PRBS Pseudo Random Binary Sequence

A Pseudo Random Binary Sequence (PRBS) is a deterministic binary sequence that appears random but is generated using a specific algorithm. PRBS is widely used in various fields, including telecommunications, cryptography, and testing of digital systems. In this article, we will explore the concept of PRBS, its properties, applications, and some common generation techniques.

A binary sequence is a sequence of 0s and 1s. A random binary sequence is a sequence where each bit has an equal probability of being 0 or 1, and the bits are independent of each other. However, truly random sequences are difficult to generate, especially in digital systems, where determinism is desirable.

PRBS offers a solution by generating a sequence that exhibits pseudo-randomness, meaning it has properties similar to a random sequence but is deterministic and can be reproduced. These sequences are valuable for various applications, such as data scrambling, channel estimation, error detection, and testing digital systems.

A PRBS is defined by its length, often denoted as N, which represents the number of bits in the sequence before it repeats. The length of a PRBS is typically a power of two, which allows for efficient implementation in digital systems. The most commonly used PRBS lengths are 2^m - 1, where m is an integer.

PRBS sequences have several properties that make them useful. Firstly, they exhibit a balanced number of 0s and 1s, which is essential for maintaining the integrity of the transmitted or stored data. Secondly, PRBS sequences have good autocorrelation properties, meaning the correlation between a sequence and its delayed version is low. This property is valuable in applications such as channel estimation, where interference from previous symbols can degrade the performance. Additionally, PRBS sequences have a flat power spectrum, which is beneficial in spread spectrum communication and other frequency-based applications.

Now let's discuss some common techniques for generating PRBS sequences. One of the simplest methods is the shift register-based approach. It involves using a linear feedback shift register (LFSR), which is a shift register with feedback connections that introduce some non-linearity into the sequence generation process.

An LFSR consists of a shift register with several stages, each holding a bit. The output bit is usually the rightmost bit of the register. At each clock cycle, the bits in the register are shifted to the right, and the feedback connections determine the value of the input bit. The feedback connections can be defined by a polynomial, often represented as a tap sequence, where the bits at specific stages are XORed together to form the input bit.

The choice of the tap sequence determines the properties of the generated PRBS sequence. Commonly used tap sequences include maximal-length sequences (MLS) and primitive polynomials. An MLS is a sequence that repeats after N - 1 clock cycles, where N is the length of the sequence. Primitive polynomials generate sequences with good randomness properties but may not have the maximum period.

Another method for generating PRBS sequences is the Galois LFSR. It uses the same principle as the shift register-based approach but with a different implementation. Instead of shifting the bits to the right, the Galois LFSR shifts the bits to the left. The feedback connections in the Galois LFSR are defined by a tap sequence, similar to the shift register-based approach.

The choice between the shift register-based approach and the Galois LFSR depends on the specific requirements of the application. Both methods have their advantages and trade-offs in terms of implementation complexity, clock frequency, and randomness properties.

In conclusion, PRBS sequences are deterministic binary sequences that exhibit pseudo-randomness. They are valuable in various applications where randomness is required, such as data scrambling, channel estimation, and testing of digital systems. PRBS sequences can be generated using techniques like shift register-based approaches and Galois LFSRs. The choice of generation technique depends on the desired properties and requirements of the application. Overall, PRBS sequences are an essential tool in the field of digital communication and system testing, providing a balance between randomness and determinism.