Telecommunications Engineering

Dr. David Tay

Room BG434
x 2529
d.tay@latrobe.edu.au

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 ELE5TEL: Telecommunication Engineering, 2015

Lecturer: David Tay

Course Objective

• Acquire knowledge on fundamental principles and techniques of mod-

ern digital communication systems.
• Analyse some important modulation and channel coding techniques in
communication systems.
• Understand issues in telecommunication systems reliability.
• To acquire sufficient working knowledge for further in-depth studies of
specialised topics in telecommunications.

Topics

1. Review - Signals and spectra

2. Formatting and baseband modulation
3. Baseband demodulation/detection
4. Bandpass modulation/demodulation
5. Linear block codes
6. Convolutional encoding and decoding
7. System Reliability

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Course Schedule

1. (Nominally, unless notified) Thursdays 9:30am - 12pm.

2. Practical: 4 labs. Alternate weeks starting from week 3 (Monday or
Friday)
3. Assignments: 2 take home and 2 quiz during lecture time.
4. Assessment:
• Exam: 2 hours - 50% (must pass this component).
• Labs - 30% (must pass this component).
• Assignments - 20% .

Textbook
Bernard Sklar, Digital communications: fundamentals and applications,
Prentice Hall, 2001. (All student should have a copy).

Other references
Mark L. Ayers, TELECOMMUNICATIONS SYSTEM RELIABILITY EN-
GINEERING, THEORY, AND PRACTICE, John Wiley and Sons, 2012.

John G. Proakis, Digital communications, McGraw Hill, 2001.

LECTURE SLIDES: Available in LMS.

Signal and Spectra

• Study principles and techniques of digital communication

systems (DCS).

• Emphasis on system requirements and trade-off among

system parameters:

1. SNR (signal to noise ratio)

2. BER (bit error rate)
3. Bandwidth
4. (Implementation complexity)

Why digital

• Simple signals transmitted - pulse like signals represent-

ing 0 or 1.

• Ability to clean-up or regenerate pulses during transmis-

sion - regenerative repeaters.

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 • Error correction/detection - enhances performance.

• Flexible - can combine different types of data; digital

hardware easy to reprogram.

Disadvantages
– More complex systems than analog - require intensive
signal processing.
– Non-graceful degradation - quality suddenly change
from very good to very poor below a certain SNR.

Block diagram of DCS

Note the optional and essential.

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DCS Terminology

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 • Information source - analog or discrete.

• Textual message - sequence of characters.

• Character - member of an alphabet.

• Binary digit (bit) - 0 or 1.

• Bit stream - sequence of bits.

• Symbol - a group of k bits. M = 2k is the size of alpha-

bets.

• Digital waveform - analog voltage or current waveform

representing a digital symbol.

• Date rate (bit/sec) R = k/T . T is symbol duration -

time it takes to transmit one digital symbol.

Classification of signals

1. Deterministic: no uncertainty in value at any time. Ran-

dom: not exactly sure of its value but have some idea -
probability.

2. Periodic signal: x(t) = x(t + T0 ) (T0 period). Non-

periodic don’t satisfy this.

3. Analog: x(t) with continuous time t. Discrete: x(kT )

with discrete time kT (k integer, T constant).

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 4. Energy/Power signals: p(t) = x2 (t) instantaneous power.
 T /2
ExT = x2 (t)dt energy
−T /2
 T /2
1
PxT = x2 (t)dt average power
T −T /2

Energy signal if 0 < ExT < ∞ as T → ∞.

Power signal if 0 < PxT < ∞ as T → ∞.

5. Unit Impulse (Delta) Function δ(t):

 ∞
δ(t)dt = 1
−∞

δ(t) = 0 for t = 0 and δ(t) → ∞ for t = 0.

 ∞
x(t)δ(t − t0 )dt = x(t0 )
−∞

Spectral density

Frequency domain characterization for deterministic signals.

• Energy Spectral Density (ESD): for energy signal. Fourier

transform
 ∞
X(f ) = x(t) exp(−j2πf t)dt
−∞

ψx (f ) = |X(f )|2 is the ESD.

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 • Power Spectral Density (PSD): for power signal. Fourier
series
∞
x(t) = cn exp (j2πfo nt)
n=−∞
f0 = 1/T = fundamental frequency. PSD
∞

Gx (f ) = |cn |2 δ(f − nf0 )
n=−∞

Autocorrelation

For energy signal x(t)

 ∞
Rx (τ ) = x(t)x(t + τ )dt
−∞

measures how closely the signal matches a copy of itself that

is shifted by τ .
See book for properties and autocorrelation of power signal.

