Correlation properties of code division multiple-access sequences

Maximal length linear recursive sequences (m-sequences) are a class of pseudo random sequences. Frequency hopping is a popular spread spectrum technique. Frequency hopping sequences are obtained here by assigning the hopping frequencies directly to the elements of m-sequences over GF(2{dollar}sp{lcub}rm m{rcub}{dollar}) as opposed to grouping m bits of m-sequences over GF(2). Using m-sequences over GF(2{dollar}sp{lcub}rm m{rcub}{dollar}) for the hopping frequencies retains the pseudo random properties associated with m-sequences which increases the security in anti-jamming and anti-intercepting system. Modified preferred pairs of m-sequences over GF(2{dollar}sp{lcub}rm m{rcub}{dollar}) are obtained for frequency hopping sequences with reduced crosscorrelation values. Modified binary Kasami sequences are obtained from a degree n (even) primitive polynomial and a degree m {dollar}<{dollar} n (m and n have common factors) primitive polynomial which yield three-level crosscorrelation values comparable to binary Kasami sequences in some cases. Nonbinary sequences over GF(p) are investigated since they are capable of achieving a smaller maximum crosscorrelation than binary sequences for the same family size. A nonbinary Kasami set of sequences is developed here that has the same small maximum crosscorrelation as Kumar and Moreno's polyphase set of sequences. The number of levels for the nonbinary Kasami sequences is p + 2 as opposed to 2p + 2 for the polyphase sequences and can be directly implemented by a linear feedback shift register.