Digital Communications - Overview

Transcription

1 EE573 : Advanced Digial Communicaions Digial Communicaions - Overview Lecurer: Assoc. Prof. Dr Noor M Khan Deparmen of Elecronic Engineering, Muhammad Ali Jinnah Universiy, Islamabad Campus, Islamabad, PAKISTAN Ph: +9 (5) , Ex. 9 noor@ieee.org, noormkhan@jinnah.edu.pk

2 Week This Lecure would be covered on Board and he following conceps would be delivered: Thermal Noise / AWGN Signal o Noise Raio (SNR) Channel Bandwidh and Daa Rae Fourier Transformaion and Time/Frequency Domains Basic Diagram of A Communicaion Sysem Modulaion Baseband and Bandpass Modulaion Advanced Digial Communicaions -Spring--Week--

3 EE 473: Digial Communicaions II Insrucor: Dr. Noor Muhammad Khan Tex book Bernard Sklar, Digial Communicaions: Fundamenals and Applicaions, Prenice Hall, nded,. References/Addiional readings: J. G. Proakis, Digial Communicaions, T. S. Rappapor, Wireless Communicaions: Principles and Pracice, Prenice Hall, 999 Marvin Kenneh Simon, Mohamed-Slim Alouini, Digial Communicaion over Fading Channels, John Wiley & Sons, 4 Lecure slides, Handous uploaded on he class folder. /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 3

4 Grading Policy Miderm: % s Major Quiz: 5% nd Major Quiz: 5% Projec/Assignmens: % Final: 4% /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 4

5 Communicaion Sysem Main purpose of communicaion is o ransfer informaion from a source o a recipien via a channel or medium. Basic block diagram of a communicaion sysem: Source Transmier Channel Receiver Recipien /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 5

6 Analog and digial communicaion sysems Communicaion sysem convers informaion ino elecrical elecromagneic/opical signals appropriae for he ransmission medium. Analog sysems conver analog message ino signals ha can propagae hrough he channel. Digial sysems conver bis (digis, symbols) ino signals Compuers naurally generae informaion as characers/bis Mos informaion can be convered ino bis Analog signals convered o bis by sampling and quanizing (A/D conversion) /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 6

7 Why digial communicaion? Digial echniques need o disinguish beween discree symbols allowing regeneraion versus amplificaion Good processing echniques are available for digial signals, such as medium. Daa compression (or source coding) Error Correcion (or channel coding) Equalizaion Securiy Easy o mix signals and daa using digial echniques /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 7

8 Digial vs Analog Advanages of digial communicaions: Regeneraor receiver Original pulse Regeneraed pulse Propagaion disance Differen kinds of digial signal are reaed idenically. Daa Voice Media A bi is a bi! 6--4 Lecure 8

9 Analog communicaion sysem example Message signals Modulaed signals /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 9

10 Digial Communicaion: Transmier /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373

11 Digial Communicaion: Receiver /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373

12 Digial communicaions: Main Poins Transmiers modulae analog messages or bis in case of a DCS for ransmission over a channel. Receivers recreae signals or bis from received signal (miigae channel effecs) Performance meric for analog sysems is fideliy, for digial i is he bi rae and error probabiliy. /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373

13 Performance Merics Analog Communicaion Sysems Meric is fideliy: wan mˆ ( ) SNR ypically used as performance meric Digial Communicaion Sysems m( ) Merics are daa rae (R bps) and probabiliy of bi error P b p( bˆ b) Symbols already known a he receiver Wihou noise/disorion/sync. problem, we will never make bi errors /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 3

14 Digial communicaion blocks /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 4

15 Processes Involved /5/3 Muhammad Ali Jinnah Universiy, Islamabad Digial Communicaions EE373 5

16 EE573 : Advanced Digial Communicaions Week -3: Digial Communicaions - Overview Deecion Mached Filer and Correlaor Filer Error Probabiliy Signal Space Orhogonal Signal Space Advanced Digial Communicaions -Spring--Week-- 6

17 Deecion Mached filer reduces he received signal o a single variable z(t), afer which he deecion of symbol is carried ou The concep of maximum likelihood deecor is based on Saisical Decision Theory I allows us o formulae he decision rule ha operaes on he daa opimize he deecion crierion zt ( ) Advanced Digial Communicaions -Spring--Week-- 7 H H

18 Deecion of Binary Signal in Gaussian Noise The oupu of he filered sampled a T is a Gaussian random process Advanced Digial Communicaions -Spring--Week-- 8

19 Hence Baye s Decision Crierion and Maximum Likelihood Deecor z H H ( a a) where z is he minimum error crierion and is opimum hreshold For anipodal signal, s () = - s () a = - a z H H Advanced Digial Communicaions -Spring--Week-- 9

20 Error will occur if s is sen s is received P( H s ) P( e s ) s is sen s is received P( H s ) P( e s ) Probabiliy of Error P( e s ) p( z s ) dz P( e s ) p( z s ) dz The oal probabiliy of error is he sum of he errors P P( e, s ) P( e s ) P( s ) P( e s ) P( s ) B i i P( H s ) P( s ) P( H s ) P( s ) Advanced Digial Communicaions -Spring--Week--

21 If signals are equally probable P P( H s ) P( s ) P( H s ) P( s ) B P( H s ) P( H s ) by Symmery PB P( H s ) P( H s) P( H s) Numerically, P B is he area under he ail of eiher of he condiional disribuions p(z s ) or p(z s ) and is given by: P P( H s ) dz p( z s ) dz B z a exp dz Advanced Digial Communicaions -Spring--Week--

