基于訓(xùn)練序列的OOFDM采樣時(shí)鐘頻率偏差估計(jì)算法

張鎮(zhèn),宋英雄,張俊杰,頓涵,郭松霖,薛子威

(上海大學(xué)特種光纖與光接入網(wǎng)省部共建重點(diǎn)實(shí)驗(yàn)室,上海 200072)

基于訓(xùn)練序列的OOFDM采樣時(shí)鐘頻率偏差估計(jì)算法

張鎮(zhèn),宋英雄,張俊杰,頓涵,郭松霖,薛子威

(上海大學(xué)特種光纖與光接入網(wǎng)省部共建重點(diǎn)實(shí)驗(yàn)室,上海 200072)

研究了光正交頻分復(fù)用(optical orthogonal frequency division multiplexing,OOFDM)系統(tǒng)中采樣時(shí)鐘同步問題,提出了一種基于訓(xùn)練序列互相關(guān)特性的易于硬件實(shí)現(xiàn)的采樣時(shí)鐘頻偏估計(jì)算法.算法的主要思想是對(duì)接收到的訓(xùn)練序列與本地已知訓(xùn)練序列作互相關(guān),利用該相關(guān)值周期性變化一次產(chǎn)生一個(gè)采樣點(diǎn)數(shù)差的特性,由少量加法器和一個(gè)除法器得到采樣時(shí)鐘頻率偏差(sampling clock frequency ofset,SCFO)值.通過在一個(gè)強(qiáng)度調(diào)制直接檢測(cè)的光正交頻分復(fù)用(intensity-modulation and direct-detection-OFDM,IMDD-OFDM)系統(tǒng)上的實(shí)驗(yàn),驗(yàn)證了該算法具有較好的準(zhǔn)確度和抗噪性能.

光正交頻分復(fù)用;采樣時(shí)鐘同步;互相關(guān);訓(xùn)練序列

光正交頻分復(fù)用(optical orthogonal frequency division multiplexing,OOFDM)憑借其高頻譜利用率、多維動(dòng)態(tài)帶寬調(diào)度和較好的抗光纖色散能力等優(yōu)點(diǎn)越來越受到人們的重視,該技術(shù)已經(jīng)成為未來光接入網(wǎng)中最具競(jìng)爭力的方案之一[1-4].然而由于在通信系統(tǒng)發(fā)送端DAC和接收端ADC所用的采樣時(shí)鐘頻率不可能完全相同,這會(huì)導(dǎo)致采樣時(shí)鐘頻率偏差(sampling clock frequency ofset,SCFO),引起OFDM符號(hào)子載波間的干擾[5].

目前,OFDM系統(tǒng)中采樣時(shí)鐘頻率偏差估計(jì)主要分為兩類:一類是在發(fā)送端插入具有特殊結(jié)構(gòu)的導(dǎo)頻序列,在接收端通過導(dǎo)頻序列對(duì)采樣時(shí)鐘頻率偏差進(jìn)行估計(jì)[6-7];另一類是基于信號(hào)本身的特征在時(shí)域?qū)Σ蓸訒r(shí)鐘頻率偏差進(jìn)行估計(jì)[8].前者需要利用固定的幾個(gè)子載波為導(dǎo)頻,這將增加系統(tǒng)的開銷,且大多需要在頻域?qū)Σ蓸訒r(shí)鐘頻率偏差進(jìn)行估計(jì).文獻(xiàn)[8]利用循環(huán)前綴的延時(shí)相關(guān)特性來對(duì)采樣時(shí)鐘頻率偏差進(jìn)行估計(jì),但該算法需要較長的循環(huán)前綴長度.

本工作從工程實(shí)現(xiàn)角度出發(fā),利用OFDM信號(hào)本身固有的訓(xùn)練序列,提出了一種易于硬件實(shí)現(xiàn)的OFDM采樣時(shí)鐘頻率偏差估計(jì)算法.

