李月貞 陳少平
摘 要: 針對基于慢變信道假設(shè)的認(rèn)知無線電不適合高速移動場景的問題,提出一種基于廣義似然比的OFDM頻譜感知算法。利用OFDM信號自身相關(guān)性得到OFDM檢測統(tǒng)計量,通過研究其統(tǒng)計分布特性得到OFDM廣義似然比檢測統(tǒng)計量,構(gòu)建快變信道檢測模型進(jìn)行頻譜感知。在原算法的基礎(chǔ)上,用檢測窗口的寬度近似替代檢測統(tǒng)計量的方差,得到廣義似然比的改進(jìn)算法。仿真結(jié)果表明,兩種感知算法在低信噪比、快變信道環(huán)境中都具有很高的認(rèn)知度,而且改進(jìn)算法對噪聲和干擾還具有很好的魯棒性。
關(guān)鍵詞: 快變信道; 正交頻分復(fù)用; 廣義似然比; 循環(huán)前綴; 頻譜感知; 認(rèn)知無線電
中圖分類號: TN911.2?34 文獻(xiàn)標(biāo)識碼: A 文章編號: 1004?373X(2018)07?0001?03
Spectrum sensing algorithm of OFDM signal in fast?varying channel environment
LI Yuezhen1, CHEN Shaoping2
(1. Wuhan Research Institute of Post and Telecommunications, Wuhan 430074, China;
2. College of Electronic and Information Engineering, South?central University for Nationalities, Wuhan 430074, China)
Abstract: Since the cognitive radio based on the assumption of a slowly?varying channel is unsuitable for the high?speed mobile scenario, an orthogonal frequency division multiplexing (OFDM) signal′s spectrum sensing algorithm based on generalized likelihood ratio is proposed, in which the autocorrelation of OFDM signal is used to get the OFDM detection statistics. Its statistics distribution characteristic is studied to get the OFDM detection statistics of generalized likelihood ratio, and construct the fast?varying channel detection model for spectrum sensing. On the basis of the original algorithm, an improved algorithm of the generalized likelihood ratio is obtained by the approximate replacement of the variance of the detection statistics with the width of the detection window. The simulation results show that the two perception algorithms both have high recognition rate in the low signal?to?noise ratio and fast?varying channel environments, but the improved algorithm has stronger robustness against noise and interference.
Keywords: fast?varying channel; orthogonal frequency division multiplexing; generalized likelihood ratio; cyclic prefix; spectrum sensing; cognitive radio
0 引 言
隨著無線通信的飛速發(fā)展與廣泛應(yīng)用,對無線電頻譜資源的需求進(jìn)一步增加,人們不得不關(guān)注未來無線頻譜資源的短缺問題[1]。OFDM技術(shù)是現(xiàn)代無線通信領(lǐng)域最重要的關(guān)鍵技術(shù)之一。它由于具有頻譜利用率高、易實(shí)現(xiàn)和接收簡單等優(yōu)點(diǎn),在很多領(lǐng)域得到了廣泛應(yīng)用[2?5]。認(rèn)知無線電最重要的功能就是頻譜感知,頻譜感知技術(shù)是在對主用戶不造成干擾的條件下感知空閑頻譜,從而提高整體的頻譜利用效率。OFDM的頻譜資源管理的靈活性和頻譜利用率的高效性使其非常適合做認(rèn)知無線電系統(tǒng)設(shè)計[6?7]。因此,基于OFDM的認(rèn)知無線電理論和技術(shù)已成為研究熱點(diǎn)。
當(dāng)前基于OFDM的認(rèn)知無線電大多是在慢變信道環(huán)境中展開研究[8?9],而在無線通信的很多高速移動場景并不適用。目前,國內(nèi)對于該問題的研究還沒有完全展開。傳統(tǒng)的基于慢變信道假設(shè)的頻譜感知算法,如能量檢測法、匹配濾波法、循環(huán)平穩(wěn)檢測法等對于快變信道中的OFDM頻譜感知根本不適用。尋找一種適用于OFDM信號的并且符合快變信道變化的感知方法是亟待解決的問題。
