Mobile Computing CS6242

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University of Manchester School of Computer
Science CS6242 Mobile Computing Introduction
layer 1 overview Barry Cheetham
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Personnel
1. Physical layer radio channel (Barry
Karim) 2. Medium access control
(Nick) 3. Error control (Barry) 4. Network
transport layer issues (Nick) 5. WLAN security
(Aleksandra) 6. Higher layer
issues (Barry Nick guest)) Demonstrators
Karim, Ian Featherstone, Basab Sen
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CS624 Mobile Computing Level MSc Credit
Rating 15 Degrees ACS/CS Pre-requisites
Basic maths Pre-course work 40 hrs Taught week
40 hours lectures laboratories Post-course
work 40 hours assessed practical Assessment 67
practical 33 exam Staff B. Cheetham, N
Filer, K Nasr, A Nenadic, guest, I.
Featherstone, B. Sen www.cs.man.ac.uk/Study_sub
web/Ugrad/coursenotes/CS6242
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Aims Learning outcomes Aims
Understanding of concepts underlying current
developments in
mobile comms wireless computer networks.
Learning Outcomes 1) Understanding of radio
propagation interference 2) Understanding of
digital transmission systems 3) Understanding
of MAC protocols for wireless networks 4)
Understanding of the systems, protocols and
mechanisms to support mobility for mobile
internet users 5) Ability to investigate
transmission modulation using MATLAB.
experience of using a network simulation package
(OPNET)
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• Reading list
• J.Schiller, Mobile communications,
  Addison-Wesley, 2003
• Supplemental books
• T.S. Rappaport, Wireless communications
  Principle and Practice,
• A S. Tanenbaum, Computer Networks (4th Edition),
  Prentice Hall,
• 
  2003.

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Detailed Syllabus Intro to wireless networking
digital trans. Characteristics of radio
propagation. MAC error control. Network
transport layers WLAN security Protocols
supporting mobility MATLAB tutorials
assignment OPNET tutorials assignment
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Aims for Barry Karim
1. Up-to-date overview of wired wireless
telephone
computer networks 2. Principles of digital
transmission (i) at base-band
(ii) by single carrier
modulation
(iii) by multi-carrier modulation 3.
Progagation of radio waves
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1.1. Principles of digital transmission for wired
wireless telephone computer networks
Transmitter like DAC receiver like ADC
DAC
ADC
10110
10111
Channel
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1.1.2 (i) Base-band transmission
volts
t
10110
Receive symbols map to bit-stream
Map to base-band
10110..
Channel
Ethernet with Manchester coding uses base-band
signalling
10
Base-band signalling
volts
t
Map to base-band
1011110
11
Manchester coding
volts
t
Map to base-band
1011110
12
1.1.2 (ii) Modulation of single carrier
volts
t
Modulate carrier
Map to base-band
10110
13
Amplitude modulation of single carrier
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Phase modulation of single carrier
15
Amplitude phase modulatn of single carrier
volts
t
Map to base-band
Multiply
10110
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Effect of single carrier modulation on frequency
spectrum
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Where do we get those side-bands from?
Message carrier A cos(?Mt) cos(?Ct)
0.5A cos(?Ct ?Mt) 0.5A
cos(?Ct - ?Mt) 0.5A cos( (?C
?M) t ) 0.5 A cos((?C - ?M)t)
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1.1.3 ASK, FSK, PSK
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ASK spectrum
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FSK_ frequency shift keying
Simple generator using voltage controlled
oscillor
21
FSK another generation method
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FSK and GMSK

• Advantages constant envelope,
• insensitivity to
  frequency shifts
• Disadvantage spectral inefficiency
• Gaussian minimum shift keying
• ?2 bits/s /Hz
• Spectrum similar to ASK
• Used for GSM

