Adaptive Design of Limiters for Impulsive Noise Suppression
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摘要:
针对脉冲型噪声的抑制问题，该文提出一种自适应的限幅器设计方法。该方法以效能函数为指标，采用自适应搜索算法，自动寻找削波器和置零器的最佳门限，且能适用于未知噪声分布的情形。首先分析了效能与非线性函数的关系，给出关键的优化问题。然后考虑到效能函数计算复杂，提出基于线搜索的自适应设计算法。其次针对未知分布情况，考虑非参数化的概率密度估计，该算法能够稳健运行且基本取得最优设计效果。最后，结合两种非高斯噪声和实测大气噪声数据仿真，结果表明：该文方法可自适应寻找最佳门限，使削波器和置零器效能达到最佳；当噪声分布未知时，该文方法无需假设噪声模型，可与非参数化概率密度估计方法结合，取得最优检测效果。
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 限幅器的自适应优化处理算法
步骤 1 设置初始值${\tau _0} > 0$，初始步长${d_0} = 0.5{\tau _0}$，迭代次数
$k = 0$，计算效能值${\eta _0} = \eta (g, f, {\tau _0})$；步骤 2 令${\tau _{k + 1}} = {\tau _k} + {d_k}$，并计算效能值${\eta _{k{\rm{ + 1}}}} = \eta (g, f, {\tau _{k + 1}})$。若
${\eta _{k{\rm{ + 1}}}} > {\eta _k}$，转步骤3；否则，转步骤4；步骤 3 正向搜索。令${d_{k + 1}} = 2{d_k}$, $\tau = {\tau _k}$, ${\tau _k} = {\tau _{k + 1}}$, ${\eta _k} = {\eta _{k{\rm{ + 1}}}}$,
$k = k + 1$，转步骤2；步骤 4 反向搜索。若$k = 0$，则令${d_1} = - {d_0}$, $\tau = {\tau _1}$, ${\tau _1} = {\tau _0}$,
${\eta _1} = {\eta _0}$, $k = 1$，转步骤2；否则，停止迭代；步骤 5 设置线搜索参数，容许误差比率$\lambda $。迭代次数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)$, ${q_0} = {l_0} + 0.618\left( {{r_0} - {l_0}} \right)$；步骤 6 条件判断。若$\eta (g, f, {p_j}) \ge \eta (g, f, {q_j})$，转步骤7，否则转
步骤8；步骤 7 计算左试探点。若$|{q_j} - {l_j}|/{r_j} > \lambda $，则令${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}})$，计算效能值$\eta (g, f, {p_{j + 1}})$,
$j = j + 1$，转步骤6；否则，停止搜索并
输出最佳门限值${p_j}$；步骤 8 计算右试探点。若$|{r_j} - {p_j}{\rm{|/}}{r_j} > \lambda $，则令${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}})$，计算效能值$\eta (g, f, {q_{j + 1}})$,
$j = j + 1$，转步骤6；否则，停止搜索并输
出最佳门限值${q_j}$。
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表 2 Class A分布下(
${A}{,} {Γ} $ )-${τ} $ 变化，${{σ}^2}$ =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
$\rm S{α} S$ 分布下限幅器自适应设计方法迭代次数$\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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