Random Signals

Message signals, electrical noise and inteference considered

random.

• Random variable X, e.g. temperature. Distribution func-

tion (see book for properties)
FX (x) = P (X ≤ x)

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 • pdf (probability density function)

dFX (x)
pX (x) =
dx
 x2
P (x1 ≤ X ≤ x2 ) = pX (x)dx (area under graph)
x1
 ∞
pX (x) ≥ 0 ; pX (x)dx = 1
−∞

• For discrete random variable

p(x) = P (X = xi ) (discrete prob. function)

Ensemble averages

Mean value
 ∞
mX = E(X) = xpX (x)dx
−∞

E() expectation operator.

 ∞
E(X n ) = xn pX (x)dx (nth order moment)
−∞

Variance
 ∞
2
Var(X) = E((X − mX ) ) = (x − mX )2 pX (x)dx
−∞

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Standard deviation σX

2
σX = Var(X)

In general  ∞
E(f (X)) = f (x)pX (x)dx
−∞

Random process

Collection (ensemble) of functions:

Technically a random process X(A, t) is a function of

1. event A of a random experiment, e.g. throwing a dice.

2. time t.

For a specific event Aj , we have a single time function X(Aj , t)

(sample function).
For a specific time tk , X(A, tk ) is a random variable whose
value depends on the event.

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Ensemble: the collection of sample functions
 ∞
E(X(tk )) = xpXk (x)dx = mX (tk )
−∞

mean value depend on time

RX (t1 , t2 ) = E(X(t1 ), X(t2 ))

autocorrelation function (measures degree of similarity) de-

pends on both t1 and t2 .

Stationarity

1. Random process X(t) is strict sense stationary (SSS)

if none of its statistics (pdf) are affected by a shift in the
time origin.

2. Random process X(t) is wide sense stationary (WSS)

if
E(X(tk )) = mX = constant
mean value independent of time

RX (t1 , t2 ) = RX (t1 − t2 ) = RX (τ )

where τ = t1 − t2 (dependent on time difference only).

SSS implies WSS but not vice-versa.

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Most signal in communication systems are assumed to be
WSS.
Ergodic: ensemble averages equal time averages of one sam-
ple function X(t)

1 T /2
mX = lim X(t)dt
T →∞ T −T /2


1 T /2
RX (τ ) = lim X(t)X(t + τ )dt
T →∞ T −T /2

Power Spectral Density (PSD) of random process:

 ∞
GX (f ) = RX (τ ) exp(−j2πf τ )dτ
−∞

measures the distribution of energy in the frequency domain

- see book for properties.
Noise in communication systems:

• Unwanted electrical signal that obscure or mask the wanted

signals.

• Most common is thermal noise due to random motion of

electrons.

Gaussian random process:

  2 
1 1 x−μ
pX (x) = √ exp −
σ 2π 2 σ

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μ: mean. σ: standard deviation.
Most types of noise have Gaussian distribution: Gaussian
noise.

White noise: constant PSD w.r.t. frequency

N0
Gn (f ) = watts/Hz
2
AWGN: Additive White Gaussian Noise (most common in
communications)

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Signals through linear systems

Characterize the effect of a linear system on signals and noise

in (1) time domain and (2) frequency domain.
Time domain: impulse response h(t) is defined as the out-
put y(t) when the input x(t) is the unit impulse, i.e. when
x(t) = δ(t) then y(t) = h(t).
For an arbitrary input x(t), the output is given by the con-
volution integral
 ∞
y(t) = x(τ )h(t − τ )dτ = x(t) ∗ h(t)
−∞

Frequency domain: Fourier transform pairs:

x(t) ←→ X(f ), h(t) ←→ H(f ), y(t) ←→ Y (f )

Input-output relationship

Y (f ) = H(f )X(f )

H(f ) = |H(f )| exp[jθ(f )]

where

1. |H(f )| is called the magnitude response.

2. θ(f ) is called the phase response.

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For no distortion y(t) = Kx(t − t0 ) require |H(f )| to be
constant and θ(f ) to be linear in f . If

• |H(f )| = constant - magnitude distortion.

• θ(f ) = constant f - phase distortion.

For random signals:

GY (f ) = |H(f )|2 GX (f )

GY (f ): output PSD. GX (f ): input PSD.

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Filters and Bandwidth

Ideal filters:

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Real filters:

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Practical definition of bandwidth:

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