抑制脈沖型噪聲的限幅器自適應(yīng)設(shè)計
doi: 10.11999/JEIT180609
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1.
重慶郵電大學(xué)通信與信息工程學(xué)院??重慶??400065
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2.
武漢船舶通信研究所??武漢??430079
Adaptive Design of Limiters for Impulsive Noise Suppression
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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:
針對脈沖型噪聲的抑制問題，該文提出一種自適應(yīng)的限幅器設(shè)計方法。該方法以效能函數(shù)為指標，采用自適應(yīng)搜索算法，自動尋找削波器和置零器的最佳門限，且能適用于未知噪聲分布的情形。首先分析了效能與非線性函數(shù)的關(guān)系，給出關(guān)鍵的優(yōu)化問題。然后考慮到效能函數(shù)計算復(fù)雜，提出基于線搜索的自適應(yīng)設(shè)計算法。其次針對未知分布情況，考慮非參數(shù)化的概率密度估計，該算法能夠穩(wěn)健運行且基本取得最優(yōu)設(shè)計效果。最后，結(jié)合兩種非高斯噪聲和實測大氣噪聲數(shù)據(jù)仿真，結(jié)果表明：該文方法可自適應(yīng)尋找最佳門限，使削波器和置零器效能達到最佳；當噪聲分布未知時，該文方法無需假設(shè)噪聲模型，可與非參數(shù)化概率密度估計方法結(jié)合，取得最優(yōu)檢測效果。
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關(guān)鍵詞:
- 非線性處理 /
- 效能函數(shù) /
- 自適應(yīng)優(yōu)化 /
- 削波器 /
- 置零器
Abstract:An adaptive method of limiter design is proposed to suppress impulsive noise. With a purpose of maximizing the efficacy function, the proposed method searches for optimal thresholds of clipper and blanker, via adaptive line search. Firstly, based on analysis on the relationship between the efficacy and the nonlinearity, the key problem of optimization is proposed. Then, since the calculation of efficacy is hard, an adaptive algorithm based on linear search approach is developed based on linear search to optimize the efficacy. Considering the noise distribution is unknown, the proposed method employs the nonparametric kernel density estimation and works robustly in the presence of estimation error. Finally, numeric simulations demonstrate that the proposed method can obtain the optimal performance of clippers and blankers successfully. In the processing of real atmospheric noise from unknown distribution, the proposed method achieves the best detection performance when combining nonparametric kernel density estimation approach.
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Key words:
- Nonlinear processing /
- Efficiency function /
- Adaptive optimization /
- Clipper /
- Blanker
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表 1 限幅器的自適應(yīng)優(yōu)化處理算法
步驟 1 設(shè)置初始值${\tau _0} > 0$，初始步長${d_0} = 0.5{\tau _0}$，迭代次數(shù)
$k = 0$，計算效能值${\eta _0} = \eta (g, f, {\tau _0})$；步驟 2 令${\tau _{k + 1}} = {\tau _k} + {d_k}$，并計算效能值${\eta _{k{\rm{ + 1}}}} = \eta (g, f, {\tau _{k + 1}})$。若
${\eta _{k{\rm{ + 1}}}} > {\eta _k}$，轉(zhuǎn)步驟3；否則，轉(zhuǎn)步驟4；步驟 3 正向搜索。令${d_{k + 1}} = 2{d_k}$, $\tau = {\tau _k}$, ${\tau _k} = {\tau _{k + 1}}$, ${\eta _k} = {\eta _{k{\rm{ + 1}}}}$,
