Tele3113 wk2tue

307 views

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
307
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
6
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Tele3113 wk2tue

  1. 1. TELE3113 Analogue and Digital Communications Introduction to Communications Wei Zhang w.zhang@unsw.edu.auSchool of Electrical Engineering and Telecommunications The University of New South Wales
  2. 2. Outline Introduction to Communications Review of Probability Theory and Random Process TELE3113 - Introduction to Communications. July 28, 2009. – p.1/2
  3. 3. History of RadioRadio is the transmission of signals, by modulation ofelectromagnetic (EM) waves with frequencies below those ofvisible light. The history of radio can be seen to have threedistinct phases: EM waves and experimentation; wireless communication and technical development; and radio broadcasting and commercialization TELE3113 - Introduction to Communications. July 28, 2009. – p.2/2
  4. 4. History of Radio - Phase IEM waves and experimentation 1820 Hans Christian Orsted discovered the relationship between electricity and magnetism in an experiment. 1831 Michael Faraday discovered EM induction and proposed Faraday’s law. 1873 Maxwell first described the theoretical basis of the propagation of EM waves. Maxwell equations. 1886 to 1888: Hertz validated Maxwell’s theory through experiments. TELE3113 - Introduction to Communications. July 28, 2009. – p.3/2
  5. 5. History of Radio - Phase IIWireless communication and technical development 1893 Telsa first demonstrated a wireless radio system. 1894 Oliver Lodge demonstrated the reception of Morse code using a radio system. 1896 Marconi established the first radio station in England. 1906 Fessenden made the first radio audio broadcast. 1912 The RMS Titantic was equipped with two Marconi radios. TELE3113 - Introduction to Communications. July 28, 2009. – p.4/2
  6. 6. History of Radio - Phase IIIRadio broadcasting and commercialization: 1920 The first radio news program was broadcast in Detroit. 1920 Radio was first used to transmit pictures as television. 1930 Frequency Modulation (FM) was invented. 1963 Color television was commercially transmitted. 1990- Beginning of Digital Era. TELE3113 - Introduction to Communications. July 28, 2009. – p.5/2
  7. 7. A Communication System Message Input signal Transmitted message Input signal Transmitter transducer Additive noise, Channel Interference, Distortion due to Message bandlimiting, Output signal EM discharges, message Output etc. Receiver transducer Received signal TELE3113 - Introduction to Communications. July 28, 2009. – p.6/2
  8. 8. Message Signal Analog signal is a continuous function of time. Examples: speech, sound, AM/FM radio Digital signal is a sequence of symbols which are selected from a finite set of discrete elements. Examples: bit stream {11010111001 · · · }, CD audio, video on DVD TELE3113 - Introduction to Communications. July 28, 2009. – p.7/2
  9. 9. Input Transducer Converts message produced by a source to an electric signal (voltage or current). Example: speech waves are converted by a microphone to voltage variations. TELE3113 - Introduction to Communications. July 28, 2009. – p.8/2
  10. 10. Transmitter Processes the message signal to a transmitted signal suitable for transmission over channel. Commonly used transmission techniques include: modulation, coding, amplifier, filtering, etc. TELE3113 - Introduction to Communications. July 28, 2009. – p.9/2
  11. 11. Channel The transmission medium that connects transmitter and receiver, such as radio over the air, cable, copper wired lines, optical fibre, etc. Signals undergo degradation whilst traveling through channel Degradation may result from noise, interference, fading, multipath, distortion from band-limiting, shadowing, etc. TELE3113 - Introduction to Communications. July 28, 2009. – p.10/2
  12. 12. Receiver Extracts desired message from the received signal. Usually includes decoding, demodulation, amplification and filtering, etc. TELE3113 - Introduction to Communications. July 28, 2009. – p.11/2
  13. 13. Output Transducer Converts the electric signal into the form desired by user, such as TV or audio. TELE3113 - Introduction to Communications. July 28, 2009. – p.12/2
