Abstract
Recently, a novel maximum-likelihood sequence estimation (MLSE) equalizer was reported that avoids the explicit estimation of the channel impulse response. Instead, it is based on the fact that the (noise-free) channel outputs, needed by the Viterbi algorithm, coincide with the points around which the received (noisy) samples are clustered and can thus be estimated directly with the aid of a supervised clustering method. Moreover, this is achieved in a computationally efficient manner that exploits the channel linearity and the symmetries underlying the transmitted signal constellation. The resulting computational savings over the conventional MLSE equalization scheme are significant even in the case of relatively short channels where MLSE equalization is practically applicable. It was demonstrated, via simulations, that the performance of this algorithm is close to that using a least-squares (LS) channel estimator, although its computational complexity is even lower than that of the least-mean squares (LMS)-trained MLSE equalizer. This paper investigates the relationship of the center estimation (CE) part of the proposed equalizer with the LS method. It is proved that, when using LS with the training sequence employed by CE, the two methods lead to the same solution. However, when LS is trained with random data, it outperforms CE, with the performance difference being proportional to the channel length. A modified CE method, called MCE, is thus developed, that attains the performance of LS with perfectly random data, while still being much simpler computationally than classical LS estimation. Through the results of this paper, CE is confirmed as a methodology that combines high performance, simplicity, and low computational cost, as required in a practical equalization task. An alternative, algebraic viewpoint on the CE method is also provided.
Highlights
One of the major problems encountered in the receiver design of any communication system is that of combatting Inter-Symbol Interference (ISI), arising due to limited channel bandwidth or multipath propagation
The equalizers based on the Maximum Likelihood Sequence Estimation (MLSE) scheme [12] are implemented via the Viterbi algorithm (VA) and they require the channel impulse response (CIR) to be known
It belongs to the class of the so-called Clustering-Based Sequence Equalizers (CBSE) (e.g., [3]), since it is based on the idea that the set of all possible channel output values, needed at the Viterbi stage, are the centers of the clusters formed by the received observations at the receiver front end and can be estimated from the noisy observations via a clustering approach
Summary
One of the major problems encountered in the receiver design of any communication system is that of combatting Inter-Symbol Interference (ISI), arising due to limited channel bandwidth or multipath propagation. A novel MLSE equalizer was proposed, that circumvents the problem of explicit CIR parametric modelling, leading to substantial computational savings [6]–[10] It belongs to the class of the so-called Clustering-Based Sequence Equalizers (CBSE) (e.g., [3]), since it is based on the idea that the set of all possible (noiseless) channel output values, needed at the Viterbi stage, are the centers of the clusters formed by the received observations at the receiver front end and can be estimated from the noisy observations via a clustering approach. It has been observed [9, 10] that the proposed CE technique exhibits a similar to Least Squares (LS) performance, despite its low computational complexity, which is even lower than that of the LMS-based method commonly employed in standard MLSE equalizers [9] These computational savings are due to the fact that the new setting allows for an efficient exploitation of the symmetries in the input constellation. The computational requirements of the two methods are compared, clearly demonstrating the computational advantage of CE over the classical LS method
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