Republic of Yemen

University of Saba Region

Faculty of IT&CS

Technology Communications 2
Lec 10

Dr. Abdullah Yahia Alamri

 Today, we are going to talk about:
✓Link model
✓The channels
▪Signal fluctuations – fading
▪Interference
✓Shannon limit
✓Comparison of different modulation schemes
✓Trade-off between modulation and coding

2
Notes and figures are based on or taken from materials in the course textbook:
Bernard Sklar, Digital Communications, Fundamentals and Applications,
 What is a Link Budget

• An analysis of the entire communications path

▪ signal, noise, interference, ISI contributions, etc.
▪ Include gains and losses
• Link Budget
• An estimate of the input to output system performance
• Will the message get communicated?
• What trade-offs can be made and what effect will they
have?
 The Channel
• The propagation medium of the communicated signal between the
transmitting device and the receiving device (e.g. RF antennas, cable
modems, fiber optic transceivers)
• For RF we think of “Free Space”
◦ An ideal approximation for near-ground, atmospheric RF
transmissions.
◦ Non ideal atmospheric impairments include: absorption, reflection,
diffraction, scattering.
Sources of Signal Loss and Noise
◦ Bandlimiting Loss ◦ Polarization Loss
◦ Intersymbol Interference (ISI) ◦ Atmospheric Loss and Noise
◦ Local Oscillator Phase Noise ◦ Space Loss
◦ AM/PM Conversion (Amplitude ◦ Adjacent Channel Interference
◦ variations) ◦ Co-channel Interference
◦ Limiter Loss or Enhancement ◦ Intermodulation Noise
◦ Multiple-carrier Intermodulation ◦ Galactic or Cosmic, Star and
Products (non-linear devices) Terrestrial Noise
◦ Modulation Loss (message content ◦ Feeder Line Loss
power) ◦ Receiver Noise
◦ Antenna Efficiency ◦ Implementation Loss
◦ Radom Loss and Noise ◦ Imperfect Synchronization
Reference
 Small scale propagation effects
What is small scale fading?
Small scale fading is used to describe the rapid fluctuation of the
amplitude, phases, or multipath delays of a radio signal over a
short period of time or travel distance.
Factors influencing small scale fading
•Multi path propagation
•Speed of the mobile
•Speed of surrounding objects
•The Transmission Bandwidth of the Signal
Presence of reflectors, scattering and terminal motion results in
multiple copies being received at the mobile terminal
▪ Distorted in amplitude, phase and with different angle of arrivals
▪ They can add constructively or destructively -> fluctuations in the received signal
▪ If there is no direct line of sight (NLOS), the received signal is

8
 Large and small time scale fading: summary
Fading effects - different at different time scales
◦ the instantaneous signal envelope (short time scales (ms)) is
◦ Rayleigh distributed (NLOS)
◦ Rice distributed (LOS)

◦ the mean value of the Rayleigh (or Rice) distribution can be considered a
constant for the shorter time scales, but in fact it is a random variable with a
lognormal distribution (large time scales (seconds))
◦ caused by the changes in scenery (occur on a larger time scale)

◦ the mean of the Lognormal distribution varies with the distance from the
transmitter according to the path loss law
◦ If the mobile moves away or towards the transmitter (e.g. base station) the received
signal will also vary in time, according to the appropriate power law loss model
(e.g. free space: decreases proportional with the square of the distance, etc.)

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Large scale fading (shadow fading)
◦ Described by a lognormal distribution, determined by
empirical measurements
◦ No underlying physical phenomenon is modeled
Small scale fading – underlying physical phenomena
◦ Multipath
◦ Multiple copies of the signal arrive at destination
◦ Doppler shift of the carrier frequency
◦ relative motion of the receiver and transmitter causes Doppler
shifts
◦ yields random frequency modulation due to different frequency
shifts on the multipath components

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Doppler effect
Can be caused by
◦ the speed of mobile
◦ speed of surrounding objects
◦ If the surrounding objects move at a greater speed than the mobile, this effect
dominates, otherwise it can be ignored

Doppler shift and Rayleigh fading

◦ Mobile moving towards the transmitter with speed v: a maximum positive Doppler
shift v
f dmax =

◦ The n-th path, moving within an angle n , has a Doppler shift of

cos( n )
v
f dn =
n-th path

The random phase for the n-th path:
n
 n = 2f nt + n
v
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Multipath delay spread
Multiple copies of the signal arrive with different delays
◦ May cause signal smearing, inter-symbol interference (ISI)
◦ The power delay profile gives the average power (spatial average over a
local area) at the channel output as a function of the time delay.

