Tele3113 wk2tue

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TELE3113 Analogue and DigitalCommunications

Introduction to Communications

Wei Zhang

w.zhang@unsw.edu.au

School of Electrical Engineering and Telecommunications

The University of New South Wales

Outline

Introduction to Communications

Review of Probability Theory and Random Process

TELE3113 - Introduction to Communications. July 28, 2009. – p.1/24

History of Radio

Radio is the transmission of signals, by modulation of

electromagnetic (EM) waves with frequencies below those of

visible light. The history of radio can be seen to have three

distinct phases:

EM waves and experimentation;

wireless communication and technical development;

and radio broadcasting and commercialization

History of Radio - Phase I

EM 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.

History of Radio - Phase II

Wireless 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.

History of Radio - Phase III

Radio 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.

A Communication System

Input transducer Transmitter

Channel

Output transducer Receiver

Additive noise, Interference,

Distortion due to bandlimiting,

EM discharges, etc.

Transmitted signal

Received signal

Message signal

Input message

Output message

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

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.

Transmitter

Processes the message signal to a transmitted signal

suitable for transmission over channel.

Commonly used transmission techniques include:

modulation, coding, amplifier, filtering, etc.

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.

Receiver

Extracts desired message from the received signal.

Usually includes decoding, demodulation, amplification and

filtering, etc.

Output Transducer

Converts the electric signal into the form desired by user,

such as TV or audio.

Communication Resources

Two 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 bandwidth

The design of a communication system boils down to a tradeoff

between signal-to-noise ratio and channel bandwidth.

Free-Space Link Budget

Let the transmitting source radiate a total power PT . The

received power PR at a distance r is given by

PR = PT GT GR

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.

Link Budget

Another expression of the link budget in dB is given by

PR = EIRP + GR − Lp, (dB)

EIRP = 10 log10(PT GT ).

Lp = 20 log10

4πrλ

Random Signals and Noise

Random 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?

Denote X a random variable (RV). The probability distribution

function FX(x) is

FX(x) = P [X ≤ x].

FX(x) is a function of x, not X.

0 ≤ FX(x) ≤ 1.

If X is a continuous-valued RV, then the probability density

function is

fX(x) =∂

∂xFX(x).

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

fX,Y (x, y) =∂2FX,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).

Conditional Probability

Consider two RVs X and Y . The conditional probability of Y

given X, written as P [Y |X], is given by

P [Y |X] =P [X,Y ]

P [X].

Likewise, we have

P [X|Y ] =P [X,Y ]

P [Y ].

Bayes’ rule:

P [Y |X] =P [X|Y ]P (Y )

P [X].

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].

If X is a continuous RV with a density function fX(x), the

expectation of X is given by

E[X] =

−∞

xfX(x)dx.

Variance

The variance of a RV is an estimate of the spread of the

probability distribution about the mean.

If X is a discrete RV, the variance, σ2

X is given by

X = E[(X − µX)2] =∑

(x − µX)2P [X = x].

If X is a continuous RV with a density function fX(x), the

variance of X is given by

−∞

(x − µX)2fX(x)dx.

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 ] − µXµY ,

E[XY ] =

−∞

xyfX,Y (x, y)dxdy.

If X and Y are independent, then E[XY ] = E[X]E[Y ].

Gaussian RV

The density function of a Gaussian RV X is

fX(x) =1

2πσ2

−(x − µX)2

For a special case when µX = 0 and σ2

X = 1, it is called

normalized Gaussian RV.

Q-function, defined as

Q(x) =1√2π

exp(−s2/2)ds.

Q-function can be viewed as the tail probability of the

normalized Gaussian RV.TELE3113 - Introduction to Communications. July 28, 2009. – p.23/24

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 .

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