The Radar Ambiguity Function - MATLAB Simulations for Radar Systems Design - page 217

x 6 x 5

++ 1

(4.58)
It follows that the shift register which generates a maximal length sequence is
shown in Fig. 4.22.

Σ

o utput

123456

Figure 4.22. Linear shift register whose characteristic polynomial is
.

x 6 x 5

++ 1

One of the most important issues associated with generating a maximal
length sequence using a linear shift register is determining the characteristic
polynomial. This has been and continues to be a subject of research for many
radar engineers and designers. It has been shown that polynomials which are
both irreducible (not factorable) and primitive will produce maximal length
shift register generators.

A polynomial of degree n is irreducible if it is not divisible by any polyno-
mial of degree less than n. It follows that all irreducible polynomials must have
an odd number of terms. Consequently, only linear shift register generators
with an even number of feedback connections can produce maximal length
sequences. An irreducible polynomial is primitive if and only if it divides
for no value of

x n 2 n

– 1 n less than – 1 .

MATLAB Function Ðprn_ambig.mÑ

The MATLAB function Ðprn_ambig.mÑ calculates and plots the ambiguity
function associated with a given PRN code. It is given in Listing 4.10 in Sec-
tion 4.6. The syntax is as follows:

[ambiguity] = prn_ambig(u)

where u is a vector that defines the input maximal length code (sequence) in
terms of Ð1ÓsÑ and Ð-1Ós.Ñ Fig. 4.23 shows the output of this function for

u31 = [1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 1 1 -1 -1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 -1]

Fig. 4.24 is similar to Fig. 4.23, except in this case the input maximal length
sequence is

u15=[1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 -1 -1]