notes - SYSC 5504 Principles of Digital Communication...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
SYSC 5504 Principles of Digital Communication Course Notes Fall 2010/11 Department of Systems & Computer Engineering Carleton University © 2010, Ian Marsland, Dept. of Systems & Computer Engineering, Carleton University
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Contents R and omV a r i ab l e s .................................................... 2 R omP ro c e s s e 8 Bandpass Signal Modulation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 V e c t o rSp a c eC on c ep t s.................................................. 1 7 S i gn a lSp a c c t 1 8 Gram-Schmidt Orthogonalization Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Geometric Representation of Bandpass Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Sp e c t ra lCh a c t e r i s t i c so fB a s eb andS i a l s ..................................... 3 0 Spectral Characteristics of Bandpass Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Bandpass Transmitter Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Th eM a t ch edF i l t e r.................................................... 4 0 Optimal Receivers for the AWGN Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Bandpass Receiver Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Probability of a Symbol Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Example: Probability of a Bit Error of 4-PAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Syn ron i z a t i on. ..................................................... 6 3 Summary of Bandpass Signalling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 In f o rm a t i onTh e o ryandCh ann e lC ap a c i t y ...................................... 7 7 E r rC t lT e chn iqu e s ................................................ 9 0 L in e a rB l o c kC od e s.................................................... 9 2 E r rD e t e c t i onandAu t om a t i cR e a tR equ e s t(ARQ ) ............................... 9 6 F o rw a rdE r o r r e c t i on(FEC ) ............................................ 1 0 0 Cy c l i cC e s ....................................................... 1 0 4 C v o lu t i a e s................................................... 1 0 8 Tutorial: Constructing Trellis Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 D e c go fC v o t i a e s............................................ 1 1 6 P e r f o an c eAn a ly s i v o t i a e s..................................... 1 2 3 MAPD e c v o t i a e s ........................................ 1 2 8 Trellis Coded Modulation (TCM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Multiple Access Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 r e adSp e c t rumS i a l s................................................. 1 4 4 S e l e c t edM a th em a t i c a l e s.............................................. 1 4 8 SYSC 5504 1 Fall 2010/11
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Review of Probability Theory Random Variables A random variable models the outcome of an experiment which is not deterministic in nature. Example: Coin Toss Let X denote the outcome from flipping a coin. Pr { X =‘heads } = 1 2 Pr { X = ‘tails’ } = 1 2 Heads or tails can occur with equal probability. Discrete Random Variables – takes on values from a set that is either Fnite or countably inFnite – takes each value with a certain probability, Pr { X = x } – one of the outcomes must occur, so X all x Pr { X = x } =1 – cumulative distribution function F X ( x )=Pr { X x } = X all a x Pr { X = a } Example: Sum of the value of two dice 2 3 4 5 6 7 8 9 10 11 12 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 x Pr{X = x} 2 3 4 5 6 7 8 9 10 11 12 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x F X (x) Joint and Conditional Probabilities Consider two random variables, X and Y . The joint probability of event X = x and event Y = y both occuring is denoted by Pr { X = x, Y = y } . Example: ±lip a coin twice Let X be the outcome of the Frst toss, and Y be the outcome of the second toss. Pr { X ,Y } = 1 4 SYSC 5504 2 ±all 2010/11
Background image of page 4
Example: Balls in an urn Consider an urn containing two red balls and two black balls. Let X denote the colour of a ball drawn randomly. Then Pr { X =‘red } =Pr { X =‘black’ } = 1 2 Now let X and Y denote the colours of two balls drawn randomly without replacement. Then Pr { X ,Y } = 1 6 Pr { X =‘b lack } = 2 6 Pr { X =‘red’ } = 2 6 Pr { X } = 1 6 The joint cdf of X and Y is F X,Y ( x, y )=Pr { X x, Y y } = X all a x X all b y Pr { X = a, Y = b } The conditional probability of event Y = y occuring given that event X = x hasoccurredisPr { Y = y | X = x } Example: Coins Pr { Y =‘heads’ | X
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/25/2011 for the course SCE 5201 taught by Professor Huang during the Spring '10 term at Carleton CA.

Page1 / 153

notes - SYSC 5504 Principles of Digital Communication...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online