23
PSK_ phase-shift keying
24
PSK waveform
DPSK more commonly used
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1.1.4 Coherent demodulation of ASK
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1.1.5 Non-coherent detection of ASK
t
Threshold detector
Rectify smooth
10110
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1.1.6. Vector modulator for single carrier
Sin(2?fCt)
10110
Map
bI(t)
Mult
ADD
Mult
Map
bR(t)
11011
Cos(2?fCt)
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Vector de-modulator
Sin(2?fCt)
bI(t)
10110
Detect
Mult
Low pass
Detect
Mult
11011
Low pass
bR(t)
Cos(2?fCt)
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Complex base-band
Transmit bR(t)cos(2?fCt)
bI(t) sin(2?fCt) Real bR(t)
jbI(t) . cos (2?fCt) j sin(2?fCt)
Real b(t) . exp(-2?fCt)
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Remember
cos 2 (2?fCt) 0.5 0.5
cos(4?fCt) sin 2 (2?fCt) 0.5 -
0.5 cos(4?fCt) sin(2?fCt) cos (2?fCt)
0.5sin(4?fCt)
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Vector modulator (again)
10110
Map
Mult
b(t)
Complex signal
11011
Complx base-band
exp(-2?fCt)
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1.1.7 QPSK _ quaternary PSK

• Where bR(t) bI(t) are bipolar,
  bR(t)cos(2?fCt) bI(t) sin(2?fCt) are PSK.
  2-channel modulation process is QPSK.
• Bandwidth efficiency twice that of PSK.
• 2 bits/second per Hz.
• Widely used.

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1.1.8 Pulse shaping bandwidth efficiency

• Spectra of pulses must be adapted to channel.
• Channel will have limited bandwidth.
• Rectangular pulses totally unsuitable in
  practice.
• Ideal pulse shaping causes each pulse to ring
  on forever
  once it has started.
• Risk bit-errors due to inter-symbol
  interference (ISI).
• Can eliminate ISI even when pulses do run into
  each other,
• At bb only when symbol rate lt 2 x bandwidth of
  pulse.
• Max bandwidth efficiency at bb 2 symbols/s per
  Hz.

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1.1.9 Bandwidth efficiency with binary

• With binary signalling, each symbol represents
  one bit.
• With a pulse-shape carefully chosen to eliminate
  ISI binary can achieve up to 2 b/s per Hz at
  base-band.
• Multiplication by sinusoidal carrier doubles
  bandwidth
• Max of 1 b/s per Hz with real base-band signal.
• With vector-modulation, 2 channels each giving 1
  b/s per Hz possible,
• Brings achievable bandwidth effic back to 2 b/s
  per Hz.
• At expense of complexity of coherent detection.
• Binary PSK can achieve up to 1 bit/s per Hz,
• QPSK can achieve 2 bit/s per Hz.

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1.1.10 Multi-level signalling

• With 2 b/s/Hz, a modem could achieve 6 kb/s over
  3 kHz.
• ?10 of what we know to be possible.
• Must use multi-level schemes where each symbol
  represents more than one bit.
• Could have pulses of amplitude 0, 1, 2, 3, 4, 5,
  6, 7 volts.
• Each pulse represents 3 bits at once (000, 001,
  010, 011, 100, 101, 110, 111).
• Bandwidth efficiency increases to 6 bit/s per Hz.
  
• Cost is increased sensitivity to effects of
  noise.
• For 56k modem, more than 6 b/s per Hz required
• Combined PSK ASK used to produce range of
  symbols.

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1.1.11 Single carrier digital modulation schemes

• ASK, FSK, PSK, DPSK, QPSK
• Differential QPSK
• Gaussian FSK MSK
• Combined ASK PSK (QAM, APK)
• etc.

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Other modulation techniques

• Direct sequence spread spectrum techniques (DSSS)
• Frequency hopping (FHSS)
• Complementary code keying (CCK)

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1.1.12 Multi-carrier modulation schemes

• Advantages with respect to multipath fading.
• OFDM used for digital radio, TV , WLANs ADSL.
  
