Fast PN sequence correlation by using FWT

Abstract

A simple relation between Walsh functions and PN (pseudonoise) sequences is derived. It is shown that by using a suitable permutation a set of discrete Walsh functions-sequences can be transformed into the set of different phase shifts of a single PN sequence. A matched filter-correlator based on the fast Walsh transform (FWT) which exploits this property is proposed. This correlator can be efficiently applied to continuous wave radar signal compression and direct-sequence spread-spectrum code acquisition. This method is shown to be much more efficient than the method based on the FFT (fast Fourier transform), which includes two FFTs and an array multiplication. As opposed to the FFT-based algorithm, the proposed method has no multiplications and the total number of operations is approximately five times smaller. As the number of operations per input samples is small, the proposed algorithm is adequate for LSI implementation even for high bit rates and for long sequences.<>