Comm 502: Communication Theory

Transcription

1 Comm 50: Communication Theory Prof. Dean of the faculty of IET The German University in Cairo 1

2 COMM 50: Communication Theory Instructor: Ahmed El-Mahdy Office : C3.319 Lecture Time: Sat. nd Slot Office Hours: Sunday (10 am- pm) ahmed.elmahdy@guc.edu.eg

3 Tet Book Tet Book: B. Sklar, Digital Communications: Fundamentals and Applications, Prentice Hall, 001 Reference Book: * Leon Couch II, Digital and Analog Communication Systems, 7 th edition, Prentice- Hall, 007 3

4 Grading Quizzes 15% Assignments 15% Practical Assignment 10% Midterm Eam 5% Final Eam 35% 4

5 No Course Contents Subject Basic Concepts of Communications: Elements of a communication system, channel impairments, baseband and band-pass signals, noise, random variable, probability density function, Gaussian distribution. Transmission of Baseband Signals: Pulse amplitude modulation: Sampling: impulse sampling, natural sampling, and flat-top sampling. Pulse code modulation: quantization, coding: Line codes. Introduction to Source Coding: Information sources, discrete sources, introduction to information theory, properties of source coding, source coding theorem, Huffman code, Lempel-Ziv Coding,.. Shannon Information Theory: Information measure, entropy, mutual information, noise,.. channel capacity: Binary symmetric channel, binary eraser channel, Shannon Theory,.. Introduction to channel coding: Types of error control, channel models, code rate and redundancy, Hamming codes. 5

6 Lecture 1 - Basic Concepts of communications: Elements of the communication system, Channel impairments, noise, baseband and band-pass signals, random variable, probability density function, Gaussian distribution 6

7 Elements of Communication System m(t) Transmitter Channel Receiver m ~ ( t ) Elements for any Communication System: - Transmitter - Channel - Receiver 7

8 A communication system consists of three main blocks: Transmitter: modifies the signal for efficient transmission. Channel: medium in which the modified signal is sent. The channel acts as a linear filter. Receiver: reprocesses the signal to get estimate of the transmitted signal. 8

9 Channel impairments Noise: Unwanted signals that disturb or contaminate the desired signals. For e. thermal noise,.. Interference: Is the miing of the transmitted signal with another signal. This interfering signal carries information from another source to another destination. 9

10 -Jamming: Channel impairments A strong signal, not carrying information transmitted on the same channel with the aim of disturbing communications. Intended to prevent reception at the required destination (in Military applications). Distortion: Is a change in the transmitted signal due to the nonideality of the channel. 10

11 Channel impairments Fading: Change in signal amplitude and phase due to motion and scattering. The receiver may receive multiple copies of the signal with short spacing. 11

12 Communication System Parameters 1. Quality of transmission: How close is the estimate m ~ ( t ) to the original signal m(t)? - Better estimate =higher quality transmission We measure the quality by: - Analog: Signal-to-noise ratio (SNR) - Digital : Bit Error Rate (BER). Power: How much power is required to transmit s(t)? Lower power=longer battery life, less interference 3. Bandwidth: How much bandwidth is required to transmit s(t)? Less BW means more users can share the channel 1

13 Baseband and bandpass Signals Baseband Signal: Has its spectrum centered around the origin f=0 and is zero elsewhere. W(f) - f m 0 +f m baseband Signal f 13

14 Bandpass Signal: Has its spectrum shifted to a higher frequency (carrier frequency ), Its frequency content is centered around. W ( f ) 0 w t cos f t W f f W f f c 1 c c 14

15 Modulation What is Modulation? Modulation is varying the parameters of signal transmission in accordance to the information to be transmitted Modulation Types Analogue Modulation Digital Modulation bit stream ( ) 15

16 Communication Systems Digital Analog Advantages: Finite set of messages (signals) Privacy & security (ease of encryption) Error detection and correction. Disadvantages: More bandwidth More overhead Synchronization is required Need for A/D and D/A converters - Continuous set of messages (signals) - Dominant. Disadvantages: More affected by noise than digital (noise is part of the signal) 16

17 Performance measure Analog communications: Output signal to noise ratio: SNR Signal power Noisepowerin signal Bandwidth Digital communications: Probability of error: P e totalnumber of bitsin error transmitted bits 17

18 Definitions of Bandwidth 18

19 Eample 1:? Eample :?? [Hz] 19

20 Eample 1: Eample : [Hz] 0

21 Eample 1:? Eample :? 9.1 khz 10.9kHz [Hz] 1

22 Eample 1: Eample : =1.8kHz 1-8=4 khz 9.1 khz 10.9kHz [Hz]

23 White Noise A white noise process has a flat PSD over a wide range of frequencies: S w ( f ) N o N o is called the height of the power spectral density of the noise. 3

24 E: White Noise With zero mean Time domain representation 4

25 Revision on some topics in probability & statistics 5

26 Random variable Random variable: Characterizes a random eperiment in terms of real numbers. Eample: X is the variable for the number of heads for a coin tossed three times, then X = 0,1,,3 Types of random variables: - Discrete Random Variables The random variable can only take a finite number of values (eample: tossing a coin) - Continuous Random Variables The random variable can take continuous values (eample: phase of the carrier in the signal: s( t) Acos o t o 6

27 Mean of a Random Variable Discrete Random Variable: i1 Continuous Random Variable: n P( X i i ) f ( ) d X f X () is probabilitydensityfunction of 7

28 Variance of the random variable Variance is a measure of the randomness of the random variable Discrete Random Variable: Var(X) n i1 ( i ) P( X i Continuous Random Variable: ) where is and the f ( d Var( X ) X ) f X ( )is the mean of probabilit the r.v. X y density function 8

29 Eample: Find the mean and the variance of the random variable X which is the number appearing on the up face of a die when rolling it. solution The random variable X takes one of the values: 1,, 3, 4, 5, and 6 n Mean P( X ) = 1*(1/6)+*(1/6)+3*(1/6)+4*(1/6)+ i1 i i 5*(1/6)+6*(1/6)=1/6=3.5 Variance= n i1 ( ) P( X i i ) [(1 3.5) ( 3.5) (3 3.5) (4 3.5) (5 3.5) (6 3.5) ]

30 Probability density f() Probability Density Functions: (Continuous random variables) f X Properties of probability density function: A probability density function: gives the probability that a random variable takes on values within a range. P( a b) f X ( ) d f X ( ) d 1 b a a P f X a X a f d P X a f d 0 a b a 30 X X

31 Eample: Gaussian Random Variable Probability density function: Where f X ( ) 1 ep is the mean of the random variable. is the variance of. 31

32 3 Probability density f() Properties of the Q(.) function 0 a 1 ) ( f X a a Q dz z a X P z ) ( ) / ep( 1 ) ( then ) / ( Let a Q a X P 1 ) ( d f a X P a X a d a X P ep 1 ) (

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34 Eample: The voltage X at the output of a noise generator has Gaussian distribution with zero mean and variance 1. Find P(X>.3) and P( X 1) Since P( X Then P( X a) P( X 1).3) Q(.3) solution a Q 0, 1 1Q