Nonlinear channel blind equalization using hybrid genetic algorithm with simulated annealing

Modification of CFCM in The Presence of Heavy AWGN for Bayesian Blind Channel Equalizer

“…As mentioned in the introduction section, the performance of CFCM in [16] was superior to the previously developed GA based [13] [14] and conventional FCM based [15] approaches in terms of speed and accuracy. Those algorithms also estimate the optimal channel states of an unknown channel to solve the blind equalization problem.…”

“…Therefore, in the proposed algorithm, the Gaussian weighted partition matrix U G along with the conditional constraint k f , shown in (13), is exploited instead of (11) and a new center set i y is derived by (14). The resulting estimation accuracy is increased even with low SNRs and it is demonstrated in the next section.…”

“…2. This relationship of desired channel states and channel output states is always valid for the channel that has a one-toone mapping between the channel inputs and outputs [13] and is successfully used in [14]- [16]. Additionally, it can be easily extended with a higher channel order such as p=2, which is evaluated in the experimental section.…”

“…Therefore, for the calculation of partition matrix U during the clustering procedure, the Gaussian probability of each of received patterns should be involved instead of the Euclidean distance measuring. The Gaussian weighted partition matrix U G , where Euclidean distance is replaced with Gaussian probability, is described by (13) and a new center set i y is sequentially derived by (14). …”

“…The optimal solution, based on maximum likelihood sequence estimation (MLSE) [4], has a complexity that grows exponentially with the dimension of the channel impulsive response (Viterbi algorithm). Alternatively, several nonlinear detection procedures have been proposed to address this problem with varying degrees of success, such as multi-layered perceptrons (MLPs) [5], radial basis function networks (RBFNs) [6], recurrent RBFNs [7], self-organizing feature maps (SOFMs) [8] [9], wavelet neural networks [10], kernel Adeline (KA) [11], support vector machines (SVMs) [12] and Genetic Algorithms [13] [14]. Such structures usually outperform linear equalizers, especially when non-minimum phase channels are encountered.…”