• Radio/TV use 1024 carriers WLANs use 64.
• Modulation achieved on all carriers by one
  inverse FFT.
• Use of cyclic extension simplifies pulse
  shaping matched filtering as required with
  single carrier systems.
• Equalisation is greatly simplified.
• More on this later

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1.1.13 Shannon Hartley Law

• Channel capacity C B log2(1 S/N) bits/s
• Max bit-rate achievable with arbitrarily small
  BER.
• Bandwidth B Hz AWGN.
• S/N is signal/noise power ratio (not in dB),
• C B log10(1S/N)/ log10(2) ? 0.332
  log10(1S/N)
• If S/N gtgt1, C ? 0.332 x B x SNR in dB.
• Valid when SNR 10log10(S/N) gtgt0
• Ex What is C for 3kHz channel with 50dB SNR?
• Ex SNR needed to convey 54 Mb/s over 20MHz ?

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1.2. Telephone networks

• 1.2.1 Introduction
• POTs Analogue using twisted pairs for last
  mile
• Digital exchange to exchange.
• 300 - 3.4kHz speech sampled at
  8kHz
• ITU-T-G711 64-bit log-PCM (8 x
  8kHz)

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1.2.2 Wireless Telephone networks

• Cordless (DECT) cellular (GSM) mobile phones.
• Wireless local loop (then wired)
• Radio medium shared
• Cellular base-stations can hand off
• Fading due to multi-path (flat or frequency
  selective)

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1.2.3 Effects of multi-path in wireless telephony

• Line of sight paths rare in cities
• Fading caused by multi-path flat or
  frequency-selective
• Affect gain phase-delay of channel.
• Coherence b/w BC is largest b/w for which fading
  appears flat.
• In a city, BC ? 30 kHz, allowing analogue mobile
  phones with 30
  kHz channels to work without equalisers.
• 900 MHz GSM phones with 200 MHz b/w need
  equalisation.
• Equaliser is filter which reverses filtering
  effect of channel.

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1.2.4 Effect of multipath on bit-errors ISI

• Reductions in gain due to fading cause small
  signals to be received, so noise will have
  greater effect produce more bit-errors.
• Frequency selective fading alters shapes of
  pulses and thus causes ISI.
• Gain and phase-delay affected

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1.3. Wired computer networks

• LAN is equiv of local telephone loop
• Ethernet (IEEE802.3)
• Orig coax, hubs contention mode (thin)
• Now twisted pairs switched Ethernet
• Manchester coding
• MAC protocols

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CSMA for wired networks

• Collision detection and avoidance
• Orig same collision domain like radio
• (When one transmits all hear it).
• Hubs obsolete now
• Switches operate at data link layer (examine
  headers to decide forwarding)

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1.3.3. Bridges, routers and gateways

• Connections from LAN to outside world
• Bridge is switch to interconnect LANs
• Router reads TCP header for destination chooses
  best way to send packet on its way. Like local
  telephone exchange.
• Gateways connect devices with different
  protocols. E.g TCP/IP telephone networks for
  VoIP.

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1.4. Protocols and Layers

• Protocols are defined in layers.
• Well-known description of computer-to-computer
  communication is
• OSI Reference Model.
• Open Systems Interconnection,
• Term invented by International Standards
  Organisation in 1983.

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1.4.2. 7-layer OSI reference model
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1.4.3. TCP/IP Reference Model

• Similar to 7 layer OSI' model pre-dates it.

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1.5. Wireless computer networks

• Convergence of
• Telephony (with expensive radio access)
• WLANs (with free radio access
  in 2.4 5 GHz bands)
• Widely used for data via hot-spots etc
• Soon for telephony, multimedia etc.

51
1.5.2 IEEE802.11 other standards

• Wi-fi IEEE802.11 a, b, g e.
• Hiperlan 1 2 (prob obsolete)
• Bluetooth
• WIMAX IEEE802.15
• Phy layer has same problems as telephony
• multi-path AWGN

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1.5.3. Orig IEEE 802.11 phy-layer for WLANs

• First in 1997 1 2 Mb/s in 2.4 GHz band
• Spectral spreading mandatory
• Two SS methods
• Freq-hopping (around 80 MHz wide
  bands)
• Direct sequence (XOR with 11-bit
  chipping
• sequence 1 0 1 1 0
  1 1 1 0 0 0 )
• DHSS multiplies bandwidth required by 11.
• Reduces effect of noise ?less power
  needed.

