Abstract
To solve the problem of large steady state residual error of momentum constant modulus algorithm (CMA) blind equalization, a momentum CMA blind equalization controlled by energy steady state was proposed. The energy of the equalizer weights is estimated during the updating process. According to the adaptive filtering theory, the energy of the equalizer weights reaches to the steady state after the algorithm is converged, and then the momentum can be set to 0 when the energy change rate is less than the threshold, which can avoid the additional gradient noise caused by momentum and further improve the convergence precision of the algorithm. The proposed algorithm takes advantage of momentum to quicken the convergence rate and to avoid the local minimum in the cost function to some extent; meanwhile, it has the same convergence precision with CMA. Computer simulation results show that, compared with CMA, momentum CMA (MCMA) and adaptive momentum CMA (AMCMA) blind equalization, the proposed algorithm has the fastest convergence rate and the same steady state residual error with CMA.
Highlights
Blind equalization can compensate and track the communication channel characteristic without training sequence, which can save the communication bandwidth and improve the communication quality [1], it can avoid the unlock of the equalizer at the same time
We proposed an adaptive momentum constant modulus algorithm (CMA) algorithm controlled by energy steady state based on the analysis of momentum term in the gradient algorithm
To verify the performance of the adaptive momentum CMA blind equalization controlled by energy steady state, computer simulation has done to compare with the statistical momentum CMA (SMCMA) and mean square error controlled momentum CMA (MSEMCMA)
Summary
Blind equalization can compensate and track the communication channel characteristic without training sequence, which can save the communication bandwidth and improve the communication quality [1], it can avoid the unlock of the equalizer at the same time. The momentum term in the algorithm produces additional gradient noise, which results in big steady state residual error after convergence. The basic ideal of AMCMA is that the bigger momentum factor is set at the initial stage of the algorithm to obtain the faster convergence rate, and with the iterative process, the momentum factor is gradually decreased to obtain the lower steady state residual error. M. Wang proposed an AMCMA blind equalization based on stop-and-go algorithm, but the parameters for adjusting the momentum factor lack of theory basis [4]. The proposed algorithm use the energy change rate of the blind equalizer weights as the threshold to judge the steady state during the convergence process, which can take full advantage of the momentum term for accelerating the convergence rate and overcome the additional gradient noise by momentum term after convergence. The computer simulation results show the effectiveness of the proposed algorithm
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