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TELE3113 Analogue and Digital
Communications
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.1/2

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

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


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


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
2
λ
PR = PT GT GR
4πr

where
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)

where
EIRP = 10 log10 (PT GT ).
4πr
Lp = 20 log10 λ .


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?


pdf

Denote X a random variable (RV). The probability distribution
function 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 density
function is
∂
fX (x) = FX (x).
∂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

∂ 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).

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.
−∞


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.
−∞


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 ].


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.

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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