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1.5.3. Original IEEE 802.11

• Released in1997 1 or 2 Mb/s
• Must use spread spectrum in 2.4 GHz band
• Two versions FHSS DSSS
• FHSS version hops around 80 carriers .4 s dwell
• DSSS uses chipping sequence 10110111000
• Each bit gt 11 chips. 1Mb/s gt 11 Mb/s
• Spreads to 22 MHz.

54
1.5.4. IEEE 802.11 frame structure
Preamble Header Payload
80 or 144 32 or 48
variable Modulation technique FHSS 2 or
4-level Gaussian FSK at 1 Mbaud DSSS 2 or 4
level DPSK at 11 Mbaud
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1.5.5. Latest IEEE802.11 standards
IEEE 802.11a OFDM in 5.17-5.8 GHz band
64 carriers each modulated with
PSK etc. Up to 54 Mb/s.
Great for multi-path. IEEE 802.11b Operates
in 2.4-2.48GHz band
Same as 802.11 for preamble / header
Replaces 11-chip Barker sequence by
codes. 1, 2, 5.5 or 11
Mb/s for payload (CCK)
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IEEE802.11g standard (Nov 2001)
Extension to IEEE802.11b in 2.4 GHz band OFDM
payload option at up to 54Mb/s Same
preamble/header as IEEE802.11 orig DSSS b
OFDM classified as a spread spectrum technique
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Bluetooth
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1.5.6. Intro to IEEE802.11 MAC layer

• Contention mode (CSMA/CA)
• Non-contention mode (central control via
  PCF but never implemented)
• 802.11e standard has EDCA HCCA
• QoS standard
• EDCA is enhanced CSMA/CA
• HCCA is new centrally controlled MAC

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1.5.7 IEEE802.11 MAC in contention mode

• Based on a DCF mechanism.
• WLAN devices can sample medium determine
  whether any device is currently transmitting.
• Collision avoidance strategies then employed to
  ensure, that a device transmits only when radio
  channel is likely to be free of other traffic.
• Nick Filer will deal with this

60
1.5.8.IEEE802.11 MAC in non-contention mode

• Possible when there is a central device, which
  can act as a controller by informing all other
  devices when they are allowed to transmit or
  receive data.
• Does this by periodically sending "beacons" to
  enable or disable non-contention mode "polling"
  devices by sending further control packets to
  request data from each device.
• A WLAN with central controller capable of
  fulfilling this co-ordination role is termed an
  "infrastructure" network
• In most cases, the central controller also
  provides access to the outside world, e.g. via a
  telephone connection, and it is then termed an
  "access point".

61
1.6. Bluetooth

• Short range piconet for computer peripherals
  etc.
• Not originally an IEEE standard
• Operates in 2.4 GHz band over 10 metres.
• FHSS over 80 carriers 160 hops /s
• Binary FSK at 1Mb/s.
• Problems with 802.11b transmissions in range.

62
1.7 Telephone computer networks

• Much commonality physically conceptually
• Connection oriented/ connectionless?
• Technologies merging VoIP
• ATM
• PPP
• Issue is quality of service (QoS)

63
1.8. Digital transmission in more detail

• Data carried by shaped waveforms or symbols.
• A symbol can carry 1 bit (binary signalling) or
  more.
• Bit-rate not same as symbol (baud) rate.
• With QPSK, each symbol carries 2 bits.
• For long term or continuous transmission receiver
  must synchronise to the transmission

64
1.8.2. Manchester coding for baseband
65
1.8.3 Digital communication system model
66
Transmitter for synchronous communication

• Analogue waveform suited to the channel.
• If base-band send suitably shaped pulses e.g.
  Manchester
• Otherwise modulate carrier with shaped pulse.
• For radio, bandlimited pulses needed.
• not time limited.
• carrier recovery must be
  possible
• May need to limit power of transmission.

