Multi-Modulus Frequency Domain Blind Equalization Algorithms Based On Lower Order Statistics

For the research of traditional blind equalization algorithm, channel noise is assumed to be as Gaussian noise, but in recent years a large number of studies show that some noise in actual channel often show strong pulse characteristic, they do not fully obey the Gauss distribution model, so a generalized Gauss distribution model called a stable distribution is introduced into the field of signal processing. In the a stable distribution noise, the two order statistics of signal are not exist, the signal processing methods based on the two order statistics of signal are not applicable, so it is necessary to adopt fractional lower order statistics (FLOS) for signal analysis and processing.When constant modulus algorithm is used to equalize multi-modulus signals, there are some defects of the slow convergence rate and big steady mean square error, and its performance degenerates in a stable distribution noise, in order to overcome these disadvantages, basing on traditional blind equalization algorithm, this paper studies some frequency domain multi-modulus blind equalization algorithms which are based on FLOS by means of fast fourier transform (FFT), wavelet transform (WT), modulus transform (MT), adaptive method (AM) and fuzzy neural network(FNN). The paper mainly includes the following points:(1) Wavelet frequency domain constant modulus blind equalization algorithm based on fractional lower order statistics is studied by using orthogonal WT and FFT, this algorithm can suppress a stable distribution noise effectively, reduce the amount of calculation, speed up the convergence rate and reduce the steady state error.(2) Wavelet frequency domain weighted multi-modulus blind equalization algorithm based on lower order statistics is studied by using frequency domain weighted multi-modulus algorithm(FWMMA), the algorithm can effectively equalize the multi-modulus signal compared with the constant modulus algorithm, it has a faster convergence speed and smaller steady state error, hardware switching judgment algorithm is introduced into FWMMA, a wavelet hardware switching judgment frequency domain weighted multi-modulus algorithm based on lower order statistics is studied, and the performance of algorithm is significantly improved.(3) By using MT to changes the multi-modulus of multi-modulus signal to single modulus, modulus transform wavelet frequency domain multi-modulus blind equalization algorithm based on fractional lower order statistics is studied, the algorithm can not only efficiently equalize multi-modulus signal, but also reduce the amount of calculation compared with FWMMA.(4) Wavelet frequency domain adaptive multi-modulus blind equalization algorithm based on fractional lower order statistics is studied by introducing an adaptive β multi-modulus algorithm into the frequency domain blind equalization algorithm. Simulation results show that the algorithm can effectively equalize high order QAM signal.(5) Frequency domain blind equalization algorithm based on low order statistics and fuzzy neural network controller are combined, the fuzzy neural network controller is used to adjust the step size based on the steady-state error of algorithm and makes the algorithm achieve better convergence effect.