1 信號(hào)模型

2 算法描述

當(dāng)?>0時(shí),發(fā)送端采樣頻率大于接收端采樣頻率,相同時(shí)間內(nèi)接收端接收到的采樣點(diǎn)數(shù)NR少于發(fā)送端發(fā)送的采樣點(diǎn)數(shù)NT;當(dāng)?<0時(shí),發(fā)送端采樣頻率小于接收端采樣頻率,相同時(shí)間內(nèi)接收端接收到的采樣點(diǎn)數(shù)NR大于發(fā)送端發(fā)送的采樣點(diǎn)數(shù)NT.因此,采樣時(shí)鐘頻率偏差

式中,ND為收發(fā)兩端的點(diǎn)數(shù)差,只要知道一定時(shí)間內(nèi)收發(fā)兩端的采樣點(diǎn)數(shù)差ND以及接收端接收到的采樣點(diǎn)數(shù)NR,即可估計(jì)出采樣時(shí)鐘頻率偏差.

本工作中使用的長訓(xùn)練序列的頻域表達(dá)式為

相應(yīng)的時(shí)域訓(xùn)練序列x(n)由式(1)計(jì)算得到.設(shè)接收信號(hào)與已知的長訓(xùn)練序列的互相關(guān)函數(shù)為

由于實(shí)際應(yīng)用中采樣時(shí)鐘頻率偏差很小,因此式(6)的(n+d)?Ts項(xiàng)可忽略.當(dāng)不考慮噪聲時(shí),式(6)可表示為

由文獻(xiàn)[9]中基于訓(xùn)練序列互相關(guān)的符號(hào)同步算法可知,找到R(d)的峰值就找到了同步位置,此時(shí)d=0,定義d=±1兩個(gè)時(shí)刻的互相關(guān)值之差為D(K),

式中,tK為第K幀OFDM信號(hào)中的訓(xùn)練序列處的采樣時(shí)鐘相位偏差.由于長訓(xùn)練序列的自相關(guān)值具有強(qiáng)相關(guān)性(在m/=0時(shí)非常小),因此式(8)可表示為

如圖1(c),(d)所示,通過計(jì)算一段時(shí)間內(nèi)D′(K)的尖峰個(gè)數(shù)就可計(jì)算出在這段時(shí)間內(nèi)收發(fā)兩端的采樣點(diǎn)數(shù)差ND.

圖1 互相關(guān)差值特性Fig.1 Characteristic of cross-correlation diference

采樣時(shí)鐘頻率偏差估計(jì)的步驟如下.

步驟(1)由式(6)計(jì)算出互相關(guān)值R(d)并存入寄存器中,再取模值|R(d)|.

步驟(2)找一幀內(nèi)|R(d)|最大值的時(shí)刻,即d=0的時(shí)刻.

步驟(3)由式(8)得D(K),由式(10)計(jì)算D′(K);當(dāng)|D′(K)|首次超過設(shè)定門限λ時(shí),差值計(jì)數(shù)器ND和接收端采樣點(diǎn)計(jì)數(shù)器NR置0;否則,當(dāng)D′(K)>λ時(shí),ND減1,當(dāng)D′(K)

步驟(4)當(dāng)接收端累計(jì)點(diǎn)數(shù)NR大于設(shè)定值時(shí),則根據(jù)式(5)計(jì)算采樣時(shí)鐘頻率偏差?;否則重復(fù)上述步驟.