67
Receiver for synchronous communications

• Symbol rate and carrier frequency known but maybe
  not exactly
• Carrier phase not known.
• Receiver must
• synchronise carrier, symbols and frames.
• then sample waveform to detect the data.
• Made difficult by attenuation, delay, Doppler
  noise.
• Improved by matched filter and equaliser

68
Receiver components
bR(t)
101.
Sample detect
Matched filter
Channel equaliser
Vector Demod
bI(t)
69
1.8.4. Digital filter

• Gain G(f) Phase ?(f)
• Gain in dB 20 log10(G(f) )
• Phase delay -?(f) / (2?f) seconds
• Linear phase constant phase delay
• Channel acts like a filter

70
Example of frequency response of a channel - gain
Gain (dB)
0
-10
-20
f
fU
fL
71
Example of frequency response of a channel -
phase
-?(f)
good
bad
f
fU
fL
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Example of frequency response of a channel -
delay
same delay
-?(f) / f
good
Different delay at different frequencies
bad
f
fU
fL
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Frequency response of a band-pass filter - gain
phase
-?(f) Gain (dB)
0
Channel acts like a filter
180O
-10
90O
-20
0
f
fU
fL
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Low-pass filter - gain phase
-?(f) Gain (dB)
Remove high frequency parts of signal
0
180O
-10
90O
-20
0
f
fC
75
High-pass filter - gain phase
-?(f) Gain (dB)
Remove low frequency parts of signal
0
180O
-10
90O
-20
0
f
fC
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Band-stop filter - gain phase
-?(f) Gain (dB)
0
180O
-10
Remove mid frequency parts of signal
90O
-20
0
f
fU
fL
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Channel acts like a filter - not a nice one
Transmitter sends this
3
Volt
t
Receiver may get this because of different gains
delays at different frequencies
0.1
Volt
t
Not nice
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1.8.5 Frequency shifts and noise
Transmitter sends this
3
Volt
t
Receiver may get this because of noise
0.1
Volt
t
Not nice at all
79
And still more bad news (for commuters)
with mobile phones. Doppler shift due to
movement of receiver of transmitter Different
frequencies received from transmitted.
80
Something about noise
Noise is an unwanted signal. Can be a sine wave
(sounds horrible) But very often a random
signal.
Sounds like waterfall or the sea.
Volt
t
81
Random signal
When examining a signal x(t) with no obvious
structure, it is useful to assume that at any
time t, x(t) is a sample of a random variable
X, with statistical properties we can discuss.
In this case, x(t) is considered to be a random
signal.
82
Random variable
Because it has no structure, you cant predict
its value. But you can say something about its
mean (average) variance (mean-square
value when mean 0) distribution of
values PDF tells you about distribution of
values.
83
Probability density function (PDF) - 2 examples
1. Gaussian (normal) with mean m standard
deviation ?
PDF(x)
variance is ?2?
0.4/?
0.24/?
x
m
m-?
m?
84
2. Uniform between x A x B
mean m (BA)/2
A
m
B
From PDF(x) can deduce mean, mean-square value
variance.
85
Gaussian PDF
Casino analogy
0
0
0.1
0.5
-0.7
3
-1.5
6
1
-4
0.5
9
Assume voltages generated by Roulette
wheel
-0.2
-0.3
0
0
86
Casino analogy
Uniform PDF
7
-8
-7
6
-6
5
-5
4
3
-4
-3
2
1
-2
-1
0
87
Statistical electrical properties of noise
Statistical Electrical mean
average voltage variance
power (if mean0 PDF
distribution of voltages
88
Exact meaning of PDF
Probability of getting a value between A B is
PDF(x)
0.4/???
(Area under curve)
x

A B
89
Gaussian PDF continued
PDF
Probability of getting a value gtZ
0.4/?
x

m Z
90
Gaussian PDF with zero mean ? 1.
Power 1
Probability of getting a value gtZ
PDF
0.4
Q(Z) _ see graph
x

Z
91
Gaussian PDF with zero mean any ? .
Power ?2
Probability of getting a value gtZ
PDF
0.4/?
Q( Z / ? )
x
Z

