| In wireless communication systems,blind equalizer refers to an equalizer that can perform adaptive equalization on the channel only by using the received signal sequence,so as to solve the problem of non-ideal characteristics such as multipath effect and impulse noise during signal transmission.Inter-symbol interference problem.Blind equalizers are widely used in adaptive filtering by virtue of the advantage of being able to effectively recover the transmission code without the need for a training sequence.However,due to the problem that a single filter cannot take into account the convergence speed and the accuracy of the steady-state error,the combined filter emerges as the times require.By combining the two filters convexly,the combined filter has the advantages of fast convergence speed and small steady-state error among different filters,and improves the overall filtering performance.In order to further improve the reliability of the convex combination blind equalization filter,the unconstrained convex programming model is used to analyze the principle of the convex combination filter.In addition,in order to further improve the research system of the convex combined constant modulus algorithm,the performance analysis of the convex combined constant modulus algorithm(CMA)is carried out in the α impulse noise environment.Based on the above description,the α impulse noise model is selected to simulate the real noise environment,and the steady-state,tracking,and transient performance of the CMA convex combination algorithm in the impulse noise environment is carried out with full consideration of the step size μ and the parameter p that affect the CMA performance.Research.It mainly includes the following aspects:(1)This thesis introduces the concept of convex programming.On this basis,from the perspective of convex combination,convex function and cost function,it is comprehensively expounded and verified that the convex programming theory is the theoretical basis of the convex combination method.In addition,this thesis simulates the change of the cost function with the parameter p.By comparing the theoretical analysis with the simulation results,it is verified that the cost function of the convex combined filter is a convex function when p>=1,and the theoretical analysis is correct.It further improves the theoretical research system of convex combination.(2)In this thesis,under the environment of α impulse noise,for the case where the input signal is real and complex,using separation assumptions and conservation relations,the Taylor series expansion of the error function is introduced,and the transient performance and tracking performance of CMA are theoretically analyzed and deduced.Accurate theoretical expression is obtained,and finally MATLAB is used to simulate.The experimental results show that the theoretical value is consistent with the experimental value,thus verifying the correctness of the theoretical analysis.(3)In this thesis,under the α-impulse noise environment,the convex combination scheme is used to perform convex combination of two blind equalization filters with different step length μ and different parameters p.One of the filters converges slowly but the error is small,and the other filter converges fast but the error is large.With the help of the convex combination scheme,the convex combination filter with fast convergence and small error is obtained.On this basis,the steady-state,tracking and transient performances of the convex combined constant modulus algorithm are analyzed for different situations where the input signal is a real number or a complex number,and the theoretical expressions are deduced respectively.Finally,the theoretical analysis results are simulated and verified correctness of the theoretical analysis.The simulation results show that the convex combined filter can combine the respective advantages of the two filters,taking into account the fast convergence and low error,and has better performance than the single filter. |
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