Variable Tailing Nonlinear Transformation Design Based on Exponential Function in Impulsive Noise
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摘要:
针对脉冲噪声中的信号检测问题，该文提出一种基于指数函数的非线性变换函数设计与优化方法。该方法利用指数函数衰减速度可调的优点，适用于脉冲噪声的各种分布模型。通过引入效能函数，将非线性函数设计问题转化为以效能最大化为目标的阈值与底数参数优化问题。由于效能是关于待优化参数的连续可导且单峰函数，该优化问题可采用数值优化方法如单纯形法快速稳健地求解。性能分析表明，针对脉冲噪声常用的对称α稳定分布、Class A分布和高斯混合分布，该文方法均能取得基本最优检测性能，基于实测大气噪声仿真的通信误码率也明显优于传统的削波器和置零器。因此，该文为各种分布的脉冲噪声提供了一个统一的最优抑制解决方法。
Abstract:A novel design of nonlinear transformation function for the signal detection in impulsive noise is proposed. The proposed method takes the advantage of adjustable fading factors of the exponential function, it can be effective for different models of impulsive noise. By introducing the efficacy as the objective function, nonlinear design is converted into the problem of optimizing the threshold and bottom parameters to maximize the efficacy. Since the efficacy is continuous, derivative, and unimodal, the optimization problem can be easily solved by the traditional optimization methods, such as the Nelder-Mead simplex method. Analysis shows that the proposed design can obtain the optimal performance in the widely-used models of impulsive noise, including the symmetric α-stable model, the Class A model, and the Gaussian mixture model. Simulation on real atmospheric noise demonstrates that the proposed design is obviously better than the traditional clipper and blanker. Thus, this paper proposes an optimal and uniform solution for suppressing impulsive noise of various models.
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图 2 在
${\rm{S}}\alpha {\rm{S}}$ 噪声下的$E\left( {{g_X},T,a} \right)$ 曲面与曲线，$\alpha $ =1.5,$\sigma $ =1表 1 高斯混合噪声中非线性变换的效能
$(\varepsilon ,\sigma _2^2)$= (0.3 10) (0.3 100) (0.3 1000) (0.1 10) (0.1 100) (0.1 1000) (0.01 10) (0.01 100) (0.01 1000) 局部最优检测 0.5198 0.5709 0.6338 0.7935 0.8316 0.8678 0.9695 0.9796 0.9846 最优置零器 0.4637 0.5421 0.6196 0.7624 0.8160 0.8611 0.9647 0.9752 0.9837 最优削波器 0.4592 0.3906 0.3662 0.7407 0.6958 0.6793 0.9568 0.9453 0.9409 GZMNL 0.5056 0.5674 0.6328 0.7883 0.8300 0.8672 0.9689 0.9774 0.9846 GGM 0.4540 0.4982 0.5791 0.7576 0.7924 0.8311 0.9620 0.9691 0.9773 X 轴平移模式 0.5079 0.5652 0.6313 0.7880 0.8286 0.8665 0.9686 0.9772 0.9845 Y 轴平移模式 0.4939 0.5044 0.5512 0.7626 0.7614 0.7858 0.9599 0.9557 0.9589 定点平移模式 0.5091 0.5282 0.5697 0.7776 0.7837 0.8032 0.9636 0.9618 0.9641 
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