92
Spectral properties of a random signal Although
x(t) random, can try to predict next value For
example, if the values are
-2 , 10, 21, 33, 41, 55, 62, 69, we may predict
that the next sample is around 80. Considering
a second example with no predictability -2, 44,
-4, -17, 9, 61, 2, -19, 3, -16, 1, -7, 30, -1,
No correlation between signal signal delayed
for any ?. No periodicity. Power spectrum will
be flat or white.
93
Power spectral density (PSD)
Power in 1Hz band centred on f Hz is PSD(f) Watts
94
Example Power signal x(t) is white has
2-sided PSD N0 /2 Watts/Hz. What is its power
in the bandwidth -B to B Hz?
PSD(f)
f
B
-B
Answer N0B Watts
95
Example Power signal x(t) is white has
1-sided PSD N0 Watts/Hz. What is its power in
the bandwidth 0 to B Hz?
PSD(f)
f
B
Answer N0B Watts
96
Example Considering the sequences of samples of
x(t), which one is more likely to be Gaussian ?
Time properties of x(t) (governing shape of
power spectrum) statistical properties are
independent. Can have white or spectrally
coloured signal with same PDF
97
Additive white Gaussian noise
The noise gets added to your nice clean
signal. Causes bit-errors - mistaking 1 or 0 or
vice-versa.
98
Additive white Gaussian noise (AWGN)
One parameter needed 1-sided power spectral
density (PSD) N0 Watts per Hz 2-sided PSD
N0/2 Watts/Hz If 1-sided bandwidth B Hz,
power B . N0 Watts Variance ?2 power
(zero mean)
99
Error performance

• Bit-error probability (PB)
• probability of a single bit being wrong at
  receiver (eg 10-3)
• Bit-error rate (BER)
• if bit-error probability is 10-3,
  BER is 1 in 103
• (average of 1 bit-error for each
  1000 bits).
• Not bit-errors per second.

100
1.8.7. Estimating effect of AWGN on BER
101
Complementary error function Q(z)

• Prob of WGN sample with zero mean variance ?21
  being greater than z is

z
102
When ?2 ? 1

• For WGN of variance ?2, probability of a sample
  exceeding z is Q(z/?),
• ?probability that sample gt A/2 is Q(A/(2?)).
• Q(z) may be obtained from a graph, erfc in
  MATLAB or an approximation valid for z gt 3
• Q(z) 0.5 erfc( z / ?2 ) ? (0.4 / z) exp (?z2 /
  2)

103
Example 1.3

• After the demodulation, a radio receiver receives
  1 volt 0 volt pulses with AWGN of variance ?2
  0.01. Estimate the bit-error probability
  assuming a 0.5 volt threshold an equal number
  of 1s and 0s.
• Solution
• 0.5 x Prob (noise gt 0.5 volts) when "0"
  transmitted, plus 0.5 x prob (noise lt -0.5)
  when "1" transmitted, is simply Q(0.5/0.1) 3
  x 10-7.
• Bit-error probability PB 3 x 10?7
• Bit-error rate (BER) is 1 in 0.33 x 107

104
Example 1.4

• A receiver receives 1 0 volt pulses and has a
  bit-error probability of 10-3. What is the
  variance of the received noise?
• Solution Q(0.5/?) 10-3.
• From graph, 0.5/? ? 3.2
• Therefore, ? 0.16 and ?2 0.026.

105
Example 1.5

• A receiver receives ?1 volt bipolar pulses with
  AWGN of 1-sided PSD N0 0.00002 Watts/Hz.
  Signal is passed thro a low-pass filter with 500
  Hz cut-off is then fed to threshold detector
  with threshold of zero. Estimate bit-error
  probability assuming equal numbers of 1s
  0s.

