PSEUDO NOISE SEQUENCE IN SPREAD SPECTRUM
A coded sequence of 1s and 0s with specific autocorrelation
properties is known as a pseudonoise (PN) sequence.
Both the transmitter and receiver are informed of the PN
sequence, which is a deterministic, periodic signal. The signal appears to have
the statistical properties of sampled white noise since the signal
is deterministic. Thus to an unauthorized listener, it appears as a
random signal.
Randomness
properties
The
important qualities of a truly random binary sequence are present in PN
sequences. A random binary sequence is one in which the existence of either a 1
or a 0 is equally likely. As a test for the appearance of randomness, any
periodic binary sequence can be given three fundamental qualities. They are as
follows:
1) Balance Property:
The number of 1s in each period of the sequence is always one
more than the number of 0s. This property is termed as 'the balance
property'.
2) Run
Property:
Onehalf of
the runs of 1s and 0s in each period of the sequence is of length one,
onefourth of the runs of length two, oneeighth of the runs of length three,
and so on. The Run property is what it's called. A run is a sequence of binary
digits of a single type. A new run starts when the alternate digit occurs in a
sequence. The number of digits in the run determines its length.
3)
Correlation Property
A sequence's
autocorrelation function is binaryvalued and periodic. This property is termed
as 'the correlation property.'
Pseudo Noise (PN) sequence generator
In spread spectrum communications, the class of sequences
utilized is frequently periodic, indicating that a series of 1s and 0s repeats
itself perfectly with a defined time. A frequently used periodic PN sequence is
represented by the maximum length sequence, a sort of cyclic coding.
Shift register circuits having feedback from one or more stages may readily construct maximum length sequences, often known as PN sequences. Figure 1 shows a PN sequence generator with a threestage shift register.
Figure 1: PN Sequence or Maximum Length Sequence Generator
T Three flipflops
are controlled by a single timing clock in the 3stage shift register. Each
flipflop's state is moved to the next one with every clock pulse. Modulo2
addition of the outputs of flipflops x2 and x3 yields the feedback function.
The input of the first flipflop, x1, receives the feedback term. By noting the
contents of flipflop x3 at each clock pulse, the maximum length sequence output
is determined. The resulting maximumlength sequence is always periodic, with a
period of:
N = 2^{m}1
 (1)
where m represents
the length of the shift register. Here, m = 3 and so N = 2^{3}1 = 7.
If we assume that the shift register contents are initially
111 for the PN sequence generator shown in Figure 2, the contents will vary
with each clocking pulse as given in Table 1.
Table 1 operation of the PN sequence generator
Shifts 
x’_{1} = X_{2} Ꚛ X_{3} 
Shift register contents 

X_{1} 
X_{2} 
X_{3} 

0 

1 
1 
1 
1 
1 Ꚛ 1 = 0 
0 
1 
1 
2 
1 Ꚛ 1 = 0 
0 
0 
1 
3 
0 Ꚛ 1 = 1 
1 
0 
0 
4 
0 Ꚛ 0 = 0 
0 
1 
0 
5 
1 Ꚛ 0 = 1 
1 
0 
1 
6 
0 Ꚛ 1 = 1 
1 
1 
0 
7 
1 Ꚛ 0 = 1 
1 
1 
1 
As a result, the output PN sequence for one period is 1 1 1 0
0 1 0, with a length of 7. The sequence will be repeated after that.
Key Points to Consider
• The PN sequence has a length of N = 2^{m}1, where
m is the number of shift register stages.
• Every 'N' clock cycles, the PN sequence repeats itself.
• The PN sequence is an NRZ type pulse signal, as shown in Figure 2, with logic 1 represented by + 1 and logic 0 represented by 1.
Figure 2: PN Sequence Waveform
• The chip
duration T_{c} is the time it takes for each bit to complete. The
number of bits (chips) per second is specified as the chip rate R_{c}.
T_{c }=
1/𝑅_{𝑐} (or) R_{c} = 1/𝑇_{𝑐}  (5.2)
• T_{b},
the period of the PN sequence can be determined as:
T_{b} = NT_{c}
• The autocorrelation function R(τ) is a twovalued periodic function of time.
Figure 3: Autocorrelation Function of a PN Sequence
Demerits
of spread spectrum system
When a
transmitter employs a spreading code, the result is a wideband broadcast signal
that seems noise to a receiver who is unaware of the spreading code. Naturally,
this technology gives better interference protection. However, there are
certain drawbacks to this strategy.
They are:
• Larger
transmission bandwidth
• System Complexity
• Large
processing time
As a result,
spread spectrum systems are only used for situations where transmission
security is essential.