MLSE Maximum-Likelihood Sequence Estimator

Maximum-Likelihood Sequence Estimator (MLSE) is a technique for estimating the most likely sequence of symbols that generated a given received signal. MLSE is widely used in digital communication systems for detecting digital signals in the presence of noise and interference.

The basic idea behind MLSE is to model the signal received by the receiver as a sequence of symbols, each of which is drawn from a finite alphabet. The goal is to find the sequence of symbols that maximizes the likelihood of the received signal, given a statistical model of the signal and the noise.

To understand MLSE, let's first consider the basic concept of likelihood. The likelihood of a parameter given some observed data is the probability of observing the data, given that the parameter has a certain value. In other words, the likelihood function tells us how probable it is that a certain parameter value produced the observed data.

In the context of MLSE, the parameter we are interested in is the sequence of symbols that generated the received signal. The likelihood of a particular sequence of symbols given the received signal is the probability of observing the received signal, given that sequence of symbols.

In a digital communication system, the received signal is often corrupted by noise and interference. The noise and interference can cause errors in the received signal, making it difficult to accurately determine the sequence of symbols that generated the signal. To overcome this problem, MLSE uses a statistical model of the signal and the noise to estimate the most likely sequence of symbols that generated the signal.

The MLSE algorithm works by building a trellis diagram that represents all possible paths that the received signal could have taken through the digital communication system. Each path in the trellis corresponds to a particular sequence of symbols that could have generated the received signal. The trellis diagram is constructed using a forward-backward algorithm that computes the probability of each path, given the received signal and the statistical model of the signal and the noise.

The MLSE algorithm then finds the path that has the highest probability, which corresponds to the most likely sequence of symbols that generated the received signal. The algorithm uses a Viterbi decoder to find the path with the highest probability. The Viterbi decoder works by recursively computing the probability of each possible path through the trellis, and keeping track of the path with the highest probability at each step.

The MLSE algorithm can be further enhanced by using a technique called soft-decision decoding. Soft-decision decoding takes into account the reliability of each bit in the received signal, based on the strength of the signal and the noise. By using soft-decision decoding, the MLSE algorithm can more accurately estimate the most likely sequence of symbols that generated the received signal.

In summary, MLSE is a technique for estimating the most likely sequence of symbols that generated a given received signal. It is widely used in digital communication systems for detecting digital signals in the presence of noise and interference. The MLSE algorithm works by building a trellis diagram that represents all possible paths that the received signal could have taken through the digital communication system, and finding the path with the highest probability using a Viterbi decoder. Soft-decision decoding can be used to further enhance the accuracy of the MLSE algorithm.