Research On The Blind Equalization Algorithm Based On PDF And The Modified CMA

For frequent channel fading, nonlinearity, multipath and time-variant characteristics, blind equalizer is a new and self-adaptive equalization technique, which can update the tap weights of equalizer and track the variance of channel. Bussgang class algorithms are widely used due to its all-around computing efficiency and easy application. Constant modulus algorithm (CMA) is the one that is used mostly and is of the best performance among Bussgang class algorithms. However, the CMA has some drawbacks. For example, the convergence speed is slow, the steady-state mean square error (MSE) after convergence is not small enough, and the equalization output has a random phase rotation, when the communication system exists frequency bias of carrier-wave and the phase rotation of channel. Specially, the equalization performance is bad for multilevel amplitude modulation signals, such as pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM).To overcome the questions of random phase rotation of CMA equalization output and slow convergent speed, S. Chen proposed a concurrent constant modulus algorithm aided soft-directed decision (CCMA+SDD) based on the rule of maximum a posteriori probability density function. The algorithm can concurrently update both the weights of CMA and the ones of SDD without worrying about the estimation error propagation. The CCMA+SDD algorithm can get a good equalization performance with fast convergence speed and small steady-state MSE. However, the computational burden of the CCMA+SDD algorithm is very heavy, and increases with the increasing of the parameter M of MQAM. In this paper, a modified low complexity CCMA+SDD algorithm is proposed, whose computational burden is fixed and decision region changes with the equalization output. This modified algorithm has a better performance then CCMA+SDD algorithm, and decreases the computational burden. With Matlab language tool for the convergence for residue ISI, the low complexity blind equalization has a good performance.Based on the probability density function with Parzen window, Marcelino and co-authors proposed a blind equalization algorithm, which has a good performance in multilevel modulation communication system, and can force the PDF of the equalizer output to match the known constellation PDF. However, similarly with CMA, the equalization output of the algorithm has a random phase rotation after convergence, since the algorithm only uses the modulus of the input and output signals, when any communication system exist frequency bias of carrier-wave and the phase rotation of channel. To guarantee the convergence of the algorithm, the kernel parameter of PPDF algorithm must be big enough, which leads to the reduced set of the constellations and increase the error-code rate.A low complexity PPDF algorithm (LCPPDF) is proposed to overcome the heavy computational burden, whose computational cost equals to the one of 4QAM, and does not increase with the parameter M increasing. Based on a concurrent filter structure, a PPDF algorithm aided directed-decision scheme (DD+PPDF) is presented to overcome the slow convergence of PPDF. Without worrying about estimation error propagation, it has a fast convergence speed. In addition, a data-dependent PPDF algorithm aided directly-directed decision (DDDD+PPDF) is present with fast convergent speed and low steady-state MSE by using Matlab language.