




版權(quán)說(shuō)明:本文檔由用戶提供并上傳,收益歸屬內(nèi)容提供方,若內(nèi)容存在侵權(quán),請(qǐng)進(jìn)行舉報(bào)或認(rèn)領(lǐng)
文檔簡(jiǎn)介
1、1,Ch.5 Signal-Space Analysis,5.1Introduction 5.2Geometric Representation of Signals 5.3Conversion of the Continuous AWGN Channel into a Vector Channel 5.4Likelihood Functions 5.5Coherent Detection of Signals in Noise: Maximum Likelihood Decoding 5.6Correlation Receiver 5.7Probability of Error 5.8Sum
2、mary and Discussion,2,5.1 Introduction,Fig. 5.1 Block diagram of a generic digital communication system.,Minimizing pe Optimum receiver in the minimum probability of error sense,3,5.2 Geometric Representationof Signals,Geometric representation To represent any set of M energy signals as linear combi
3、nations of N orthonormal basis functions, where N M. Gram-Schmidt orthogonalization procedure How to choose the N orthonormal basis functions for M energy signals,4,Basic Representations,Orthonormal,5,Illustration of Concepts,Figure 5.4 Illustrating the geometric representation of signals for the ca
4、se when N 2 and M 3.,6,Orthonormal Basis Functions,Fig. 5.3 Geometric representation of signals.,7,Orthonormal Basis Functions (Contd),The signal vector si si(t) is completely determined by si , length (or “absolute value”, “norm”) of si,8,Orthonormal Basis Functions (Contd),Euclidean distance betwe
5、en si and sk,9,Example: Schwarz Inequality,For real-valued signals:,For complex-valued signals:,For either case, the equality holds if and only if s2(t) = cs1(t), where c is any constant.,10,Example: Schwarz Inequality (Contd),11,Gram-Schmidt Orthogonalization Procedure,12,Example: 2B1Q Code,Fig. 5.
6、5 Signal-space representation of the 2B1Q code.,M = 4 and N = 1,13,5.3 Conversion of the Continuous AWGN Channel into a Vector Channel,In this section, we show that: In an AWGN channel, only the projections of the noise onto the basis functions of the signal set affect the sufficient statistics of t
7、he signal detection; the remainder of the noise is irrelevant.,14,Signal Analysis with AWGN Channel,Fig. 5.2 The AWGN Channel.,Noise element affecting signal detection,Irrelevant noise element,15,Statistical Characterization,X(t), W(t) : Random Processes x(t), w(t) : Sample Functions Xj, Wj : Random
8、 Variables xj, wj : Sample Values,Since Xj are Gaussian random variables, they are statistically independent.,16,Statistical Characterization (Contd),Observation vector,Memoryless channel,17,Theorem of Irrelevance,Insofar as signal detection in AWGN is concerned, only the projections of the noise on
9、to the basis functions of the signal set affects the sufficient statistics of the detection problem; the remainder of the noise is irrelevant.,18,5.4 Likelihood Functions,Likelihood function:,Log-likelihood function:,AWGN channel:,Given the observation vector x, which message symbol mi is transmitte
10、d,?,19,5.5 Coherent Detection of Signals in Noise: Maximum Likelihood Decoding,The signal constellation The signal detection problem The optimal decision rules,20,The Signal Constellation,Set of N orthonormal basis functions,A Euclidean space of dimension N,The set of message points in this space co
11、rresponding to the set of transmitted signals is called a signal constellation.,The observation vector x is represented by a received signal vector in the same Euclidean space.,21,The Signal Constellation (Contd),Fig. 5.7 Illustrating the effect of noise perturbation, depicted in (a), on the locatio
12、n of the received signal point, depicted in (b).,22,Given the observation vector x, perform a mapping from x to an estimate of the transmitted symbol, mi, in a way that would minimize the probability of error in the decision-making process.,The Signal Detection Problem,Probability of error when make
13、 the decision:,23,The Optimum Decision Rules,The maximum a posteriori probability (MAP) rule:,The maximum likelihood rule:,24,The Optimum Decision Rules (Contd),Graphical interpretation of the maximum likelihood decision rule Dividing the observation space Z into M-decision regions Z1, Z2, , ZM The
14、rule is: Observation vector x lies in region Zi if l(mk) is maximum for k = i,25,The Optimum Decision Rules (Contd),With AWGN channel:,Maximizing:,Equals minimizing:,Equals maximizing:,Fig. 5.8 An illustration of the decision rule with AGWN channel.,26,5.6 Correlation Receiver,Fig. 5.9 The optimal r
15、eceiver using correlators.,Detector/Demodulator,Signal transmission decoder,27,Correlation Receiver (Contd),Therefore, the correlator equals sampling at time T after a matched filter.,28,Correlation Receiver (Contd),Fig. 5.10 The optimal receiver using matched filters.,Detector/Demodulator,Signal tr
16、ansmission decoder,29,5.7 Probability of Error,Average probability of symbol error Invariance of the probability of error to rotation and translation Minimum energy signals Union bound on the probability of error Bit versus symbol error probabilities,30,Average Probability of Symbol Error,31,Invaria
17、nce of the Probability of Error to Rotation and Translation,Rotation:,Translation:,Distance invariance:,Error probability invariance,Maximum likelihood detection AWGN channel,32,Rotational Invariance,Figure 5.11 A pair of signal constellations for illustrating the principle of rotational invariance.
