Shlisel Shay, Pinchas Monika
Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, Israel.
Entropy (Basel). 2021 Apr 28;23(5):547. doi: 10.3390/e23050547.
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.
适用于高斯情况的概率密度函数（pdf）通常用于描述盲自适应反卷积问题中的卷积噪声pdf，尽管已知它仅能应用于反卷积过程的后期阶段，此时卷积噪声pdf趋于近似高斯分布。最近，对于16正交幅度调制（QAM）输入，用埃奇沃思展开和最大熵密度函数对反卷积噪声pdf进行了近似，但与原始最大熵算法相比，基于卷积噪声pdf的最大熵密度函数方法的均衡算法在硬信道情况下未观察到均衡性能的改善，而对于埃奇沃思展开近似技术，算法中需要额外的预定义参数。在本文中，广义高斯密度（GGD）函数和埃奇沃思展开被用于近似16 QAM输入情况下的卷积噪声pdf，在所得到的均衡方法中无需额外的预定义参数。仿真结果表明，与原始最大熵算法相比，对于硬信道情况，基于卷积噪声pdf新模型的新提出的均衡方法从收敛时间角度来看，在大约15000个符号时获得了改进的均衡性能。这里所说的收敛时间，是指达到残余码间干扰（ISI）所需的符号数，此时可以对均衡输出序列做出可靠的决策。
