Pseudo-random numbers are statistically random values that are derived from a known starting point and can be repeated. They are useful for processes that require randomness. PN sequences are generated using a linear feedback shift-register circuit with M registers. At each clock pulse, the data shifts one position and a PN datum is output from the last register. The sequence is defined by a generator polynomial where the coefficients determine which registers are used to generate the next value. Autocorrelation and cross-correlation can be used to measure the similarity between a time series and lagged or shifted versions of itself.

1. PN Sequence
Unit – 5
Presented by
Mrs. M.P.Sasirekha

2. Pseudo-random-numbers
• A set of values or elements that is statistically random, but it is
derived from a known starting point and is typically repeated
over and over. Pseudo-random numbers provide necessary
values for processes that require randomness, such as creating
test signals or for synchronizing sending and receiving devices
in a spread spectrum transmission. It is called "pseudo"
random, because the algorithm can repeat the sequence, and
the numbers are thus not entirely random

5. • Autocorrelation is a mathematical representation of the degree
of similarity between a given time series and a lagged version of
itself over successive time intervals.
• In signal processing, cross-correlation is a measure of
similarity of two series as a function of the displacement of one
relative to the other.

6. PN Sequence Generation
• A PN data sequence is an M-sequence that is generated using
a linear feedback shift-register circuit.
• M is the number of shift registers. D(M) is the mth shift register,
and {c1,c2,…,cM} are the coefficients of them.
• At each clock pulse, the data in the registers will right shift once
and one PN datum is output from register D(M).

8. • Mathematically, the procedure can be defined by a generator
polynomial. {c1,c2,…,cM} becomes the coefficients of the
generator polynomial. For instance, the polynomial for PN9
is x9+x5+1, therefore, M=9 and
• c9=1, c5=1, ci∈{1~9},and i≠9,i≠5=0
• The PN sequence, {an}, 0 ≤ n < 2M, is generated by the equation
below.

9. PN Sequence Generation
• where, the initial state of registers {D1,D2…DM} is the seed.
D(M) stores the LSB of the seed, and D1 stores the MSB of the
seed. For example, if the seed is 10 (binary form 1010), the
initial state in register {D1,D2…DM} is {0 0 0 0 0 1 0 1 0}.
• The figure below shows the initial state of each register for PN9.
It’s obvious that LSB of the seed comes out first.
• Afterwards, the registers store previously generated
data, Dm=an-m,m∈(1,M).

10. The generator polynomial for PN15 is x15+x14+1, therefore
M=15 and c15=1, c14=1, ci∈{1~15},and i≠15,i≠14=0.

13. Thank you