18、,33,Minimum Energy Signals,Energy of a signal constellation:,Translating the signal constellation by a vector amount a:,where,34,Minimum Energy Signals (Contd),Figure 5.12 A pair of signal constellations for illustrating the principle of translational invariance.,35,Union Bound on the Probability of
19、 Error,For AWGN channel, the symbol error probability is:,where,The above formulations are impractical to calculate,Using bounds,Union bound: one of the bounds, made by simplifying the region of integration in the top formulation,36,Union Bound (Contd),Fig. 5.13 Illustrating the union bound. (a) Constellation of four message points. (b) Three constellations with a common message point and one other message point retained from the original constellation.,The probability of x is closer t
溫馨提示
- 1. 本站所有資源如無(wú)特殊說(shuō)明,都需要本地電腦安裝OFFICE2007和PDF閱讀器。圖紙軟件為CAD,CAXA,PROE,UG,SolidWorks等.壓縮文件請(qǐng)下載最新的WinRAR軟件解壓。
- 2. 本站的文檔不包含任何第三方提供的附件圖紙等,如果需要附件,請(qǐng)聯(lián)系上傳者。文件的所有權(quán)益歸上傳用戶所有。
- 3. 本站RAR壓縮包中若帶圖紙,網(wǎng)頁(yè)內(nèi)容里面會(huì)有圖紙預(yù)覽,若沒(méi)有圖紙預(yù)覽就沒(méi)有圖紙。
- 4. 未經(jīng)權(quán)益所有人同意不得將文件中的內(nèi)容挪作商業(yè)或盈利用途。
- 5. 人人文庫(kù)網(wǎng)僅提供信息存儲(chǔ)空間,僅對(duì)用戶上傳內(nèi)容的表現(xiàn)方式做保護(hù)處理,對(duì)用戶上傳分享的文檔內(nèi)容本身不做任何修改或編輯,并不能對(duì)任何下載內(nèi)容負(fù)責(zé)。
- 6. 下載文件中如有侵權(quán)或不適當(dāng)內(nèi)容,請(qǐng)與我們聯(lián)系,我們立即糾正。
- 7. 本站不保證下載資源的準(zhǔn)確性、安全性和完整性, 同時(shí)也不承擔(dān)用戶因使用這些下載資源對(duì)自己和他人造成任何形式的傷害或損失。
最新文檔
- 醫(yī)療器械認(rèn)證的現(xiàn)場(chǎng)審查與審核流程考核試卷
- 隧道支護(hù)設(shè)計(jì)考核試卷
- 企業(yè)環(huán)境績(jī)效與社會(huì)責(zé)任報(bào)告編制規(guī)范考核試卷
- 兔舍建設(shè)成本控制與養(yǎng)殖行業(yè)標(biāo)準(zhǔn)化推進(jìn)研究考核試卷
- 廢氣處理技術(shù)綠色化學(xué)與清潔生產(chǎn)理念融合研究考核試卷
- 交通基礎(chǔ)設(shè)施布局與城市居民出行公平性研究考核試卷
- 計(jì)劃生育練習(xí)試卷1(共388題)
- 做最好的員工演講稿
- 保安公司工作總結(jié)
- 畢業(yè)生創(chuàng)意線上活動(dòng)方案
- 動(dòng)物園野生動(dòng)物馴養(yǎng)繁殖或馴養(yǎng)觀賞可行性研究報(bào)告
- 江蘇2024年江蘇省美術(shù)館招聘筆試歷年典型考題及考點(diǎn)附答案解析
- 2023-2024學(xué)年浙江省杭州市小升初考試數(shù)學(xué)試卷含解析
- DZ∕T 0215-2020 礦產(chǎn)地質(zhì)勘查規(guī)范 煤(正式版)
- GB/T 3428-2024架空導(dǎo)線用鍍鋅鋼線
- 中國(guó)特色社會(huì)主義民族發(fā)展理論研究
- 《責(zé)任勝于能力》課件
- GB/T 5465.2-2023電氣設(shè)備用圖形符號(hào)第2部分:圖形符號(hào)
- 廢氣治理設(shè)施運(yùn)行管理規(guī)程制度
- 市政工程質(zhì)量通病防治措施
- 漢字的發(fā)展(英文版介紹)Chinese-character
評(píng)論
0/150
提交評(píng)論