DNA Genetic Optimization Bat Algorithm Based Fractionally Spaced Multi-modulus Blind Equalization Algorithm

Abstract

A DNA genetic optimization bat algorithm based fractionally spaced multi-modulus blind equalization algorithm (DNA-GBA-FS-MMA) is proposed. This proposed algorithm uses fractionally spaced equalizer(FSE) with ability to oversample to input signals to get more channel information and compensate for channel with the depth spectrum zero, employs DNA genetic optimization bat algorithm(DNA-GBA) for searching the global optimal position vector, which are simultaneously regarded as the real and imaginary parts of the initial weight vector of multi-modulus blind equalization algorithm(MMA) in order to improve convergence speed and reduce mean square error(MSE). Simulation results show that DNA-GBA-FS-MMA has the best equalization effect. Introduction Multi-modulus blind equalization algorithm(MMA) can simultaneously carry out the function of blind equalization and carrier recovery in the absence of the carrier-recovery system[1]. Fractionally spaced equalizer(FS) combined with the MMA can reduce the mean square error (MSE) and the calculation load via oversampling to the input signals[2], but its convergence speed is still slow. DNA genetic algorithm(DNA-GA) uses DNA molecular operation to improve crossover, mutation, and selection operations of the genetic algorithm(GA), as well as strong global search ability, whereas the echo location characteristics of bat algorithm (BA) can avoid falling into local searching of the searching process and improve the success rate of searching global optimal position vector. In this paper, after we introduce DNA-GA into BA, a DNA genetic optimization bat algorithm based fractionally spaced multi-modulus blind equalization algorithm(DNA-GBA-FS-MMA) is proposed to search the global optimal position vector, which is used to optimize the weight vector of the MMA. Simulation results verify the effectiveness of DNA-GBA-FS-MMA algorithm. DNA Genetic Optimization Bat Algorithm Based Fractionally Spaced MMA When we introduce the DNA-GA into the BA, the DNA-GA based BA is called as DNA genetic optimization bat algorithm(DNA-GBA). When we introduce the DNA-GBA and the MMA into fractionally spaced equalizer, DNA genetic optimization bat algorithm based fractionally spaced multi-modulus blind equalization algorithm(DNA-GBA-FS-MMA) is obtained and shown in Figure 1. Fig.1(a) is a principle of the fractionally spaced MMA(FS-MMA), Fig.1(b) corresponds to the MMA module in Fig.1(a).In the MMA module, the wR(k) and wI(k) are updated as follows: ( 1) ( ) 4 ( ) ( ) ( 1) ( ) 4 ( ) ( ) R R R R I I I I k k e k k k k e k k μ μ + = −   + = −  w w y w w y (1) where μ is the step-size, 0 ≤ μ ≤ 1. To simplify calculation and reduce the MSE, we introduce T/2 FSE into MMA to obtain more detailed channel information and compensate the fuzzy channels better. FSE based multi-modulus algorithm(FS-MMA) can decrease the MSE, but its convergence speed is still slow. International Industrial Informatics and Computer Engineering Conference (IIICEC 2015) © 2015. The authors Published by Atlantis Press 581 For the purpose of accelerating convergence speed and reducing the MSE, we use the BA to a(k) n1(k) z1(k) y1(k) c1(k) n2(k) c2(k) y2(k) z(k)