Power Power
 ( ) P( k )

Delay ( ) Delay ( k )

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Interpreting the delay spread in the frequency domain
◦ While the delay spread is a natural phenomenon, we can define the coherence
bandwidth as a measure derived from the RMS delay spread
◦ Coherence bandwidth Bc = statistical measure of the range of frequencies over which
the channel can be considered to be flat (i.e., the channel passes all the spectral
components with approx. equal gain and phase)
1
Bc 
T
◦ T and Bc describe the nature of the channel in a local area; they offer no information
about the relative motion of the transmitting and the receiving mobile terminals.

Doppler effect interpretation

◦ Spectral broadening BD is a measure for the rate of changes of the mobile radio
channel due to Doppler effects
◦ If the bandwidth of the baseband signal is much greater than B D, the effect of doppler shift is
negligible

1
◦ TC  is the time duration over which the channel impulse response is
BD
essentially invariant

13
 Small scale fading: classification

Flat Fading: the channel has a constant response for bandwidth greater than
the transmitted signal bandwidth

S(f) C(f) R(f)

BS  BC
TS   T  

Frequency Selective Fading

BS  BC S(f) C(f) R(f)
TS   T
 

Needs channel equalization

14
Small scale fading: classification
Fast fading – channel impulse response changes rapidly within the symbol duration TS
BS  B D
TS  TC

Slow fading – channel impulse response changes at a rate much slower than the
transmitted symbol bandwidth
BS  BD
TS  TC

Summary of channel fading characteristics

BS Freq. sel. Freq. sel.

TS Fast slow
Flat Flat
slow fast BC
T Flat Flat
Freq sel. Freq sel.
slow fast Fast Slow

TC TS BD BS
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Fading and time scales
Time scales for analysis are important for selecting the correct
fading model
◦ If lots of averaging – ignore Rayleigh fading
◦ If analysis looks at the bit level: Rayleigh fading counts
To combine the effects, consider the averaging of the conditional pdf (Y/X) –
obtain the marginal pdf of Y

b
fY ( y ) =  fY / X ( y / X = x ) f X (x )dx
a

a, b − support of distribution f X (x)

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Physical Layer: Link Model
Link probability = probability that a
link is going to be available for
transmission, i.e., meet target SIR
requirements

A p B

p affected by:
- path loss (depends on the distance to the receiver) - mobility
- Lognormal fading (depends on the location and environment)
- mobility
- Rayleigh fading – mobility
- Interference → may dynamically vary
- mobility
- traffic burstiness
- arrival/departure statistics
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Dynamic adaptation algorithms
◦ Fading → affects useful signal strength
◦
◦
◦
◦
Power control
Adaptive modulation
Adaptive coding
Antenna Diversity
} Physical layer

◦ Adaptive MAC
◦
◦
Route diversity
Adaptive channel allocation } Network Layer

◦ Interference: determines the equivalent noise level → SINR

◦
◦
◦
◦
Power control
Adaptive modulation
Adaptive coding
Smart Antennas – beamforming
} Physical layer

◦
◦
Interference cancellation
Adaptive channel allocation (frequency, time slot, code)
}
Network Layer

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 General model of signals and interference in a
multi-user wireless system
Desired signal

s0 (t )
Transfer function of the channel
– incorporates the fading effects
H1
Received signal
s2 (t )
H2
r0 (t )
+ Receiver
sM −1 (t )
H3

sM (t ) n (t ) (AWGN)
H4

If the channel response is flat: multiply the signal with an attenuation factor
- this factor is a random variable (pdf selected according to the appropriate fading model)

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 Shannon
▪ Shannon limit
▪ Comparison of different modulation schemes
▪ Trade-off between modulation and coding
Goals in designing a DCS
◼ Maximizing the transmission bit rate
◼ Minimizing probability of bit error

◼ Minimizing the required power

◼ Minimizing required system bandwidth

◼ Maximizing system utilization

◼ Minimize system complexity

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 Limitations in designing a DCS
◼ Limitations:
◼ The Nyquist theoretical minimum bandwidth
requirement
◼ The Shannon capacity theorem (and the Shannon
limit)
◼ Government regulations
◼ Technological limitations

21
 Nyquist minimum bandwidth requirement

◼ The theoretical minimum bandwidth needed

for baseband transmission of Rs symbols per
second is Rs/2 hertz.
H( f ) (t)=sinc(
h t/T)
T 1

0 f − 2T − T 0 T 2T t
−1 1
2T 2T
Lecture 13 22
 Shannon limit
◼ Channel capacity: The maximum data rate at which error-
free communication over the channel is performed.
◼ Channel capacity of AWGV channel (Shannon capacity
theorem):

S 
=
CW
log
21+ [bits/s
]
N 
W
[Hz
]
:Bandwidth
=
SE
bC[
Watt
]
:Average
received
signal
powe
=
NN
W
0 [Watt]
:Average
noise
power

23
 Shannon limit …
◼ The Shannon theorem puts a limit on the
transmission data rate, not on the error
probability:
◼ Theoretically possible to transmit Rb
information at any rate Rb  C , with an small
error probability by using a sufficiently
complicated coding scheme

◼ For an information rate Rb  C, it is not possible

to find a code that can achieve an small error
probability.

