賈國(guó)慶 張寒
摘 要:干擾對(duì)齊(IA)是一種有效消除干擾的管理機(jī)制。為了徹底消除干擾信號(hào)對(duì)期望信號(hào)的影響,通過(guò)預(yù)編碼技術(shù)處理使干擾在接收端重疊,使接收端的干擾信號(hào)與期望信號(hào)有效分開(kāi)。在傳統(tǒng)最小均方誤差(Minimum Mean Square Error,MMSE)算法和最小二乘(least square,LS)算法基礎(chǔ)上,提出基于符號(hào)檢測(cè)輔助的最小均方誤差(Symbol Detection Aided Minimum Mean Square Error,SDA-MMSE)算法和最小二乘(Symbol Detection Aided Least Square,SDA-LS)算法。分別基于傳統(tǒng)算法和改進(jìn)算法進(jìn)行迭代計(jì)算,通過(guò)仿真可看出SDA-MMSE算法的MSE較SDA-LS算法的MSE降低約20%。理論分析與仿真結(jié)果表明,改進(jìn)算法較傳統(tǒng)算法具有更好的系統(tǒng)性能,且SDA-MMSE算法系統(tǒng)性能最優(yōu)。
關(guān)鍵詞:干擾對(duì)齊;符號(hào)檢測(cè);最小均方誤差;最小二乘算法
DOI:10. 11907/rjdk. 191305 開(kāi)放科學(xué)(資源服務(wù))標(biāo)識(shí)碼(OSID):
中圖分類(lèi)號(hào):TP312文獻(xiàn)標(biāo)識(shí)碼:A 文章編號(hào):1672-7800(2019)009-0072-05
MMSE and LS Interference Alignment Algorithm Based on Symbol Detection
JIA Guo-qing,ZHANG Han
(School of Physics & Electronic Information Engineering,Qinghai Nationalities University,Xining 810007,China)
Abstract:Interference alignment (IA) is an effective management mechanism for eliminating interference. In order to eliminate the influence of interference signal on the desired signal thoroughly, we use precoding technology to process the interference at the receiver so that the interference signal at the receiver can be effectively separated from the desired signal. In this paper, a symbol detection aided minimum mean square error (SDA - MMSE) algorithm and a symbol detection aided least squares (SDA - LS) algorithm based on symbol detection are proposed on the traditional MMSE algorithm and LS algorithm. Firstly, the iterative calculation is carried out based on the traditional algorithm, and then the iterative calculation is carried out by using the improved algorithm. The simulation results show that the MSE of SDA-MMSE algorithm is about 20% lower than that of SDA-LS algorithm. The theoretical analysis and results show that the proposed algorithm has better system performance than the traditional algorithm, and the performance of SDA-MMSE algorithm is the best.
Key Words: interference alignment;symbol detection;minimum mean square error;least square algorithm
