Wavelet Transform Multi-Modulus Blind Equalization Algorithms Based On Fractional Lower Order Statistics

In the traditional blind equalization algorithm, it was assumed that the surrounding environment noise obeyed Gaussian distribution, on the basis of this assumption, a variety of blind equalization algorithms which are based on second and higher order statistics emerged. However, impulse noise existing in real life can not be ignored, and it obeys fractional lower order a stable distribution, only its fractional lower order statistics (FLOS) exist, in this case, the blind equalization algorithms which are proposed on the basis of Gaussian assumption do not apply.In order to suppress the fractional lower order α stable distribution noise, basing on previous researches, this paper studies some blind equalization algorithms which are based on FLOS by means of wavelet transform, multi-modulus algorithm (WMMA), decision feedback algorithm (DFE) and fuzzy immune algorithm (FIA). The paper mainly includes the following points:(1) Wavelet transform blind equalization algorithm based on FLOS is studied by using wavelet transform who has strong decorrelation, simulation results show that this algorithm can suppress α stable noise, speed up the convergence rate and reduce the steady state error.(2) By using WMMA, wavelet transform weighted multi-modulus blind equalization algorithm based on FLOS is proposed, simulation results show that in the environment of α stable distribution noise this algorithm can recover the higher order QAM signals well, and its steady state error is lower than constant modulus blind equalization algorithm.(3) DFE can reduce the inter-symbol interference, due to this character, this paper studies the wavelet transform weighted multi-modulus decision feedback blind equalization algorithm based on FLOS, simulation results show that the proposed algorithm has lower steady state error and faster convergence rate.(4) Fractional lower order statistics wavelet transform weighted multi-modulus blind equalization algorithm based on FIA is studied in order to overcome the defect of immerging easily in local convergence, simulation results show that this proposed algorithm has better convergence performance.