Nonlinear orthogonal spreading sequence design for third generation DS-CDMA systems

Binary sequences with ideal autocorrelation can be defined as the incidence functions for Hadamard difference sets. The authors consider a length of the form M=2^m-1, m=nk, such that N=2ⁿ-1 and T=M/N are relatively prime. Width analyses show that a N×T generating array can be formed with shifted (and decimated) versions of subsequences of length N as its columns except for zero column(s), to generate a Hadamard difference set sequence. The subsequences can be generated by utilising a general model for shift register sequence generators associated with shift sequences, σ and γ, which represent primitive connections and initial loadings of the shift registers, respectively