0 引言
多入多出(Multiple-Input Multiple-Output,MIMO)是第四代移動(dòng)通信關(guān)鍵技術(shù)之一,不斷增加系統(tǒng)帶寬和天線發(fā)射功率可以顯著提高信道容量及頻譜利用率[1]。對(duì)單一用戶(hù) MIMO系統(tǒng),若配置的天線數(shù)受限會(huì)使系統(tǒng)降低所獲得的容量增益,而多用戶(hù) MIMO 系統(tǒng)允許多個(gè)用戶(hù)同時(shí)進(jìn)行通信傳輸,可達(dá)到更高的容量。但天線數(shù)目和用戶(hù)數(shù)量增加時(shí)會(huì)引起無(wú)線介質(zhì)的廣播與疊加, 此時(shí)產(chǎn)生的干擾成為制約多用戶(hù) MIMO 系統(tǒng)可靠通信的重要因素之一[2]。因此,為了改善系統(tǒng)性能,需采用有效措施對(duì)用戶(hù)引起的干擾進(jìn)行管理。
隨著無(wú)線通信網(wǎng)絡(luò)的發(fā)展,信道中的干擾成為限制無(wú)線通信網(wǎng)絡(luò)系統(tǒng)性能的瓶頸,近年來(lái)也有一些干擾管理方法被提出,比如干擾信號(hào)解調(diào)消除方法[3-5]、對(duì)干擾以噪聲形式剔除的方法[6-8]以及干擾對(duì)齊(Interference Alignment,IA)技術(shù)[9]。
在各種網(wǎng)絡(luò)拓?fù)渲校蓴_對(duì)齊技術(shù)得到廣泛應(yīng)用,如干擾信道[10-14]、干擾多址接入信道[15]、干擾廣播信道[16]、具有中繼的信道[17]等。干擾對(duì)齊可以使干擾信號(hào)在接收端重疊,降低干擾信號(hào)所占用的資源,減弱干擾信號(hào)對(duì)有用信號(hào)的影響,能更好地管理干擾[18-19]。當(dāng)前,隨著用戶(hù)數(shù)的不斷增加,干擾問(wèn)題也變得愈加嚴(yán)重,發(fā)射端預(yù)編碼的設(shè)計(jì)顯得更為重要。通過(guò)適當(dāng)?shù)念A(yù)編碼,可以有效控制多用戶(hù)之間的干擾,從而大大提高多用戶(hù)系統(tǒng)容量[20]。
干擾對(duì)齊作為一種干擾消除技術(shù),能在高信噪比情況下獲得很好的系統(tǒng)容量。另外,在優(yōu)化不同標(biāo)準(zhǔn)的基礎(chǔ)上,大量的迭代收發(fā)器設(shè)計(jì)方法被提出和研究[21-22]。傳統(tǒng)算法沒(méi)有考慮數(shù)據(jù)流的影響,特別是在數(shù)據(jù)流非常小的情況下是不合理的。鑒于此,本文提出傳統(tǒng)算法基礎(chǔ)上符號(hào)檢測(cè)輔助的干擾對(duì)齊算法,它是兩種基于傳統(tǒng)算法迭代收發(fā)器聯(lián)合設(shè)計(jì)的算法。一種是輔助最小均方(MMSE)誤差干擾對(duì)齊的符號(hào)檢測(cè)技術(shù),它是一種基于最小均方誤差的迭代收發(fā)器聯(lián)合設(shè)計(jì)的符號(hào)檢測(cè)算法;另一種是輔助最小二乘(LS)的符號(hào)檢測(cè)技術(shù),它是一種基于最小二乘的迭代收發(fā)器聯(lián)合設(shè)計(jì)的符號(hào)檢測(cè)算法[23-25]。通過(guò)系統(tǒng)仿真驗(yàn)證了這兩者改進(jìn)干擾對(duì)齊方法均比傳統(tǒng)干擾對(duì)齊算法具有更好的系統(tǒng)性能;并且通過(guò)比較發(fā)現(xiàn)SDA-MMSE算法比SDA-LS算法有更好的系統(tǒng)性能,可以更好地抑制干擾。
1 系統(tǒng)模型
如圖1所示的[K]用戶(hù)MIMO-OFDM干擾信道,[K]個(gè)發(fā)射機(jī)分別獨(dú)立地同時(shí)發(fā)送數(shù)據(jù)給[K]個(gè)接收機(jī),接收機(jī)既能接收到期望信號(hào),也能接收到來(lái)自于其它發(fā)射機(jī)的干擾。在無(wú)線干擾信道中,每個(gè)發(fā)射機(jī)僅嘗試與一個(gè)接收機(jī)通信。進(jìn)一步講,每個(gè)發(fā)射機(jī)上帶有的[N]個(gè)天線發(fā)送[d]個(gè)獨(dú)立的數(shù)據(jù)流與相應(yīng)接收器上的[M]個(gè)天線進(jìn)行通信。則第[i]個(gè)接收機(jī)接收的數(shù)據(jù)可以表示為:
2 算法描述
2.1 MMSE算法
根據(jù)MMSE標(biāo)準(zhǔn),[Ui]的求解可根據(jù)以下推導(dǎo)出:
