Hi Nauka,
In a communication system using a Pseudo-Noise (PN) sequence for spreading the signal, the length of the PN sequence is determined by the properties of the Linear Feedback Shift Register (LFSR) that generates it. This involves the generator polynomial and the initial state.Understanding PN Sequence Length
1.Generator Polynomial:
- The generator polynomial defines how the feedback is applied in the LFSR. In your case, the polynomial is represented as ([1, 1, 0, 0, 0, 1, 1]), which corresponds to (x^6 + x^5 + 1).
- The degree of the polynomial is 6 (the highest power of (x)), which typically means the LFSR has 6 stages.
2. Initial State:
- The initial state of the LFSR is given as ([1, 0, 1, 0, 0, 1]).
- This initial state is the starting configuration of the LFSR's stages.
3. Sequence Length:
- The maximum possible length of a PN sequence generated by an LFSR is (2^n - 1), where (n) is the degree of the polynomial. For a polynomial of degree 6, the maximum length is (2^6 - 1 = 63).
- This length is achieved if the polynomial is primitive. A primitive polynomial ensures that the LFSR cycles through all possible states except the all-zero state.
Measuring the PN Sequence Length
To determine the actual length of the sequence generated by your specific setup, you can simulate the LFSR operation. Here's a step-by-step approach:
Simulate the LFSR:
- Use the generator polynomial and initial state to simulate the LFSR. Shift the bits according to the feedback defined by the polynomial until the register returns to the initial state.
Count the Steps:
- Count the number of shifts (or steps) it takes for the LFSR to return to the initial state. This count is the length of the PN sequence.
Hope this helps.
