For the contradiction between convergence rate and convergence precision in the CMA blind equalization with the fixed momentum factor, a variable momentum CMA blind equalization is proposed The output error power of the blind equalizer is acted as the parameter, which control the adjustment of the momentum factor adaptively based on nonlinear transformation function. The algorithm can obtain faster convergence rate and higher convergence precision, also the performance of the blind equalization is improved. The simulation results show that, compared with the CMA blind equalization with the fixed momentum factor, CMA blind equalization with variable momentum based on nonlinear transform can obtain better performance
Hereby a normalized p-norm blind equalization algorithm with adaptive momentum was proposed. Normalized p-norm LMS-CMA can obtain robust convergence performance under impulsive noise environment, however, the convergence rate is slow. To further improve the performance of the normalized p-norm LMS-CMA, adaptive momentum according to the instantaneous error is designed. If the instantaneous error based on CMA criterion and DD criterion has the same sign, the momentum factor remains unchanged. Otherwise, the momentum factor is set to 0. The simulation results show that, the proposed algorithm has faster convergence rate than the normalized p-norm blind equalization algorithm, furthermore, it has robust convergence performance under impulsive noise environment.
The CMA cost function is simplified to meet the second norm form, and a new CMA blind equalization based on quasi-newton algorithm is proposed. Since the CMA cost function does not meet the second norm form, it is difficult to use quasi-newton algorithm to update the blind equalizer directly based on the cost function of CMA. If the cost function is simplified to meet the second norm form, it can use quasi-newton algorithm to update the blind equalizer directly. Thus, the convergence rate and convergence precision of CMA blind equalization can be improved effectively. Simulation results under the acoustic channels show that CMA blind equalization with quasi-newton algorithm based on the simplified cost function has faster convergence rate and less steady state residual error, which has practical value in the blind equalization of fast time-varying underwater acoustic channels
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