為了滿足式(3-4)的IA條件,首先將矩陣[Vi]初始化,使矩陣[Vi]為一個(gè)隨機(jī)的單式矩陣,然后將式(10)和式(11)進(jìn)行迭代計(jì)算直到迭代結(jié)束或達(dá)到某些條件滿足[K]個(gè)用戶(hù),得到的數(shù)據(jù)流即為所需。
2.1.2 改進(jìn)MMSE算法
實(shí)際上,傳統(tǒng)算法根據(jù)式(7)、式(8)期望得到的式(10)、式(11)并不嚴(yán)格等于后者,尤其是當(dāng)總傳輸數(shù)據(jù)流數(shù)較小時(shí)。本文給出一種基于式(7)、式(8)使[sj=sj]的改進(jìn)算法。
2.2 LS算法
LS算法與MMSE算法類(lèi)似,在算法設(shè)計(jì)中僅僅是將噪聲看作零。
2.2.1 傳統(tǒng)LS算法
傳統(tǒng)LS算法認(rèn)為在迭代計(jì)算中收發(fā)器不與碼流相關(guān),為剔除干擾符號(hào)流[sj];傳統(tǒng)LS算法把對(duì)[Ui]和[Vi]的期望轉(zhuǎn)變?yōu)閷?duì)數(shù)據(jù)流[sj]的期望。通常情況下,符號(hào)流[sj]滿足以下條件:
為了滿足式(3)、式(4)的IA條件,首先將矩陣[Vi]初始化為一個(gè)隨機(jī)的單式矩陣,然后將式(15)和式(16)進(jìn)行迭代計(jì)算直到迭代結(jié)束或者達(dá)到某些條件滿足[K]個(gè)用戶(hù),最后根據(jù)[Ui]和[Vi]檢測(cè)得到的數(shù)據(jù)流即為所需。
2.2.2 改進(jìn)LS算法
首先,利用LS傳統(tǒng)算法進(jìn)行迭代計(jì)算出預(yù)編碼矩陣[Ui]和[Vi],然后通過(guò)符號(hào)檢測(cè),最后根據(jù)[sj=sj]再一次迭代計(jì)算[Ui]和[Vi],因此得到最優(yōu)[Ui]和[Vi]如下:
3 性能分析與仿真
仿真結(jié)果是在[K=3],[N=4],[M=4],[d=2]條件下得到,首先基于傳統(tǒng)算法設(shè)計(jì)收發(fā)機(jī)的預(yù)編碼矩陣[Ui]和抑制矩陣[Vi],進(jìn)行符號(hào)檢測(cè)得到[si],然后將檢測(cè)符號(hào)[si]代入本文改進(jìn)算法中,再進(jìn)行[Ui]和[Vi]的迭代計(jì)算,直至干擾已對(duì)齊。每個(gè)節(jié)點(diǎn)用QPSK的調(diào)制方式,分別對(duì)MMSE、SDA-MMSE和LS、SDA-LS進(jìn)行仿真,分別作出這4種符號(hào)檢測(cè)算法的均方誤差(Mean Squared Error,MSE)與迭代次數(shù)的關(guān)系曲線、誤碼率(Beat Error Rate,BER)與信噪比(Signal Noise Ratio,SNR)的關(guān)系曲線,如圖2-圖5所示。
圖2和圖3中的仿真參數(shù):信噪比SNR=15dB,[α]=7,[β]=93,信道遍歷次數(shù)為100 000。對(duì)比圖2和圖3可以看出, SDA-LS干擾對(duì)齊算法與SDA-MMSE干擾對(duì)齊算法在同一迭代次數(shù)下,SDA-MMSE算法檢測(cè)得到的符號(hào)更加接近發(fā)送符號(hào),且SDA-MMSE算法的MSE相比SDA-LS算法的MSE降低約20%,因此SDA-MMSE算法有更好的系統(tǒng)性能。
圖4和圖5是兩種算法下SNR與BER的關(guān)系曲線。SNR取0~15dB,通過(guò)增加信噪比,本文提出的兩種改進(jìn)干擾對(duì)齊算法均可獲得比傳統(tǒng)干擾對(duì)齊算法更好的BER性能,尤其是在高SNR區(qū)域。并且SDA-MMSE 算法的誤碼率較 SDA-LS 算法低,例如在15dB時(shí),SDA-MMSE算法比SDA-LS 算法約有8個(gè)dB的增益,因此SDA-MMSE算法的BER性能更優(yōu)。
4 結(jié)語(yǔ)
為了更好地消除多用戶(hù)間的干擾,本文在傳統(tǒng)算法基礎(chǔ)上針對(duì)在數(shù)據(jù)流較小的缺點(diǎn),提出了兩種基于符號(hào)檢測(cè)的干擾對(duì)齊算法:SDA-MMSE算法和SDA-LS算法。從均方誤差與誤碼率方面證明改進(jìn)算法均優(yōu)于傳統(tǒng)算法,本文提出的算法因?yàn)榉?hào)檢測(cè)的增益較傳統(tǒng)干擾對(duì)齊算法具有更好的MSE和BER性能,并且得到SDA-MMSE 算法的性能最優(yōu)。但在算法迭代計(jì)算過(guò)程中沒(méi)有考慮到復(fù)雜度的變化,后續(xù)研究可考慮在改進(jìn)算法基礎(chǔ)上降低復(fù)雜度。
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