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 Shannon limit …
C/W [bits/s/Hz]

Unattainable
region

Practical region

SNR [bits/s/Hz]

25
 Shannon limit …
 S
C =Wlog21+ 
 N C  EbC

= 
log
21
+ 

S = EbC W  N0W

N = N0W
C
As
W→or →0, weget
:
W
E 1 Shannon limit
b
→ = 0 −
.6931.6[dB]
N
0 log
2e

◼ There exists a limiting value of Eb / N 0 below which there can

be no error-free communication at any information rate.
◼ By increasing the bandwidth alone, the capacity can not be
increased to any desired value.

26
 Shannon limit …
W/C [Hz/bits/s]

Practical region

Unattainable
region

-1.6 [dB] Eb / N0 [dB]

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 Bandwidth efficiency plane
R/W [bits/s/Hz]
R=C
R>C M=256
Unattainable region
M=64
M=16 Bandwidth limited
M=8
M=4

M=2 R<C
Practical region

M=4 M=2
M=8
M=16
Shannon limit MPSK
MQAM PB =10−5
Power limited MFSK

Eb / N0 [dB]
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 Power and bandwidth limited systems

◼ Two major communication resources:

◼ Transmit power and channel bandwidth
◼ In many communication systems, one of these
resources is more precious than the other. Hence,
systems can be classified as:
◼ Power-limited systems:
◼ save power at the expense of bandwidth (for example by using
coding schemes)

◼ Bandwidth-limited systems:
◼ save bandwidth at the expense of power (for example by using
spectrally efficient modulation schemes)

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 Design example of uncoded systems
◼ Design goals:
1. The bit error probability at the modulator output must meet the
system error requirement.
2. The transmission bandwidth must not exceed the available
channel bandwidth.

Input M-ary
modulator R
R [bits/s] R
s= [symbols
]
log
2M

Output M-ary
demodulator P E E
  r
= bR= sR
P
(
EM=
) 
f

E
s

 =
,P
B 
g
P(
EM
) N N N
s

0
N  0 0 0

Lecture 13 30
 Design example of coded systems
◼ Design goals:
1. The bit error probability at the decoder output must meet the
system error requirement.
2. The rate of the code must not expand the required transmission
bandwidth beyond the available channel bandwidth.
3. The code should be as simple as possible. Generally, the shorter
the code, the simpler will be its implementation.

Input M-ary
Encoder
R [bits/s] modulator =
R
n R
s [sym
]
R
c= R[bits/s] log
2M

k

Output M-ary
Decoder
PB = f (pc) demodulator
  P E E E
P
(
EM=
) 
f

Es

,
 p
c=
g
P(
EM
) r
=b
R=c
Rc=s
Rs
0
N  N
0 N0 N0 N
0
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 Course summary
◼ In a big picture, we studied:
◼ Fundamentals issues in designing a digital
communication system (DSC)
◼ Basic techniques: formatting, coding, modulation
◼ Design goals:
◼ Probability of error and delay constraints
◼ Trade-off between parameters:
◼ Bandwidth and power limited systems
◼ Trading power with bandwidth and vise versa

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 Block diagram of a DCS

Source Channel Pulse Bandpass

Format
encode encode modulate modulate

Digital modulation

Channel
Digital demodulation

Source Channel Demod.

Format Detect
decode decode Sample

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 Course summary – cont’d
1. Modulation
◼ Baseband modulation
◼ Signal space, Euclidean distance
◼ Orthogonal basic function
◼ Matched filter to reduce ISI
◼ Equalization to reduce channel induced ISI
◼ Pulse shaping to reduce ISI due to filtering at the
transmitter and receiver
◼ Minimum Nyquist bandwidth, ideal Nyquist pulse
shapes, raise cosine pulse shape

34
 Course summary – cont’d
◼ Passband modulation
◼ Modulation schemes
◼ One dimensional waveforms (ASK, M-PAM)

◼ Two dimensional waveforms (M-PSK, M-QAM)

◼ Multidimensional waveforms (M-FSK)

◼ Coherent and non-coherent detection

◼ Average symbol and bit error probabilities
◼ Average symbol energy, symbol rate, bandwidth
◼ Comparison of modulation schemes in terms of error
performance and bandwidth occupation (power and
bandwidth)

35