverse merit-factor are proved to decrease with the order √N+1, which indicates excellent auto-correlation properties of the sequence.