基于回聲狀態(tài)網(wǎng)絡的衛(wèi)星信道在線盲均衡算法
doi: 10.11999/JEIT190034
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蘭州大學信息科學與工程學院 蘭州 730000
基金項目: 中央高?；究蒲袠I(yè)務費專項資金項目(lzujbky-2017-38)，甘肅省自然科學基金(縱20180322)
Online Blind Equalization Algorithm for Satellite Channel Based on Echo State Network
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School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China
Funds: The Fundamental Research Fund for the Central Universities (lzujbky-2017-38), The Natural Science Foundation of Gansu Province (Longitudinal 20180322)
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摘要: 針對非線性衛(wèi)星信道，該文提出了兩種基于回聲狀態(tài)網(wǎng)絡(ESN)的在線盲均衡算法。利用ESN良好的非線性逼近能力，將發(fā)送信號的高階統(tǒng)計量(HOS)代入ESN，結(jié)合常模算法(CMA)和多模算法(MMA)構(gòu)造盲均衡的代價函數(shù)，并采用遞歸最小二乘(RLS)算法對ESN輸出權(quán)值進行迭代尋優(yōu)，實現(xiàn)了Volterra衛(wèi)星信道下常模和多模信號的在線盲均衡。實驗表明，該文算法可以有效降低非線性信道對發(fā)送信號產(chǎn)生的畸變，相較于傳統(tǒng)的Volterra濾波方法，有更快的收斂速度和更低的均方誤差值。
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關(guān)鍵詞:
- Volterra衛(wèi)星信道 /
- 回聲狀態(tài)網(wǎng)絡 /
- 常模算法 /
- 多模算法 /
- 遞歸最小二乘算法
Abstract: Two online blind equalization algorithms based on Echo State Network (ESN) in this paper are proposed for the nonlinear satellite channel. These two algorithms take advantage of the good nonlinear approximation of ESN to bring the High-Order Statistics (HOS) of the transmitted signal into the ESN, and constructing cost function of blind equalization by combining Constant Modulus Algorithm (CMA) and Multi-Modulus Algorithm (MMA). Then, the Recursive Least Squares (RLS) algorithm is used to iteratively optimize the network output weights, and the online blind equalization of the constant modulus signals and the multi-modulus signals over the channel of Volterra satellite are realized. Experiments show that the proposed algorithms can effectively reduce the distortion of the transmitted signal by the nonlinear channel. Compared with the traditional Volterra filtering method, they have faster convergence speed and lower mean square error. -
表 1 ESN-RLS-CMA算法
步驟 1 ?均衡器初始化：隨機生成(${{\text{W}}_{{\rm{res}}}},{{\text{W}}_{{\rm{in}}}}$)，初始化
${\text{u}}(0)$,${{\text{W}}_{{\rm{out}}}}$和$\lambda $; ${\text{P}}(0) = {\delta ^{ - 1}}{\text{I}}$($\delta $是一個很小的正數(shù))；步驟 2 ?For：n=1, 2,···, N； ???(1) 更新儲備池狀態(tài)：${\text{u}}(n) = f({{\text{W}}_{{\rm{res}}}}{\text{u}}(n - 1) + {{\text{W}}_{{\rm{in}}}}x(n))$； ? ??(2) 計算$y\left( n \right) = {{\text{W}}_{{\rm{out}}}}\left( {n - 1} \right){\text{u}}\left( n \right)$； ???(3) 由式(7)得到${\tilde{\text U}}(n,n)$，通過式(11)計算自相關(guān)矩陣${\text{P}}(n)$； ???(4) 按照式(12)更新ESN的輸出權(quán)值${{\text{W}}_{{\rm{out}}}}(n)$； ? ??(5) 根據(jù)文獻[14]的方法調(diào)整$\lambda $值。 ???End； 步驟 3 ?迭代直到網(wǎng)絡收斂為止。 
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表 2 ESN-RLS-MMA算法
步驟 1 ?均衡器初始化：隨機生成(${{\text{W}}_{{\rm{res}}}},{{\text{W}}_{{\rm{in}}}}$)；初始化
${\text{u}}(0)$,${{\text{W}}_{{\rm{out}}}}$,$\lambda $($0 \ll \lambda < 1$),${{\hat{\text R}}^{ - 1}}(0){\rm{ = }}\delta {\text{I}}$($\delta $是一個很小的正
數(shù))；設置$\gamma {\rm{ \!=\! }}3{\rm{E}} \{ s_{\rm{R}}^2(n)\} \!-\! {R_{{\rm{MMA}}}}$，門限值T=$3{\rm{E}}\{ {\left|\! {s(n)}\! \right|^2}\} $；步驟 2 ?For：n=1,2,···,N； ? ??(1) 更新儲備池狀態(tài)：${\text{u}}(n) = f({{\text{W}}_{{\rm{res}}}}{\text{u}}(n - 1) + {{\text{W}}_{{\rm{in}}}}x(n))$； ? ??(2) 計算$y(n) = {{\text{W}}_{{\rm{out}}}}(n - 1){\text{u}}(n)$； ???(3) 通過式(30)計算${{\hat{\text R}}^{ - 1}}(n)$； ???(4) 計算：${d_{\rm{R}}}(n) = \left[ {\gamma + {R_{{\rm{MMA}}}} - y_{\rm{R}}^2(n)} \right]{y_{\rm{R}}}(n)$,
${d_{\rm{I}}}(n) = \left[ {\gamma + {R_{{\rm{MMA}}}} - y_{\rm{I}}^2(n)} \right]{y_{\rm{I}}}(n)$?? ???????????$d(n) = {\gamma ^{{\rm{ - }}1}}\left[ {{d_{\rm{R}}}(n) + j{d_{\rm{I}}}(n)} \right]$； ? ??(5) If ${\left| {y(n)} \right|^2}$>T； ??? ?????????$d(n) = 0$ ???? ????End； ? ??(6) 根據(jù)式(32)更新${{\text{W}}_{{\rm{out}}}}(n)$。 ?? ?End； 步驟 3 ?迭代直到網(wǎng)絡收斂為止。
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表 3 取不同儲備池規(guī)模N時兩種算法的MSE值(dB)
算法 N=20 N=50 N=100 N=200 N=300 ESN-RLS-CMA –22.56 –28.12 –29.06 –28.41 –28.72 ESN-RLS-MMA –18.12 –29.58 –30.62 –29.10 –29.29
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表 4 本文算法與5階Volterra濾波算法的運算復雜度對比
算法 運算復雜度 Volterra O(24M5+16M3+8M) ESN-RLS-CMA O(4N3+18N2+10N) ESN-RLS-MMA O(4N3+19N2+10N)
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