Pseudo Noise Sequence in Spread Spectrum

PSEUDO NOISE SEQUENCE IN SPREAD SPECTRUM

A coded sequence of 1s and 0s with specific autocorrelation properties is known as a pseudo-noise (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:

One-half of the runs of 1s and 0s in each period of the sequence is of length one, one-fourth of the runs of length two, one-eighth 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 binary-valued 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 three-stage shift register.

Figure 1: PN Sequence or Maximum Length Sequence Generator

 

T Three flip-flops are controlled by a single timing clock in the 3-stage shift register. Each flipflop's state is moved to the next one with every clock pulse. Modulo-2 addition of the outputs of flip-flops x2 and x3 yields the feedback function. The input of the first flip-flop, 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 maximum-length 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 = 2³-1 = 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 = X2 Ꚛ X3	Shift register contents
		X1	X2	X3
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 two-valued 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.