1 廣義似然比頻譜感知算法
OFDM信號頻譜感知就是從接收信號中提取有用信息,建立合適的檢測模型進(jìn)行頻譜感知。而實(shí)現(xiàn)信號頻譜感知關(guān)鍵的一環(huán)是從接收信號中提取出用于感知的檢測統(tǒng)計量。
1.1 廣義似然比頻譜感知模型
設(shè)數(shù)據(jù)矢量[d0,d1,d2,…,dc-1]經(jīng)過OFDM發(fā)送器后轉(zhuǎn)換成時域信號[s(n)]:
式中:[Es]是每個子載波的符號能量;[N]是FFT變換的大小;[L]是保護(hù)間隔的長度;且[Edk2=1, ][Es(n)2=cEsN]。發(fā)送信號[s(n)]經(jīng)過脈沖響應(yīng)為[h(n,l)]的多徑快變信道后,感知設(shè)備接收端的信號[y(n)]為:
在保護(hù)間隔內(nèi),接收信號未受到之前的多載波符號的影響,變?yōu)椋?/p>
式中:[y(n)=1Nk=0c-1dkHk(n)ei2πnkN,]是經(jīng)過快變信道后的信號部分;[ω(n)]是均值為0的高斯白噪聲。因此,OFDM信號的頻譜感知模型為:
1.2 廣義似然比檢測統(tǒng)計量
感知設(shè)備接收的信號是經(jīng)過多徑快變信道后的衰落信號,采樣間隔為[N,]同未加循環(huán)前綴(CP)的OFDM符號長度相等,如圖1所示。
當(dāng)采樣點(diǎn)落在任何一條路徑的CP持續(xù)時間內(nèi),這兩個采樣點(diǎn)就會呈現(xiàn)出很強(qiáng)的相關(guān)性,據(jù)此可假設(shè):
式中:“*”表示共軛轉(zhuǎn)置運(yùn)算;[m]為觀測窗口的長度。根據(jù)快變信道中[H0]和[H1]條件下[ξ]的概率密度函數(shù),得到廣義似然比的檢測統(tǒng)計量為:
[G=lnpξH1(ξH1)pξH0(ξH0)=ξ+v2] (7)
式中:[v=μ1σ2 1σ20-1,][μ1=βm?sr(1+sr),][σ20=m,σ21=][m1+2β2s2r(1+sr)2]。
1.3 廣義似然比頻譜感知流程
認(rèn)知無線電系統(tǒng)信號檢測時間規(guī)定為幾百毫秒[10?11],對應(yīng)的觀測窗口采樣點(diǎn)數(shù)上億。經(jīng)推導(dǎo),[Gσ2ξ2]服從[χ2(2,λ)]分布。[H0,][H1]條件下的非中心參數(shù)[λ]分別為:
式中:[sr]是接收端的信噪比;[β]是循環(huán)比。[Gσ2ξ2]在[H0,][H1]條件下的累積分布函數(shù)分別記作[Fx;2,λ0H0]和[Fx;2,λ1H1,]可得虛警概率[PFA]和檢測概率[PD:]
由式(10)可得廣義似然比的理論閾值:
由上面推導(dǎo)可得OFDM廣義似然比頻譜感知流程:根據(jù)式(7)計算[G,]式(12)計算[η];將[G]和預(yù)定義的閾值[η]進(jìn)行比較。若[G>η,]則判為OFDM頻譜存在,否則OFDM頻譜不存在。
2 廣義似然比的改進(jìn)算法
廣義似然比感知算法的性能與接收信號的信噪比[sr]有關(guān)。當(dāng)接收信號很強(qiáng)時,[sr]就很大,[1sr]項(xiàng)就可以忽略不計。在[H1]條件下,[ξ]的均值和方差是[sr]的單調(diào)遞增函數(shù)。經(jīng)過簡單處理,得到:
在OFDM系統(tǒng)中,一般[β≤0.2,]得[0≤μ1≤0.2m,][m≤σ21≤1.08m,]由此[σ21≈m,]式(7)近似為:
式中[Re(ξ)]表示取[ξ]的實(shí)部。[H0]條件下,[δ]的方差是[σ202]。經(jīng)推導(dǎo),[δ]服從高斯分布,理論檢測概率為:
任意給定[PFA,]根據(jù)NP準(zhǔn)則可得閾值[γ:]
[γ=m?erfc-1(2PFA)] (16)
由此可得廣義似然比的改進(jìn)算法為:給定虛警概率[PFA,]根據(jù)式(14)計算[δ,]按式(16)計算閾值[γ;]通過比較[δ]和[γ]進(jìn)行判決。如果[δ>γ,]判決為OFDM頻譜存在,反之,不存在。
3 仿真結(jié)果
假設(shè)傳輸系統(tǒng)是WiMax系統(tǒng)[10?11],采樣率為8 MHz,[β]為[14。]無線信道是多徑快變信道,路徑數(shù)為5,檢測時間為10 ms。虛警概率[PFA]嚴(yán)格定為0.01,歸一化多普勒頻移將圖2和圖3進(jìn)行對比可看出:在信噪比小于-10 dB時,廣義似然比改進(jìn)算法的感知性能較好;在信噪比為-10 dB時,兩種算法的頻譜檢測概率都達(dá)到100%。總體來看,廣義似然比算法和其改進(jìn)算法的頻譜感知性能相差不大,都可用于快變信道環(huán)境下OFDM信號的頻譜感知。通過比較兩種算法的檢測統(tǒng)計量可知,改進(jìn)算法的計算復(fù)雜度更低,而且改進(jìn)后的算法無需信噪比的先驗(yàn)知識,從而對未知噪聲和干擾具有很好的魯棒性。
4 結(jié) 語
在快變信道環(huán)境下,利用OFDM和CP的自相關(guān)性,提出基于廣義似然比的OFDM頻譜感知算法,并通過仿真驗(yàn)證了OFDM感知算法的有效性。在此基礎(chǔ)上,又對原算法中的檢測統(tǒng)計量進(jìn)行優(yōu)化,在保證感知效果不降低的情況下,忽略信噪比的先驗(yàn)知識得到了新的感知算法。仿真結(jié)果顯示改進(jìn)算法不僅具有很好的感知效果,而且對噪聲和干擾具有很好的魯棒性。
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