3 實(shí)驗(yàn)及仿真數(shù)據(jù)分析

3.1實(shí)驗(yàn)平臺(tái)搭建

為了驗(yàn)證所提算法的性能和有效性,本工作搭建了一個(gè)強(qiáng)度調(diào)制直接檢測(cè)的OFDM (intensity-modulation and direct-detetion-OFDM,IMDD-OFDM)離線實(shí)驗(yàn)系統(tǒng),系統(tǒng)框圖如圖2所示.首先由Matlab離線程序產(chǎn)生OFDM信號(hào),并送入任意波形發(fā)生器(arbitrary waveform generator,AWG).發(fā)送端的數(shù)據(jù)源由偽隨機(jī)二進(jìn)制序列(pseudo random binary sequence,PRBS)模塊產(chǎn)生,每個(gè)子載波使用64元正交振幅調(diào)制,為了使64點(diǎn)IFFT的輸出為實(shí)信號(hào),對(duì)IFFT的輸入作了厄米共軛處理.在這64個(gè)子載波中包含48個(gè)數(shù)據(jù)子載波和8個(gè)導(dǎo)頻,其他為空子載波.導(dǎo)頻的位置和值分別為[?24,?18,?12,?6,6,12,18,24]和[?1,1,1,?1,?1,1,1,?1].循環(huán)前綴為16點(diǎn),每幀包含80個(gè)OFDM符號(hào)以及用于同步的幀頭訓(xùn)練序列. AWG將OFDM數(shù)字信號(hào)轉(zhuǎn)換成模擬信號(hào)輸出,AWG的采樣速率為2 GS/s,量化位寬為10 bit,輸出電壓峰峰值為2 Vpp,該電壓通過3 dB帶寬為880 MHz的低通濾波器(low pass flter,LPF)后驅(qū)動(dòng)分布反饋激光器(distributed feedback laser,DFB),DFB輸出光功率為6.8 dBm,光信號(hào)通過25 km標(biāo)準(zhǔn)單模光纖(standard single mode fber,SSMF)和可變光衰減器(variable optical attenuator,VOA)后進(jìn)入光電轉(zhuǎn)換器(positive intrinsic negative, PIN)轉(zhuǎn)換成電信號(hào),在經(jīng)過一個(gè)3 dB的帶寬為880 MHz的低通濾波器后送到數(shù)字存儲(chǔ)示波器(digital storage oscilloscope,DSO)去采樣,示波器的采樣速率為2 GS/s,12 bit.為了避免AWG和DSO的參考時(shí)鐘不同,將DSO輸出的10 MHz參考時(shí)鐘作為AWG的參考時(shí)鐘,在AWG端改變采樣頻率來產(chǎn)生采樣時(shí)鐘頻率偏差.

圖2 離線實(shí)驗(yàn)系統(tǒng)框圖Fig.2 Diagram of of-line experimental system

3.2 算法分析

3.2.1 采樣時(shí)鐘頻率偏差估計(jì)精度

由式(5)可知,本算法的理論估計(jì)精度為

式中,NR為接收到的采樣點(diǎn)數(shù).

理論上,本算法的估計(jì)精度只取決于接收端的采樣點(diǎn)累計(jì)長度,在實(shí)現(xiàn)過程中算法的精度還與相關(guān)差值微分D′(K)的峰值判斷有關(guān).由于長訓(xùn)練序列是經(jīng)過精心設(shè)計(jì)的,將其用作互相關(guān)具有尖銳的峰值特性能容忍較低的信噪比.圖3為2.0×10?5頻率偏差時(shí)不同接收光功率下D′(K)的概率密度分布,D′(K)分布在兩個(gè)值附近,接收光功率越低,D′(K)的值就越分散,但在不同的接收光功率下,D′(K)的判決空間依然很大.圖4為不同接收光功率下算法的性能,采樣時(shí)鐘頻率偏差?=2.0×10?5,統(tǒng)計(jì)次數(shù)Ntimes=500次.算法性能采用均方誤差(mean squared error,MSE)衡量,其中︿?i為?的估計(jì)值,MSE定義為

可以看出,當(dāng)統(tǒng)計(jì)時(shí)間越長時(shí)算法性能越好.算法在不同的接收光功率下的性能相當(dāng).

