陳 萍 熊蔚明

(1中國科學(xué)院國家空間科學(xué)中心, 北京 100190)(2中國科學(xué)院大學(xué), 北京 100049)(3中國船舶工業(yè)系統(tǒng)工程研究院, 北京 100094)

一種可用于萊斯衰落信道的信噪比估計(jì)算法

陳 萍1,2,3熊蔚明1

(1中國科學(xué)院國家空間科學(xué)中心, 北京 100190)(2中國科學(xué)院大學(xué), 北京 100049)(3中國船舶工業(yè)系統(tǒng)工程研究院, 北京 100094)

針對萊斯衰落信道條件下,常規(guī)非數(shù)據(jù)輔助信噪比估計(jì)算法復(fù)雜度高、適用調(diào)制類型單一等問題,提出了一種信噪比估計(jì)算法.在建立系統(tǒng)等效模型的基礎(chǔ)上,推導(dǎo)出信噪比與接收信號期望和方差的關(guān)系表達(dá)式.由于在萊斯衰落信道下,該表達(dá)式無解析解,故提出用多項(xiàng)式擬合法得到一定范圍內(nèi)的信噪比近似解.仿真和對比分析實(shí)驗(yàn)表明,提出的信噪比估計(jì)算法不需要使用訓(xùn)練序列,不僅對低階和高階多種調(diào)制方式具有普適性,而且當(dāng)信道萊斯因子K=10 dB且信噪比為5～25 dB時,歸一化估計(jì)偏差均小于0.2,計(jì)算時間復(fù)雜度與M2M4算法相當(dāng),適合一般工程應(yīng)用需要.

信噪比估計(jì);萊斯衰落信道;多項(xiàng)式擬合;非數(shù)據(jù)輔助

信噪比是衡量通信質(zhì)量的重要指標(biāo),也是無線通信技術(shù)的研究熱點(diǎn)之一.由于信號在傳輸過程中受到復(fù)雜傳播環(huán)境的影響,因此需要針對不同應(yīng)用場景設(shè)計(jì)高效的信噪比估計(jì)方法[1].目前,對于SNR的估計(jì)方法主要分為2類:一類為基于數(shù)據(jù)輔助(data-aided,DA)的方法,另一類則不需要數(shù)據(jù)輔助(non-data-aided,NDA).NDA 類算法包括最大似然類算法[2]、矩估計(jì)類算法[3-4]、子空間類算法[5]等.NDA類算法無需訓(xùn)練序列,因而被廣泛應(yīng)用.

根據(jù)樣本選取的差異,NDA類信噪比估計(jì)算法可以分為:判決域和非判決域的信噪比估計(jì)[6].判決域的信噪比估計(jì)是指用于估計(jì)的信號樣本已經(jīng)經(jīng)過了同步和均衡操作,其調(diào)制方式已知.非判決域的信噪比估計(jì)指信號未進(jìn)行同步和均衡處理(如中頻信號),其調(diào)制方式未知.

針對高斯白噪聲(AWGN)信道,許多學(xué)者對信噪比估計(jì)方法開展了深入研究.經(jīng)典信噪比估計(jì)算法有最大似然(ML)估計(jì)、信號噪聲方差(SNV)估計(jì)、分離符號矩估計(jì)(SSME)、二階-四階矩估計(jì)(M2M4)以及信號-變換比估計(jì)(SVR)算法等.Pauluzzi等[7]利用均方誤差(MSE)對上述5種估計(jì)方法進(jìn)行了詳細(xì)的分析和比較,并通過與克拉美羅界(CRB)[8]的比較,得出了M2M4算法、SNV算法和ML算法有較好估計(jì)效果的結(jié)論.

在萊斯衰落信道下,由于存在乘性衰落因子,信噪比估計(jì)方法一般比在AWGN信道中更復(fù)雜.在準(zhǔn)靜態(tài)平坦衰落信道下,對于恒幅調(diào)制信號,矩估計(jì)器(如M2M4估計(jì)器)可以用于衰落信號信噪比估計(jì)[9].針對移動通信中廣泛使用的 Nakagami-m信道,Ramesh等[10]給出了一種萊斯衰落信道信噪比估計(jì)方法.但這種估計(jì)方法只考慮了BPSK調(diào)制,無法應(yīng)用于高階調(diào)制.楊俊等[11]主要針對QPSK提出改進(jìn)的信噪比估計(jì)方法.韓博等[12]提出了一種基于相關(guān)向量機(jī)的信噪比估計(jì)方法,該方法應(yīng)用相關(guān)向量機(jī)建立估計(jì)模型,通過訓(xùn)練學(xué)習(xí)得到可靠的模型權(quán)值.但是該方法需要進(jìn)行矩陣求逆運(yùn)算,復(fù)雜度較高,不適用于硬件實(shí)現(xiàn).李晉等[13]提出了一種低復(fù)雜度盲信噪比估計(jì)方法,但是該方法只針對瑞利(Rayleigh)衰落信道進(jìn)行了分析,沒有針對萊斯衰落信道提出信噪比估計(jì)方法.

