脈沖噪聲中基于指數(shù)函數(shù)的可變拖尾非線性變換設計
doi: 10.11999/JEIT190401 cstr: 32379.14.JEIT190401
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1.
重慶郵電大學通信與信息工程學院 重慶 400065
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2.
武漢船舶通信研究所 武漢 430079
Variable Tailing Nonlinear Transformation Design Based on Exponential Function in Impulsive Noise
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1.
School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
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2.
Wuhan Maritime Communication Research Institute, Wuhan 430079, China
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摘要:
針對脈沖噪聲中的信號檢測問題，該文提出一種基于指數(shù)函數(shù)的非線性變換函數(shù)設計與優(yōu)化方法。該方法利用指數(shù)函數(shù)衰減速度可調(diào)的優(yōu)點，適用于脈沖噪聲的各種分布模型。通過引入效能函數(shù)，將非線性函數(shù)設計問題轉(zhuǎn)化為以效能最大化為目標的閾值與底數(shù)參數(shù)優(yōu)化問題。由于效能是關(guān)于待優(yōu)化參數(shù)的連續(xù)可導且單峰函數(shù)，該優(yōu)化問題可采用數(shù)值優(yōu)化方法如單純形法快速穩(wěn)健地求解。性能分析表明，針對脈沖噪聲常用的對稱α穩(wěn)定分布、Class A分布和高斯混合分布，該文方法均能取得基本最優(yōu)檢測性能，基于實測大氣噪聲仿真的通信誤碼率也明顯優(yōu)于傳統(tǒng)的削波器和置零器。因此，該文為各種分布的脈沖噪聲提供了一個統(tǒng)一的最優(yōu)抑制解決方法。
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關(guān)鍵詞:
- 脈沖噪聲 /
- 非線性變換 /
- 指數(shù)函數(shù) /
- 優(yōu)化算法
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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圖 2 在
${\rm{S}}\alpha {\rm{S}}$ 噪聲下的$E\left( {{g_X},T,a} \right)$ 曲面與曲線，$\alpha $ =1.5,$\sigma $ =1表 1 高斯混合噪聲中非線性變換的效能
$(\varepsilon ,\sigma _2^2)$= (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) 局部最優(yōu)檢測 0.5198 0.5709 0.6338 0.7935 0.8316 0.8678 0.9695 0.9796 0.9846 最優(yōu)置零器 0.4637 0.5421 0.6196 0.7624 0.8160 0.8611 0.9647 0.9752 0.9837 最優(yōu)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 軸平移模式 0.5079 0.5652 0.6313 0.7880 0.8286 0.8665 0.9686 0.9772 0.9845 Y 軸平移模式 0.4939 0.5044 0.5512 0.7626 0.7614 0.7858 0.9599 0.9557 0.9589 定點平移模式 0.5091 0.5282 0.5697 0.7776 0.7837 0.8032 0.9636 0.9618 0.9641 
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