  14. 14. Communication ResourcesTwo primary resources for communications: Transmitted power: the average power of the transmitted signal. Channel bandwidth: width of the passband of the channel.Two important system-design parameters : Signal-to-Noise Ratio (SNR) Channel bandwidthThe design of a communication system boils down to a tradeoffbetween signal-to-noise ratio and channel bandwidth. TELE3113 - Introduction to Communications. July 28, 2009. – p.13/2
  15. 15. Free-Space Link BudgetLet the transmitting source radiate a total power PT . Thereceived power PR at a distance r is given by 2 λ PR = PT GT GR 4πrwhere GT : the gain of transmitting antenna. The product PT GT is called the effective isotropic radiated power (EIRP). GR : the gain of receiving antenna. λ: the wavelength of the transmitted EM wave. TELE3113 - Introduction to Communications. July 28, 2009. – p.14/2
  16. 16. Link BudgetAnother expression of the link budget in dB is given by PR = EIRP + GR − Lp , (dB)where EIRP = 10 log10 (PT GT ). 4πr Lp = 20 log10 λ . TELE3113 - Introduction to Communications. July 28, 2009. – p.15/2
  17. 17. Random Signals and NoiseRandom refers to “unpredictable”. Signals are random. (e.g., voice or data over Internet) Noise is random. Although they are random, they can be analyzed in average sense.What is the probability of “heads” in tossing a coin? TELE3113 - Introduction to Communications. July 28, 2009. – p.16/2
  18. 18. pdfDenote X a random variable (RV). The probability distributionfunction FX (x) is FX (x) = P [X ≤ x].Note FX (x) is a function of x, not X. 0 ≤ FX (x) ≤ 1.If X is a continuous-valued RV, then the probability densityfunction is ∂ fX (x) = FX (x). ∂x TELE3113 - Introduction to Communications. July 28, 2009. – p.17/2
  19. 19. Joint Distribution Consider two RVs X and Y . The joint probability distribution function FX,Y (x, y) is FX,Y (x, y) = P [X ≤ x, Y ≤ y]. The joint probability density function is ∂ 2 FX,Y (x, y) fX,Y (x, y) = . ∂x∂y If X and Y are statistically independent, then FX,Y (x, y) = FX (x)FY (y). fX,Y (x, y) = fX (x)fY (y). TELE3113 - Introduction to Communications. July 28, 2009. – p.18/2
  20. 20. Conditional Probability Consider two RVs X and Y . The conditional probability of Y given X, written as P [Y |X], is given by P [X, Y ] P [Y |X] = . P [X] Likewise, we have P [X, Y ] P [X|Y ] = . P [Y ] Bayes’ rule: P [X|Y ]P (Y ) P [Y |X] = . P [X] TELE3113 - Introduction to Communications. July 28, 2009. – p.19/2
  21. 21. Expectation The statistical average or expectation of a RV X is denoted by E[X]. If X is a discrete RV, the mean µX is given by µX = E[X] = xP [X = x]. X If X is a continuous RV with a density function fX (x), the expectation of X is given by ∞ E[X] = xfX (x)dx. −∞ TELE3113 - Introduction to Communications. July 28, 2009. – p.20/2
  22. 22. Variance The variance of a RV is an estimate of the spread of the probability distribution about the mean. 2 If X is a discrete RV, the variance, σX is given by σX = E[(X − µX )2 ] = 2 (x − µX )2 P [X = x]. X If X is a continuous RV with a density function fX (x), the variance of X is given by ∞ 2 σX = (x − µX )2 fX (x)dx. −∞ TELE3113 - Introduction to Communications. July 28, 2009. – p.21/2
  23. 23. Covariance The covariance of two RVs X and Y is given by Cov(X, Y ) = E[(X − µX )(Y − µY )]. Further it has (Can you prove this?) Cov(X, Y ) = E[XY ] − µX µY , where ∞ ∞ E[XY ] = xyfX,Y (x, y)dxdy. −∞ −∞ . If X and Y are independent, then E[XY ] = E[X]E[Y ]. TELE3113 - Introduction to Communications. July 28, 2009. – p.22/2
  24. 24. Gaussian RV The density function of a Gaussian RV X is 1 (x − µX )2 fX (x) = exp − 2 . 2 2πσX 2σX 2 For a special case when µX = 0 and σX = 1, it is called normalized Gaussian RV. Q-function, defined as 1 ∞ Q(x) = √ exp(−s2 /2)ds. 2π x Q-function can be viewed as the tail probability of the normalized Gaussian RV. TELE3113 - Introduction to Communications. July 28, 2009. – p.23/2
  25. 25. Random Process The random process X(t) is viewed as RV in term of time. At a fixed tk , X(tk ) is a RV. Autocorrelation of the random process is RX (t, s) = E[X(t)X ∗ (s)]. Wide-sense stationary requires: 1) the mean of the random process is a constant independent of time, and 2) the autocorrelation E[X(t)X ∗ (t − τ )] = RX (τ ) of the random process only depends upon the time difference τ , for all t and τ . TELE3113 - Introduction to Communications. July 28, 2009. – p.24/2

×