22 Advanced Digial Communicaions -Spring--Week-- The above equaion canno be evaluaed in closed form (Qfuncion) Hence, ( ) exp ( ) exp B a a z a P dz z a u u du.8 B a a P Q equaion B ( ) exp z Qz z

23 Recall: Error probabiliy for binary signals P B a Q a equaion B Where we have replaced a by a..8 To minimize P B, we need o maximize: a a We have Therefore, or ( a a ) ( a a) Ed Ed N / N a a a a E E ( ) d d N N Advanced Digial Communicaions -Spring--Week-- 3

24 Table for compuing of Q-Funcions Advanced Digial Communicaions -Spring--Week-- 4

25 Signals vs vecors Represenaion of a vecor by basis vecors Orhogonaliy of vecors Orhogonaliy of signals Advanced Digial Communicaions -Spring--Week-- 5

26 Wha is a signal space? Signal space Vecor represenaions of signals in an N-dimensional orhogonal space Why do we need a signal space? I is a means o conver signals o vecors and vice versa. I is a means o calculae signals energy and Euclidean disances beween signals. Why are we ineresed in Euclidean disances beween signals? For deecion purposes: The received signal is ransformed o a received vecors. The signal which has he minimum disance o he received signal is esimaed as he ransmied signal. Advanced Digial Communicaions -Spring--Week-- 6

27 Orhogonal signal space N-dimensional orhogonal signal space is characerized by N linearly independen funcions N j( ) called basis funcions. j The basis funcions mus saisfy he orhogonaliy condiion T ( i ),)( j i )( * j d )( T K iji j, i,..., N where ij i j i j If all K i =, he signal space is orhonormal. Advanced Digial Communicaions -Spring--Week-- 7

28 Advanced Digial Communicaions -Spring--Week-- 8 Example of an orhonormal bases Example: -dimensional orhonormal signal space Example: -dimensional orhonornal signal space ( ) ( ) ( ) ( ) ( ) ( ), ) / sin( ( ) ) / cos( ( ) d T T T T T T T T ) ( T ) ( ) ( ) ( ) (

29 Signal space Any arbirary finie se of waveforms where each member of he se is of duraion T, can be expressed as a linear combinaion of N orhonogal waveforms where. j( N ) N j N M s i( ) aij j () i,..., M j N M s M i( ) i where T * ij j)( j j a i ( s ),)( j i s )( K K j,..., N d i,..., M T saa,,..., a) i ( i i in Vecor represenaion of waveform N EK a i j Waveform energy (Parseval s heorem) j ij Advanced Digial Communicaions -Spring--Week-- 9

30 Signal space * aij si ( ) j ( ) d K j T Waveform o vecor conversion i N a ij s () () j Vecor o waveform conversion j ( ) ( ) s i () N () T T a i a in a i a in s m s m a i a in a i a in N () s i () s m ( ai, ai,..., a in ) Advanced Digial Communicaions -Spring--Week-- 3

31 Example: Baseband Anipodal Signals Advanced Digial Communicaions -Spring--Week-- 3

32 Example: BPSK Advanced Digial Communicaions -Spring--Week-- 3

33 Example QPSK Advanced Digial Communicaions -Spring--Week-- 33

34 Synhesis Equaion = Modulaion Advanced Digial Communicaions -Spring--Week-- 34

35 Example: Baseband Anipodal Signals Advanced Digial Communicaions -Spring--Week-- 35

36 Example: BPSK Advanced Digial Communicaions -Spring--Week-- 36

37 Correlaion Measure of similariy beween wo signals c n E g E z g( ) z( ) d. Cross correlaion gz ( ) g( ) z( ) d. Auocorrelaion ( ) g g( ) g( ) d. Advanced Digial Communicaions -Spring--Week-- 37

38 Analysis Equaion = Deecion Advanced Digial Communicaions -Spring--Week-- 38

39 Correlaion Deecor Advanced Digial Communicaions -Spring--Week-- 39

40 Correlaion Deecor: Examples Advanced Digial Communicaions -Spring--Week-- 4

41 Correlaion Deecor Example: QPSK Advanced Digial Communicaions -Spring--Week-- 4

42 Advanced Digial Communicaions -Spring--Week-- 4 T T T T d s s d s d s d s s E ) ( ) ( ) ( ) ( ) ( ) ( (3.63) N E Q P d B The probabiliy of bi error is given by:

43 Advanced Digial Communicaions -Spring--Week-- 43 The probabiliy of bi error for anipodal signals: The probabiliy of bi error for orhogonal signals: The probabiliy of bi error for unipolar signals: N E Q P b B N E Q P b B N E Q P b B

44 Bipolar signals require a facor of increase in energy compared o orhogonal signals Since log = 3 db, we say ha bipolar signaling offers a 3 db beer performance han orhogonal Advanced Digial Communicaions -Spring--Week-- 44

45 Comparing BER Performance For P P E b / N B, orhogonal B, anipodal db 9.x 7.8x 4 For he same received signal o noise raio, anipodal provides lower bi error rae han orhogonal Advanced Digial Communicaions -Spring--Week-- 45

46 Relaion Beween SNR (S/N) and E b /N In analog communicaion he figure of meri used is he average signal power o average noise power raion or SNR. In he previous few slides we have used he erm E b /N in he bi error calculaions. How are he wo relaed? E b can be wrien as ST b and N is N/W. So we have: Eb STb S W N where N N / W N Rb Thus E b /N can be hough of as normalized SNR. Makes more sense when we have muli-level signaling. Reading: Page 7 and 8. Advanced Digial Communicaions -Spring--Week-- 46