TELE3113 Analogue and DigitalCommunications
Introduction to Communications
Wei Zhang
School of Electrical Engineering and Telecommunications
The University of New South Wales
Outline
Introduction to Communications
Review of Probability Theory and Random Process
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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
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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.
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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.
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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.
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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
Message signal
Input message
Output message
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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
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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.
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Transmitter
Processes the message signal to a transmitted signal
suitable for transmission over channel.
Commonly used transmission techniques include:
modulation, coding, amplifier, filtering, etc.
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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.
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Receiver
Extracts desired message from the received signal.
Usually includes decoding, demodulation, amplification and
filtering, etc.
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Output Transducer
Converts the electric signal into the form desired by user,
such as TV or audio.
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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.
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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
(
λ
4πr
)2
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.
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Link Budget
Another expression of the link budget in dB is given by
PR = EIRP + GR − Lp, (dB)
where
EIRP = 10 log10(PT GT ).
Lp = 20 log10
(
4πrλ
)
.
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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?
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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) =∂
∂xFX(x).
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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).
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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].
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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] =∑
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.
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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
σ2
X = E[(X − µX)2] =∑
X
(x − µX)2P [X = x].
If X is a continuous RV with a density function fX(x), the
variance of X is given by
σ2
X =
∫
∞
−∞
(x − µX)2fX(x)dx.
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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 ,
where
E[XY ] =
∫
∞
−∞
∫
∞
−∞
xyfX,Y (x, y)dxdy.
.
If X and Y are independent, then E[XY ] = E[X]E[Y ].
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Gaussian RV
The density function of a Gaussian RV X is
fX(x) =1
√
2πσ2
X
exp
{
−(x − µX)2
2σ2
X
}
.
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
∫
∞
x
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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