本文從工程應(yīng)用的角度出發(fā),針對萊斯衰落信道提出一種屬于判決域的非數(shù)據(jù)輔助信噪比估計(jì)方法.該方法具有估計(jì)精度高、適用范圍寬、計(jì)算復(fù)雜度低的特點(diǎn),適用于低階和高階多種調(diào)制信號的信噪比估計(jì).

1 信噪比估計(jì)模型

在AWGN信道下,信號輸入判決器基本消除了載波偏差和碼間干擾,僅混有加性高斯白噪聲信號,接收信號rk可表示為

rk=xk+nkk=1,2,…,L

(1)

對于萊斯衰落信道,需改進(jìn)上述信號模型.設(shè)tn為信號源,dk為采樣后信號,mk為經(jīng)過成形濾波器后的信號.ri為信道功率因子(對于萊斯衰落信道,信道增益ri服從萊斯分布),ni為噪聲信號,si為接收信號,sk為經(jīng)過匹配濾波器的信號,信噪比估計(jì)的系統(tǒng)等效模型如圖1所示[14].在本文的分析中,假設(shè)系統(tǒng)均衡和同步誤差足夠小,不會對信噪比估計(jì)造成明顯影響.

圖1 系統(tǒng)等效模型

過采樣和脈沖成形后的信號可表示為

(2)

式中,hk-n為成形濾波器系數(shù);dk為過采樣后的信號.則接收信號表示為

si=rimk+ni

(3)

匹配濾波器輸出信號為

(4)

則信噪比SNR表示為

(5)

可見,信噪比SNR估計(jì)的關(guān)鍵是對式(5)中接收信號功率以及噪聲信號方差進(jìn)行準(zhǔn)確估計(jì).

2 萊斯信道信噪比估計(jì)算法

2.1 估計(jì)算法原理

根據(jù)圖1所示的系統(tǒng)等效模型,假設(shè)用于估計(jì)的信號樣本經(jīng)過同步和均衡操作,而且其調(diào)制方式已知.設(shè)Es為發(fā)送符號的能量,接收信號si表示為

(6)

式中,ni與衰落因子ri為相互獨(dú)立的隨機(jī)變量.ri服從萊斯分布,表示為[15]

(7)

(8)

萊斯因子K可以表示信道的衰落程度,K越大，信道條件越好；反之，則表示多徑衰落越嚴(yán)重.K=∞時表示信道條件近似為理想高斯信道,K=0時表示信道條件多徑影響嚴(yán)重,可近似認(rèn)為瑞利信道.可見,瑞利信道是萊斯信道的一種特例.萊斯信道中信號的包絡(luò)服從萊斯分布,其概率密度函數(shù)為

(9)

(10)

(11)

考慮到衰落因子ri和信道噪聲ni為相互獨(dú)立的隨機(jī)變量,故E(rini)=E(ri)E(ni)=0,從而,式(11)改寫為

(12)

(13)

對于萊斯衰落信道,有

(14)

(15)

(16)

故信噪比表示為

(17)

(18)

(19)

從工程應(yīng)用角度出發(fā),在保證一定精度的前提下,為降低運(yùn)算復(fù)雜度,本文采用三階擬合系數(shù).

2.2 估計(jì)算法

① 設(shè)接收端收到I路和Q路N個數(shù)據(jù)分別為Ii和Qi.

② 根據(jù)下式計(jì)算接收數(shù)據(jù)的幅值A(chǔ)i和相位φi:

(20)

(21)

③ 按照調(diào)制階數(shù)和劃分區(qū)間的準(zhǔn)則將接收到的數(shù)據(jù)劃分為M個區(qū)間.

⑧ 對接收數(shù)據(jù)進(jìn)行多項(xiàng)式擬合,以p為自變量,理論信噪比γ為應(yīng)變量,得到擬合多項(xiàng)式f(p),則信噪比估計(jì)近似結(jié)果γfit=f(p).

上述步驟③中,針對不同的調(diào)制方式應(yīng)用如下準(zhǔn)則劃分區(qū)間:

1) QPSK調(diào)制.區(qū)間1為0≤φi<π/2;區(qū)間2為π/2≤φi<π;區(qū)間3為π≤φi<3π/2;區(qū)間4為3π/2≤φi<2π.

2) 8PSK調(diào)制.區(qū)間1為0≤φi<π/8或15π/8≤φi<2π;區(qū)間2～區(qū)間8為mπ/4-π/8≤φi

3) 16APSK調(diào)制.區(qū)間1為Ai<(Rin+Rout)/2,0≤φi<π/4或7π/4≤φi<2π;區(qū)間2～區(qū)間4為Ai<(Rin+Rout)/2,mπ/2-π/4≤φi

4) 32APSK調(diào)制.區(qū)間1為Ai<(Rin+Rmid)/2,0≤φi<π/4或7π/4≤φi<2π;區(qū)間2～區(qū)間4為Ai<(Rin+Rmid)/2,mπ/2-π/4≤φi(Rout+Rmid)/2,0≤φi<π/16或31π/16≤φi<2π;區(qū)間6～區(qū)間20為Ai>(Rout+Rmid)/2,mπ/8-π/16≤φi

3 仿真結(jié)果及分析

3.1 歸一化估計(jì)偏差

定義信噪比的歸一化估計(jì)偏差為[19]

(22)

(a) QPSK

(b) 16APSK

(a) QPSK

(b) 16APSK

圖2(a)和(b)分別是估計(jì)數(shù)據(jù)長度為5 000時QPSK調(diào)制信號和16APSK調(diào)制信號的信噪比估計(jì)仿真結(jié)果,圖3(a)和(b)是對應(yīng)信噪比估計(jì)結(jié)果的歸一化偏差.