$k = k + 1$，轉(zhuǎn)步驟2；步驟 4 反向搜索。若$k = 0$，則令${d_1} = - {d_0}$, $\tau = {\tau _1}$, ${\tau _1} = {\tau _0}$,
${\eta _1} = {\eta _0}$, $k = 1$，轉(zhuǎn)步驟2；否則，停止迭代；步驟 5 設(shè)置線搜索參數(shù)，容許誤差比率$\lambda $。迭代次數(shù)j=0；令
${l_0} = {\rm{min}}\{ \tau, {\tau _{k + 1}}\} $, ${r_0} = {\rm{max}}\{ \tau, {\tau _{k + 1}}\} $, ${p_0} = {l_0} $
$ 0.382\left( {{r_0} - {l_0}} \right)$, ${q_0} = {l_0} + 0.618\left( {{r_0} - {l_0}} \right)$；步驟 6 條件判斷。若$\eta (g, f, {p_j}) \ge \eta (g, f, {q_j})$，轉(zhuǎn)步驟7，否則轉(zhuǎn)
步驟8；步驟 7 計算左試探點。若$|{q_j} - {l_j}|/{r_j} > \lambda $，則令${l_{j + 1}} = {l_j}$, ${r_{j + 1}} $
$ ={q_j}$, $\eta (g, f, {q_{j + 1}}) = \eta (g, f, {p_j})$, ${q_{j + 1}} = {p_j}$, ${p_{j + 1}} = $
$ {l_{j + 1}} + 0.382({r_{j + 1}} - {l_{j + 1}})$，計算效能值$\eta (g, f, {p_{j + 1}})$,
$j = j + 1$，轉(zhuǎn)步驟6；否則，停止搜索并
輸出最佳門限值${p_j}$；步驟 8 計算右試探點。若$|{r_j} - {p_j}{\rm{|/}}{r_j} > \lambda $，則令${l_{j + 1}} = {p_j}$, ${r_{j + 1}} $
$={r_j}$, $\eta (g, f, {p_{j + 1}}) = \eta (g, f, {q_j})$, ${p_{j + 1}} = {q_j}$, ${q_{j + 1}} =$
$ {l_{j + 1}} + 0.618({r_{j + 1}} - {l_{j + 1}})$，計算效能值$\eta (g, f, {q_{j + 1}})$,
$j = j + 1$，轉(zhuǎn)步驟6；否則，停止搜索并輸
出最佳門限值${q_j}$。
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表 2 Class A分布下(
${A}{,} {Γ} $ )-${τ} $ 變化，${{σ}^2}$ =1$A, {\rm{ }}\varGamma $ $0.1, {\rm{ }}{10^{ - 3}}$ $0.35, {\rm{ }}{10^{ - 3}}$ $0.5, {\rm{ }}{10^{ - 3}}$ $0.1, {\rm{ }}{10^{ - 2}}$ $0.35, {\rm{ }}{10^{ - 2}}$ $0.5, {\rm{ }}{10^{ - 2}}$ ${\tau _{{\rm{opt\_}}b}}{\rm{ - PDF}}$(${\eta _{{\rm{opt\_}}b}}$) 0.1296(888.8429) 0.1094(647.4406) 0.0996(532.3140) 0.3397(87.5188) 0.2898(59.1912) 0.2698(46.5176) ${\tau _{{\rm{opt\_}}c}}{\rm{ - PDF}}$(${\eta _{{\rm{opt\_}}c}}$) 0.0386(671.5877) 0.0232(356.9533) 0.0188(257.2668) 0.1181(69.5440) 0.0743(38.4601) 0.0623(28.4378) ${\tau _{{\rm{opt\_}}b}}{\rm{ - KDE}}$(${\eta _{{\rm{opt\_}}b}}$) 0.1199(877.9385) 0.1094(631.7642) 0.0994(510.9088) 0.3494(85.5270) 0.2937(57.2562) 0.2708(43.9273) ${\tau _{{\rm{opt\_}}c}}{\rm{ - KDE}}$(${\eta _{{\rm{opt\_}}c}}$) 0.0396(665.3161) 0.0239(349.5658) 0.0197(247.0483) 0.1197(68.3936) 0.0786(36.7663) 0.0651(26.4190)
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表 3
$\rm S{α} S$ 分布下限幅器自適應(yīng)設(shè)計方法迭代次數(shù)$\alpha $ 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Iterb-PDF 15 15 15 15 15 15 15 15 15 Iterc-PDF 17 17 17 16 16 16 16 15 15 Iterb-KDE 15 15 15 15 15 15 15 15 14 Iterc-KDE 17 17 17 16 16 16 16 15 15
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