This paper proposes a neuro-fuzzy filter for equalization of time-varying channels. Additionally, it proposes to tune the equalizer with a hybrid algorithm between Genetic Algorithms (GA) and Bacteria Foraging (BFO), termed as GBF. The major advantage of the method developed in this paper is that all parameters of the neuro-fuzzy network, including the rule base, are tuned simultaneously through the proposed hybrid algorithm of genetic Algorithm and bacteria foraging. The performance of the Neuro-Fuzzy equalizer designed using the proposed approach is compared with Genetic algorithm based equalizers. The results confirm that the methodology used in the paper is much better than existing approaches. The proposed hybrid algorithm also eliminates the limitations of GA based equalizer, i.e. the inherent characteristic of GA, i.e. GAs risk finding a sub-optimal solution.
Top1. Introduction
Communication channels medium are often modeled as band limited channel for which the channel impulse response is that of an ideal low pass filter. When a sequence of symbols is transmitted, the low pass filtering of the channel distorts the transmitted symbols over successive time intervals causing symbols spread and overlap with adjacent symbols. This resulting linear distortion is known as inter symbol interference (ISI). In addition nonlinear distortion is also caused by cross talk in the channel and use of amplifiers. Adaptive channel equalizers play an important role in recovering digital information from digital communication channels. Preparta (1989) had suggested a simple and attractive scheme for dispersal recovery of digital information based on the Discrete Fourier Transform. Subsequently Gibson et al. (1991) have reported an efficient nonlinear ANN structure for reconstructing digital signals, which have been passed through a dispersive channel and corrupted with additive noise. In a recent publication (Voulgaris & Hadjicostics, 2004) the authors have proposed optimal preprocessing strategies for perfect reconstruction of binary signals from a dispersive communication channels. Touri et al. (2006) have developed deterministic worst-case framework for perfect reconstruction of discrete data information from digital communication channels. Preparta (1989) had suggested a simple and attractive scheme for dispersal recovery of digital information based on the Discrete Fourier Transform. Subsequently Gibson et al. (1991) have reported an efficient nonlinear ANN structure for reconstructing digital signals, which have been passed through a dispersive channel and corrupted with additive noise.
In a recent publication (Voulgaris & Hadjicostics, 2004) the authors have proposed optimal preprocessing strategies for perfect reconstruction of binary signals from a dispersive communication channels. Touri et al. (2006) have developed deterministic worst case frame work for perfect reconstruction of discrete data transmission through a dispersive communication channel. In recent past new adaptive equalizers have been suggested using soft computing tools such as Artificial Neural Network (ANN), PPN and the FLANN (Patra, Pal, Baliarsingh, & Panda, 1999). It has been reported that these methods are best suited for nonlinear and complex channels. Recently, Chebyshev Artificial Neural Network has also been proposed for nonlinear channel equalization (Patra, Poh, Chaudhari, & Das, 2005). The drawback of these methods is that the estimated weights may likely fall to local minima during training. For this reason Genetic Algorithm (GA) has been suggested for training adaptive channel equalizers (Panda, Majhi, Mohanty, Choubey, & Mishra, 2006). The main attraction of GA lies in the fact that it does not rely on Newton-like gradient-descent methods, and hence there is no need for calculation of derivatives. This makes them less likely to be trapped in local minima. But only two parameters of GA, the crossover and the mutation, help to avoid local minima problem. There are still some situations when the weights in GA optimization are trapped to local minima.
In recent days Bacterial Foraging Optimization (BFO) has been proposed (Passino, 2002) and has been applied for signal recovery (Acharya, Panda, & Lakshmi, 2009; Majhi & Panda, 2010; Guzmán, Delgado, & De Carvalho, 2009; Shoorehdeli, Teshnehlab, & Sedigh, 2009). The BFO is a useful alternative to GA and requires less number of computations. In addition BFO is also derivative free optimization technique. The number of parameters that are used for searching the total solution space are much higher in BFO compared to those in GA. Hence the possibility of avoiding the local minimum is higher in BFO. In this scheme, the foraging (methods for locating, handling and ingesting food) behavior of E. Coli bacteria present in our intestines is mimicked.