What is a PN Sequence?
A PN sequence, or Pseudo-Noise sequence, is a deterministic sequence of binary values (0s and 1s) that appears to be random but is generated by a specific algorithm or generator. Although it mimics the statistical properties of noise, it is entirely predictable and repeatable. PN sequences are widely used in telecommunications, particularly in spread spectrum systems like CDMA (Code Division Multiple Access), radar systems, and cryptography.
Generation of PN Sequences
PN sequences are typically generated using Linear Feedback Shift Registers (LFSRs). An LFSR is a shift register whose input bit is a linear function of its previous state. In most cases, this linear function is the XOR (exclusive OR) of selected bits of the register. The initial state of the register is known as the “seed,” and the resulting sequence is determined by the feedback taps and the seed value.
The structure of an LFSR used to generate a PN sequence includes:
- A register consisting of several flip-flops (usually D flip-flops) connected in series.
- A feedback network using XOR gates that taps specific bits of the register.
- A clock that shifts the bits at each cycle, generating a new output bit per shift.
Characteristics of a PN Sequence
A good PN sequence exhibits certain mathematical properties that make it ideal for spread spectrum communications and other signal processing applications. These include:
| Characteristic | Description |
|---|---|
| Balance Property | The number of 1s and 0s in the sequence differs by at most one, creating a balanced signal. |
| Run Length Property | All possible run lengths of consecutive 0s or 1s occur as expected in a random sequence. |
| Auto-Correlation Property | The sequence has a sharp peak when correlated with itself and low values otherwise, aiding in synchronization. |
| Periodicity | The sequence repeats after a certain number of bits, defined by the register size and tap positions. |
Applications of PN Sequences
PN sequences are used in a variety of communication and signal processing systems due to their noise-like properties and predictable nature. Some of the most common applications include:
- CDMA Systems: Each user is assigned a unique PN sequence to spread and despread their signal, allowing multiple users to share the same frequency band.
- GPS Systems: Each satellite transmits a unique PN code, enabling receivers to distinguish between different satellite signals.
- Radar: PN sequences modulate the transmitted pulse to improve range resolution and reduce interference.
- Secure Communications: Used for data scrambling and encryption due to their deterministic yet seemingly random nature.
- Wireless Networks: PN codes are used in 3G systems like WCDMA for scrambling and channel separation.
Types of PN Sequences
There are several types of PN sequences, each with specific use-cases and generation techniques. Common types include:
- Maximal Length Sequences (m-sequences): Generated by LFSRs, these sequences have a period of 2n-1 for a register of length n. They are widely used due to their excellent correlation properties.
- Gold Codes: Generated by combining two m-sequences with specific phase shifts, offering better cross-correlation properties, suitable for CDMA systems.
- Kasami Sequences: Known for very low cross-correlation values, often used in more complex spread spectrum systems.
PN Sequence vs. True Random Sequence
Unlike true random sequences, which are generated from unpredictable physical processes (like thermal noise), PN sequences are completely deterministic. Given the generator and the seed, the sequence can be reproduced exactly. This determinism is crucial for communication systems, where both transmitter and receiver must use the same sequence for synchronization and decoding.
Here’s a brief comparison:
| Aspect | PN Sequence | True Random Sequence |
|---|---|---|
| Generation | Deterministic, using algorithms | Non-deterministic, using physical processes |
| Reproducibility | Yes, with same seed and method | No |
| Use in Communications | Preferred for synchronization | Rarely used due to unpredictability |
| Statistical Properties | Close to random, predictable | Truly random, not predictable |
Synchronization and Despreading Using PN Sequences
In spread spectrum communication, the receiver must align its PN generator with the incoming signal’s PN sequence. This process is called synchronization. Once synchronized, the same PN sequence is used to despread the signal, effectively extracting the original narrowband message from the spread spectrum.
Proper synchronization ensures that only signals with the correct PN code are correctly received and decoded. Signals with different codes will have low correlation, thereby appearing as noise and being filtered out.
In summary, a PN sequence is a core building block in digital communication systems, especially in those requiring robustness against interference, security, and efficient bandwidth utilization.