Constant Modulus Blind Equalization Algorithm Based On Algorithm Based On Minimum Correntropy Induced Metric Criterion

With the development of wireless communication,the industry and service industry are becoming more intelligent.However,there are still some urgent problerms remaining to be solved.Channel equalization is an important research problem in the field of wireless communication.There is a kind of non-Gaussian impulsive noise in the wireless channel and underwater acoustic channel,which can be described by ?-stable distribution or mixed Gaussian distribution mathematical model.The traditional channel equalization algorithm based on the Gaussian noise assumption has a performance degradation phenomenon in such a noise environment.Firstly,this paper addresses the problem of single-user constant modulus blind equalization algorithm(CMA)performance degradation in non-Gaussian impulse noise environment.Based on the minimum correntropy induced distance(CIM)criterion,the single-user constant modulus blind equalization algorithm based on the minimum mean square error(MSE)criterion is modified,and a single-user constant modulus blind equalization algorithm(CIM_CMA)based on the minimum CIM criterion is derived.Simulation experiments on Gaussian noise and channel equalization in two impulse noise environments show that the CIM_CMA algorithm does not rely on prior knowledge of noise and can obtain good equalization results in impulse noise environments with different pulse strengths,indicating that CIM_CMA the algorithm is very robust.Secondly,the steady-state mean square error characteristics of the proposed CIM_CMA algorithm are analyzed based on the energy conservation relationship proposed by Sayed et al.For the CIM_CMA algorithm,due to the introduction of the non-linear function of correntropy,the original energy conservation relationship based on the linear error function cannot be directly applied.In this paper,the estimated error function of the CIM_CMA algorithm with the nonlinear operation of correntropy is first processed by Taylor series expansion,and the theoretical formulas of steady-state mean aquare error and steady-state tracking mean square error of CIM_CMA algorithm can be derived with the stationary environment and non-stationary environment.Based on the deduced steady-state mean square error formula,the optimal step size selection under non-stationary environment is discussed.The correctness of the theoretical analysis formula was verified and discussed through simulation experiments.Finally,the problem of constant-modulus blind equalization in multi-input multi-output(MIMO)systems under non-Gaussian impulse noise environment is focused and discussed in depth.Based on the minimum CIM criterion constant modulus cost function proposed in this paper,in order to solve the phenomenon that the output signals of multiple equalizers will be locked to the same signal under the impulse noise environment,a cross correntropy function for strictly stationary signals is defined,and minimize the cross-correntropy function between the output signals of different equalizers,so a multi-user constant modulus blind equalization algorithm(CMU_CMA)based on the minimum CIM criterion is proposed.Simulation experiments of MIMO channel equalization under Gaussian noise and two impulse noise environments show that compared with the classic multi-user adaptive constant modulus blind equalization algorithm,the CMU_CMA algorithm can not only solves the one-to-many problem with faster convergence speed,but also lowers overall channel coefficient interference with better equalization results under impulse noise environments whith different pluse strengths,all of these indicate that the CMU_CMA algorithm is very robust.