Performance Research Of Decision-Assisted Blind Equalization Algorithm

Wireless digital communication technology is developing rapidly in contemporary communication technology,but due to various factors such as multi-path propagation of wireless signals and limited channel bandwidth resources,inter-symbol interference will occur,reducing communication quality and transmission rate.Blind equalization technology can effectively control inter-symbol interference and compensate for channel characteristics.Unlike traditional adaptive equalizers that require training sequences,channel equalization can be achieved only by transmitting the prior information of the sequences themselves without relying on the training sequences.The constant modulus algorithm is the most widely used blind equalization algorithm.In order to pursue a better equalization effect,a probability density function blind equalization algorithm(PPDF)based on the Parzen window method is proposed.However,both of these two blind equalization algorithms have the problem of phase rotation.The emergence of the decision-assisted blind equalization algorithm overcomes this problem,reduces the steady-state error and improves the convergence speed.Therefore,it is very important to analyze the performance of the algorithm.This thesis mainly studies the transient performance,steady-state performance and tracking performance of the algorithm,and proposes a performance analysis method for decision-assisted blind equalization algorithm when the transmitted signal is real-valued or complex-valued.The specific work content is as follows:(1)Aiming at the value of the compensation factor of the PPDF algorithm,the numerical solution method is used to give the curves of the corresponding compensation factor values when the Gaussian kernel function takes different standard deviations under four modulation signals.The mutation phenomenon that occurs is explained.Secondly,the transient performance of PPDF algorithm under real-valued and complex-valued data conditions is analyzed by using the principles of energy conservation and separation.On this basis,the nonlinear error function is expanded by Taylor series expansion,and the transient performance of the decision-assisted blind equalization algorithm is analyzed.The expressions for the mean square deviation of the real and complex forms of the PPDF algorithm and the decision-assisted blind equalization algorithm are derived.The theoretical value and simulation value of the mean square deviation of real and complex values of each algorithm are verified,and the simulation results are relatively consistent.(2)Based on the weighted variance relation in the transient analysis,when the blind equalization algorithm reaches the steady-state condition,the analytical expressions of the steady-state mean square error of the PPDF algorithm and the PPDF+DD algorithm under real and complex conditions are derived.The simulation results show that the theoretical values of the real-valued and complex-valued steady-state mean square errors of each algorithm are in good agreement with the simulation values in a noise-free environment,which verifies the accuracy of the theoretical analysis.(3)Using the random walk model,according to the weight vector iteration and the separation assumption principle of the Bussgang-like blind equalization algorithm,the energy conservation equation containing the random interference factor term is deduced.And based on the weighted variance relation in transient analysis,the theoretical expression of steady-state tracking mean square error with interference factor term under real-valued and complex-valued data is obtained.The theoretical value and simulation value of the tracking performance of each algorithm are verified respectively,and the results show that the theoretical value is in good agreement with the simulation value.