分析圖2和圖3的結(jié)果,得出如下結(jié)論:

1) 在信道萊斯衰落因子K=10 dB的條件下,本文提出的估計(jì)算法歸一化偏差不超過0.2,說明該算法在信道衰落較嚴(yán)重時仍然具有較高的估計(jì)精度.

2) 本文提出的信噪比估計(jì)算法對低階和高階調(diào)制具有普適性:對于低階QPSK調(diào)制和高階16APSK調(diào)制,都具有較精確的估計(jì)結(jié)果,估計(jì)偏差不超過0.2.而M2M4算法在高階16APSK調(diào)制下的估計(jì)偏差趨近于1,說明該算法已失效,不適用于高階調(diào)制.

3) 本文提出的信噪比估計(jì)算法具有較寬的適用范圍,在信噪比為5～25 dB范圍內(nèi)都保持較低估計(jì)偏差.

3.2 計(jì)算復(fù)雜度

本文提出的信噪比估計(jì)算法需要計(jì)算信號幅值A(chǔ)i和相位φi,可采用CORDIC(coordinate rotation digital computer, CORDIC)算法完成.CORDIC算法的思想是通過迭代方法,不斷旋轉(zhuǎn)特定角度,使得累計(jì)旋轉(zhuǎn)角度和無限接近某一設(shè)定角度.CORDIC算法的每個迭代需要2次移位、1次查找表和3次加法.設(shè)每個用于估計(jì)的接收幀長度為N,即利用接收到的N個數(shù)據(jù)進(jìn)行信噪比估計(jì),則本文算法的時間復(fù)雜度為O(N).本文算法的時間復(fù)雜度與M2M4算法的時間復(fù)雜度相當(dāng),遠(yuǎn)低于文獻(xiàn)[12]算法的時間復(fù)雜度O(N3)+O(N2M).

4 結(jié)語

針對萊斯衰落信道,提出了一種屬于判決域的非數(shù)據(jù)輔助信噪比估計(jì)算法.在推導(dǎo)出信噪比與接收信號期望和方差的關(guān)系表達(dá)式基礎(chǔ)上,對接收數(shù)據(jù)按照相應(yīng)準(zhǔn)則進(jìn)行數(shù)理統(tǒng)計(jì)和分析,采用多項(xiàng)式擬合法得到信噪比估計(jì)結(jié)果.在同樣的信道條件和信號采樣長度下,本文算法具有估計(jì)結(jié)果精度高、適用范圍寬、適用于低階和高階多種調(diào)制類型的特點(diǎn),且計(jì)算時間復(fù)雜度與M2M4算法相當(dāng),是一種高效的信噪比估計(jì)方法.

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An SNR estimation algorithm for Rician fading channel

Chen Ping1,2,3Xiong Weiming1

(1National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China)(2University of Chinese Academy of Sciences, Beijing 100049, China)(3China State Shipbuilding Corporation System Engineering Research Institute, Beijing 100094, China)

Aimed at the problems in Rician fading channel, i.e. general Non-Data-Aided signal-to-noise ratio(SNR) estimation algorithms were very complex and usually suitable for a certain modulation pattern. This paper proposed an SNR estimation algorithm. On the basis of establishing equivalent system model, the relationship expression of SNR, expectation and variance of received signals were deduced. Under the conditions of the Rician fading channel, the deduced expression had no analytic solutions, thus using the polynomial fitting method to obtain approximate solutions of SNR during a certain range. Simulations and comparison experiments show that, the algorithm does not need any training sequence and is universal for both lower and higher order modulations. If the channel Rician factorK=10 dB and the SNR is between 5 and 25 dB, the normalization bias is lower than 0.2, the computational complexity is comparable with M2M4 algorithm, thus satisfying requirements of general engineering application.

signal-to-noise ratio(SNR) estimation; Rician fading channel; polynomial fitting;non-data-aided

10.3969/j.issn.1001-0505.2017.02.002

2016-07-18. 作者簡介: 陳萍(1983—)，女，博士生；熊蔚明(聯(lián)系人)，男，研究員，博士生導(dǎo)師，xwm@nssc.ac.cn.

國家高技術(shù)發(fā)展計(jì)劃(863計(jì)劃)資助項(xiàng)目(2011AA7033045).

陳萍,熊蔚明.一種可用于萊斯衰落信道的信噪比估計(jì)算法[J].東南大學(xué)學(xué)報(bào)(自然科學(xué)版),2017,47(2):209-214.

10.3969/j.issn.1001-0505.2017.02.002.

TN911.22

A

1001-0505(2017)02-0209-06