We observe that that autocorrelation of m-sequence carries some similarities with that of a random sequence. The normalized autocorrelation of an m-sequence of length, takes two values. Typically, the autocorrelation function of m-sequences are two valued. The coefficients of the characteristic polynomial is and let’s start the generator with initial seed. Let’s generate an m-sequence of period using the order characteristic polynomial. It uses the sequence_correlation function defined in section 12.2.1 in the book (click here). With the initial state of the shift registers represented by the vector, and is an dimensional vector given byĬorrelation properties of m-sequences are demonstrated here. The function implements the LFSR structure Figure 1 by using the following equivalent matrix equation: If we could exploit the linear recursion property of LFSR and its equivalent matrix model, the LFSR can be implemented using only one for loop as shown in the Matlab function given in the book (click here). Table 1: Primitive polynomials up to degree L=12 used in m-sequence generatorįor implementation in Matlab, the LFSR structure can be coded in a straightforward manner that involves at least two for loops. What follows in this discussion is the implementation of an m-sequence generator based on Galois LFSR architecture (Figure 1). The Galois LFSR structure is a high speed implementation structure, since it has less clock to clock delay path compared to its Fibonacci equivalent. There are two types of LFSR structures available for implementation – 1) Galois LFSR and 2) Fibonacci LFSR. Maximum length sequences are generated using linear feedback shift registers (LFSR) structures that implement linear recursion. Wireless Communication Systems in Matlab (second edition), ISBN: 979-8648350779 available in ebook (PDF) format and Paperback (hardcopy) format.A detailed treatment on the subject of Galois field theory can be found in references and.

Maximum-length sequences (also called as m-sequences or pseudo random (PN) sequences) are constructed based on Galois field theory which is an extensive topic in itself. Key focus: Model and simulate m-sequence generator using Galois linear feedback shift registers (LFSR) that implement linear recursion.

Linear feedback shift registers