圖3 D′(K)的概率密度分布Fig.3 Probability density distribution of D′(K)

圖4 不同接收光功率下的算法性能Fig.4 Performance of algorithm under diferent received optical powers

3.2.2 算法運(yùn)算量

本算法的運(yùn)算量主要集中在互相關(guān)模值|R(d)|的計(jì)算及其峰值的搜索,即步驟(1)和(2).步驟(1)和(2)即基于訓(xùn)練序列互相關(guān)的OFDM符號(hào)同步[9],步驟(3)中相關(guān)差值的差分D′(K)與閾值λ作比較,其結(jié)果控制著收發(fā)端采樣點(diǎn)數(shù)差值計(jì)數(shù)器ND.閾值λ的選取也很簡單,只需用|R(d)|峰值的一半作為λ即可.步驟(3)和(4)只是進(jìn)行了簡單的判斷和計(jì)數(shù)得到ND和NR,并通過式(5)計(jì)算采樣時(shí)鐘頻率偏差?.由于OFDM符號(hào)同步是必不可少的,故在利用文獻(xiàn)[9]中的算法進(jìn)行符號(hào)同步的前提下,本算法運(yùn)算量小且易于硬件實(shí)現(xiàn).

表1是本算法和基于導(dǎo)頻的算法[6-7]以及基于循環(huán)前綴算法[8]的復(fù)雜度比較.為了公平起見,表1中的比較都是基于實(shí)信號(hào)傳輸?shù)南到y(tǒng),其中M為導(dǎo)頻數(shù)量,Nc為循環(huán)前綴點(diǎn)數(shù),在本實(shí)驗(yàn)中M=8,Nc=16.從表中可以看出,本算法具有最低復(fù)雜度.另外,式(8)和(10)各需一個(gè)加法操作,步驟(3)中計(jì)數(shù)器ND和NR的計(jì)數(shù)累加各需一個(gè)加法操作,式(5)計(jì)算時(shí)鐘頻率偏差需要一個(gè)除法操作.基于導(dǎo)頻的算法不僅復(fù)雜度高于本算法,還需要插入導(dǎo)頻子載波,這將增加系統(tǒng)的開銷.基于循環(huán)前綴延時(shí)相關(guān)的算法[8]精度受循環(huán)前綴點(diǎn)數(shù)影響,在本算法Nc為16的情況下,該循環(huán)前綴的延時(shí)相關(guān)的峰值不明顯.

表1 復(fù)雜度比較Table 1 Complexity comparisons

3.3 實(shí)驗(yàn)結(jié)果分析和比較

信號(hào)經(jīng)過了25 km單模光纖,估計(jì)頻率偏差使用200幀(1 344 000個(gè)采樣點(diǎn),0.672 ms).本算法采用的采樣時(shí)鐘頻率偏差補(bǔ)償算法[6]是在快速博里葉變換(fast Fourier transformation, FFT)輸出的第l個(gè)符號(hào)乘以一個(gè)旋轉(zhuǎn)因子exp(j2πl(wèi)k?Ns/Nu),其中Nu是OFDM符號(hào)中有用數(shù)據(jù)的長度,Ns是OFDM的符號(hào)長度.EVM[10]表示接收機(jī)對(duì)信號(hào)進(jìn)行解調(diào)時(shí)產(chǎn)生的信號(hào)與理想信號(hào)的接近程度,是考量調(diào)制信號(hào)質(zhì)量的一種指標(biāo).EVM(dB)的定義為

式中,Yk為接收符號(hào),Xk為該信號(hào)的理想符號(hào),Ns為測(cè)量的符號(hào)個(gè)數(shù),ek為符號(hào)誤差量.圖5為在不同采樣時(shí)鐘頻率偏差下經(jīng)采樣時(shí)鐘頻率偏差補(bǔ)償和未補(bǔ)償情況下的EVM情況,其接收光功率為?5 dBm.在未補(bǔ)償情況下,采樣時(shí)鐘頻率偏差越大,EVM越高.利用本算法的估計(jì)結(jié)果來補(bǔ)償后,系統(tǒng)的EVM與無采樣時(shí)鐘頻率偏差時(shí)的EVM相同,其性能略優(yōu)于用基于導(dǎo)頻[7]的估計(jì)結(jié)果來補(bǔ)償時(shí)的性能.圖6為不同接收光功率下的EVM.本算法在不同的接收光功率下都工作穩(wěn)定.圖7和8分別為?5 dBm接收光功率和4.0×10?5采樣時(shí)鐘頻率偏差下信號(hào)補(bǔ)償前后的星座圖.

