The probability density function (pdf) valid for the Gaussian case is often applied for describing the convolutional noise pdf in the blind adaptive deconvolution problem, although it is known that it can be applied only at the latter stages of the deconvolution process, where the convolutional noise pdf tends to be approximately Gaussian. Recently, the deconvolutional noise pdf was approximated with the Edgeworth Expansion and with the Maximum Entropy density function for the 16 Quadrature Amplitude Modulation (QAM) input but no equalization performance improvement was seen for the hard channel case with the equalization algorithm based on the Maximum Entropy density function approach for the convolutional noise pdf compared with the original Maximum Entropy algorithm, while for the Edgeworth Expansion approximation technique, additional predefined parameters were needed in the algorithm. In this paper, the Generalized Gaussian density (GGD) function and the Edgeworth Expansion are applied for approximating the convolutional noise pdf for the 16 QAM input case, with no need for additional predefined parameters in the obtained equalization method. Simulation results indicate that improved equalization performance is obtained from the convergence time point of view of approximately 15,000 symbols for the hard channel case with our new proposed equalization method based on the new model for the convolutional noise pdf compared to the original Maximum Entropy algorithm. By convergence time, we mean the number of symbols required to reach a residual inter-symbol-interference (ISI) for which reliable decisions can be made on the equalized output sequence.

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最大熵反卷积问题的改进方法

对于高斯情况有效的概率密度函数（pdf）通常用于描述盲自适应反卷积问题中的卷积噪声pdf，尽管已知它只能在反卷积过程的后期使用，其中卷积噪声pdf趋于近似高斯。最近，对于16正交幅度调制（QAM）输入，使用Edgeworth扩展和最大熵密度函数对反卷积噪声pdf进行了近似，但是在基于最大熵的均衡算法的情况下，硬通道情况下的均衡性能未见改善。卷积噪声pdf的密度函数方法与原始的最大熵算法相比，而Edgeworth扩展近似技术的密度函数方法为 该算法中需要其他预定义参数。在本文中，使用通用高斯密度（GGD）函数和Edgeworth扩展来近似估计16 QAM输入情况下的卷积噪声pdf，而在获得的均衡方法中不需要其他预定义参数。仿真结果表明，与原始的最大熵算法相比，基于卷积噪声pdf的新模型的新提出的均衡方法从硬通道情况的收敛时间观点出发，从大约15,000个符号的收敛时间角度获得了改进的均衡性能。所谓收敛时间，是指达到残余符号间干扰（ISI）所需的符号数量，对此可以在均衡的输出序列上做出可靠的决策。