106
Solution to 1.5

• Variance ?2 N0 B where B 500 Hz.
• ? ?2 0.01 and ? 0.1.
• PB 0.5 Q(1/s) 0.5 Q(1/s) Q(1/0.1)
  Q(10).
• This is off scale of graph, but we can use MATLAB
  or the approximation given earlier to obtain
• PB Q(10) 0.04 e?50 7.7 x 10?24 (with
  calculator)
• PB 0.5 erfc(10/ ?2 ) 7.7e-24 (from MATLAB)

107
Example 1.6

• A digital transmission system is affected by
  AWGN. Received power decreases with increasing
  distance according to a inv-square law", i.e.
  P(d) ? 1/d2 where P(d) is power at distance d.
• If distance is currently 200 metres, how much
  nearer must we move towards receiver if the
  bit-error probability is be reduced from its
  current value of 10-5 to 10-7.
• Solution Exercise for student.

108
1.8.8 Waterfall graphs
Consider the unipolar bipolar signals below
109
Energy per bit EB

• Tells us how much energy (in Joules) taken from
  battery to transmit 1 bit.
• Could estimate how many bits could be transmitted
  before battery runs out.
• For unipolar at 1/T bits/s with rect pulses of
  voltage V, EB V2T/2 Joules/ bit.
• For equivalent bipolar, EB V2T Joules/bit.

110
Example 1.6

• A receiver receives a 10 b/s bit stream as ?V
  volt bipolar pulses with AWGN of 1-sided PSD N0
  0.00002 Watts/Hz. The signal is passed thro a
  low-pass filter with cut-off frequency 500 Hz and
  then fed to a threshold detector with a threshold
  of zero.
• For a range of values of 10 log10 (EB/N0) dB, say
  from -1 to 30 dB, estimate the bit-error
  probability assuming equal numbers of 1s and
  0s. and plot a waterfall graph of bit-error
  probability against EB/N0.

111
Solution to 1.6

• Variance ?2 500 N0. ? ?2 0.01 and ? 0.1.
• PB 0.5 Q(V/?) 0.5 Q(V/?) Q(V/0.1) Q(10V).
• Now EB V2T V2/10
• and EB/N0 V2 / (2x10-4) 5000
  V2
• Therefore, V ?(EB/N0 / 5000)
  and PB Q(10 ?(EB/N0 / 5000) )
• Q(?(0.02EB/N0) 0.5
  erfc(?(0.01EB/N0)

112
MATLAB program for PB against E EB/No

• clear
• for i 1 32
• EdB(i)i-2 This is EB/N0 in dB
• E 10(EdB(i) / 10) This is EB/N0
• PBu(i) 0.5 erfc ( sqrt(E0.01) )
• end
• semilogy( EdB, PBu, 'b') grid on
• need to label axes

113
Waterfall graph for Ex 1.6
114
Waterfall graphs of PB against Eb/N0

• PB bit-error probability
• Eb energy per bit
• Power used to transmit data at a given
  bit-rate
• (watts (joules/s) bit-rate (bits/s)
  joules/bit)
• N0 1-sided PSD of AWGN
• Eb/N0 is sort of signal-to-noise ratio

115
Example of a better waterfall graph
116
1.8.9 Matched filtering equalisation
117
Single carrier digital radio tansmitter/receiver
s(t)
t
t
r (t)


Map to b-b
Mod -ulate
H
Adapt Equal iser
De- modulate
Channel
Detect bits
RF filter
channel noise
system noise
Carrier
Initialise
Derive local carrier
Sync bit sampling points
118
Problems discussion points
1. As this is a course on digital transmission,
why need analog FT? 2.Why is lowest 300Hz
bandwidth lost on POTs telephones? 3.Why do we
need a hybrid what happens when it works
badly? 4. What causes fading in a mobile
telephone channel? 5. What is meant by the rms
delay spread? 6. From list, what do you consider
the main advantage of digital? 7. If IEEE802.11
is wi-fi what is IEEE802.3 ? 8. What is the
mac-sub-layer?
119
Further problems discussion points
9. Why is the 11-chip Barker sequence used with
IEEE802.11b? 10. Design a telephone modem using a
PC sound card. 11. What does FHSS have to do with
the first nude actress? 12. What are the
ISMbands what are they used for? 13. Why are
there no bit-errors in emails? 14. Why is TCP/IP
not ideal for VoIP? 15. What is the hidden node
problem how is it solved? 16. What is the
difference between CSMA/CD CSMA/CA?