圖5 不同頻率偏差下的EVMFig.5 EVM versus diferent frequency ofsets

圖6 不同接收光功率下的EVMFig.6 EVM versus diferent received optical powers

圖7 補(bǔ)償前星座圖Fig.7 Constellation before compensation

圖8 補(bǔ)償后星座圖Fig.8 Constellation after compensation

4 結(jié)束語

本工作提出了一種基于訓(xùn)練序列的易于硬件實(shí)現(xiàn)的采樣時(shí)鐘頻率偏差估計(jì)算法.由于采樣時(shí)鐘頻率偏差的存在,在基于訓(xùn)練序列互相關(guān)的符號(hào)同步算法中,互相關(guān)峰值大小會(huì)發(fā)生周期性變化,通過統(tǒng)計(jì)一段時(shí)間內(nèi)該相關(guān)峰值的周期數(shù)可得到收發(fā)兩端的采樣點(diǎn)數(shù)之差,再根據(jù)接收到的采樣點(diǎn)數(shù)得到采樣時(shí)鐘頻率偏差.在利用訓(xùn)練序列互相關(guān)算法進(jìn)行符號(hào)同步的前提下,本算法的復(fù)雜度低,利于硬件實(shí)現(xiàn).對(duì)于絕大多數(shù)晶振而言,其頻率的短時(shí)間穩(wěn)定度要高于頻率準(zhǔn)確度,因此利用本算法可以較準(zhǔn)確地估計(jì)出采樣時(shí)鐘頻率偏差.另外,本工作還搭建了一個(gè)IMDD-OFDM離線實(shí)驗(yàn)系統(tǒng),實(shí)驗(yàn)結(jié)果表明本算法的采樣時(shí)鐘頻率偏差估計(jì)準(zhǔn)確,并且具有優(yōu)良的抗噪性能.

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Estimation algorithm of sampling clock frequency ofset for OOFDM system based on training sequence

ZHANG Zhen,SONG Yingxiong,ZHANG Junjie,DUN Han, GUO Songlin,XUE Ziwei
(Key Laboratory of Specialty Fiber Optics and Optical Access Networks,Shanghai University, Shanghai 200072,China)

This paper studies sampling clock synchronization for optical orthogonal frequency division multiplex(OOFDM)systems,and proposes a simple sampling clock frequency ofset(SCFO)estimation algorithm for hardware implementation based on crosscorrelation properties of the training sequence.The main idea is as follows.First,correlation between the received training sequence and the known training sequence is obtained, and then sampling clock frequency ofset found with a few adders and one divider based on the property that an additional sampling point is introduced when the cross-correlation value periodically changes a cycle.An optical OFDM system with intensity-modulation and direct-detection(IMDD-OFDM)is set up to show performance of the algorithm.Experimental and simulated results indicate that the algorithm has good accuracy and noise immunity.

optical orthogonal frequency division multiplex(OOFDM);sampling clock synchronization;cross-correlation;training sequence

TN 915.63

A

1007-2861(2017)01-0138-09

10.3969/j.issn.1007-2861.2015.02.011

2015-04-22

國家自然科學(xué)基金資助項(xiàng)目(61132004,61275073,61420106011);上海市科委重點(diǎn)資助項(xiàng)目(13JC1402600,14511100100)

宋英雄(1973—),男,研究員,博士生導(dǎo)師,博士,研究方向?yàn)楣饨尤刖W(wǎng).E-mail:herosf@shu.edu.cn