• Essential equipment
• Lecture recording
• Hands-on Tutorial 1
Housekeeping
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300952
Wireless and Mobile Networks
Lecture 2. Transmission Fundamentals
Lecture objectives
• Understand basic concepts of signals for conveying information
• Differentiate and characterize analog and digital data transmission
• Identify the different factors that affect the capacity of a communication channel
• Understand the concept of multiplexing
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Can you ‘hear’ light or ‘see’ sound? Why? How?
SIGNALS
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• Functionoftime
Electromagnetic Signal
• Canalsobeexpressedasafunctionoffrequency – Signal consists of components of different frequencies
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Time-Domain Concepts (1)
• Analogsignal:signalintensityvariesinasmoothfashionovertime
– No breaks or discontinuities in the signal
• Digital signal: signal intensity maintains a constant level for some
period of time and then changes to another constant level
• Periodicsignal:analogordigitalsignalpatternthatrepeatsovertime
s(t +T) = s(t) -∞ < t < +∞ • where T is the period of the signal
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Amplitude (volts)
Amplitude (volts)
Analog and Digital Waveforms
(a) Analog
Time
Time
(b) Digital
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Time-Domain Concepts (2)
• Aperiodic signal: analog or digital signal pattern that doesn't repeat over time
• Peak amplitude (A): maximum value or strength of the signal over time; typically measured in volts
• Frequency (f): rate, in cycles per second, or Hertz (Hz) at which the signal repeats
• Period (T): amount of time it takes for one repetition of the signal – T = 1/f
• Phase (φ [phi]): measure of the relative position in time within a single period of a signal
• Wavelength (λ [lambda]): distance occupied by a single cycle of the signal
– Or, the distance between two points of corresponding phase of two consecutive cycles
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Examples of Periodic Signals
A
0
–A
A
0
–A
Time
period = T = 1/f
(a) Sine wave
Time
period = T = 1/f
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(b) Square wave
Amplitude (volts)
Amplitude (volts)
Sine Wave Parameters
• Generalsinewave
– s(t)=Asin(2πft+φ)
• Nextslideshowstheeffectofvaryingeachofthethreeparameters – (a)A=1,f=1Hz,φ=0;thusT=1s
– (b) Reduced peak amplitude; A=0.5
– (c) Increased frequency; f = 2, thus T = 1⁄2
– (d) Phase shift; φ = π/4 radians (45 degrees)
• Note:2πradians=360°=1period
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1.0 s(t) 0.5
0.0 –0.5 –1.0
0.0
s(t)
0.5
1.0
1.0 s(t)
0.5
0.0
–0.5
t –1.0 1.5 s 0.0
0.5 1.0
(b) A = 0.5, f = 1, f = 0
t
1.5 s
1.0 0.5 0.0
–0.5 –1.0
t
1.5 s
(a) A = 1, f = 1, f = 0
1.0 0.5 0.0
–0.5 t –1.0
s(t)
0.0
0.5
1.0
1.5 s 0.0
0.5 1.0
(d) A = 1, f = 1, f = p/4
(c) A = 1, f = 2, f = 0
s(t) = A sin (2πft + φ)
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Find the following in a sample Sine wave -
• Aperiodic or Periodic
• Peak amplitude (A)
• Frequency (f)
• Period (T)
• Wavelength (λ [lambda])
A
1m
Examples of Periodic Signals
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–A
0
-1
A
0
Time
period = T = 1/f
1s 2s Time
(a) Sine wave
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mplitude (volts)
Amplitude (volts)
Examples of Periodic Signals
Examine another sample Sine wave, and find -
100m
A
• Frequency (f)
• Period(T) 0
• Wavelength (λ [lambda])
• Velocity – how fast is this wave travelling
• Aperiodic or Periodic 10
• Peak amplitude (A)
0.01s 0.02s
Time
–A
-10
A
period = T = 1/f
(a) Sine wave
0 13 Time
mplitude (volts)
Amplitude (volts)
Putting more waves together
1.0 0.5 0.0
–0.5 –1.0
1.0 0.5 0.0
–0.5 –1.0
1.0 0.5 0.0
–0.5 –1.0
0.0T 0.5T 1.0T 1.5T 2.0T (a) sin (2fft)
0.0T 0.5T 1.0T 1.5T 2.0T (b) (1/3) sin (2f(3f )t)
0.0T 0.5T 1.0T 1.5T 2.0T (c) (4/f) [sin (2fft) + (1/3) sin (2f(3f )t)]
Addition of frequency Components(T = 1/f)
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Frequency Components of Square Wave
1.0 0.5 0.0
–0.5 –1.0
1.0 0.5 0.0
–0.5 –1.0
1.0 0.5 0.0
–0.5 –1.0
0.0
0.5T 1.0T 1.5T 2.0T (a) (4/f) [sin (2fft) + (1/3) sin (2f(3f )t) + (1/5) sin (2f(5f )t)]
0.0
0.5T 1.0T 1.5T 2.0T (b) (4/f) [sin(2fft) + (1/3)sin(2f(3f )t) + (1/5)sin(2f(5f )t) + (1/7)sin(2f(7f )t)]
0.0 0.5T 1.0T
(c) (4/f) ©(1/k) sin (2f(kf )t), for k odd
1.5T 2.0T
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Light transmits in Sine waves
Q: What is the range of frequency for Visible Light?
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Frequency-Domain Concepts (1)
• Fundamentalfrequency:whenallfrequencycomponentsofasignalare integer multiples of one frequency, it’s referred to as the fundamental frequency
• Spectrum:rangeoffrequenciesthatasignalcontains
• Absolutebandwidth:widthofthespectrumofasignal
• Effectivebandwidth(orjustbandwidth):narrowbandoffrequencies that most of the signal’s energy is contained in
– The greater the bandwidth (in Hz), the higher the information-carrying capacity (in bps)
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Frequency-Domain Concepts (2)
• Anyelectromagneticsignalcanbeshowntoconsistofacollectionof periodic analog signals (sine waves) at different amplitudes, frequencies, and phases
• Theperiodofthetotalsignalisequaltotheperiodofthefundamental frequency
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Relationship between Data Rate and Bandwidth
• Thegreaterthebandwidth,thehighertheinformation-carryingcapacity • Conclusions
– Any digital waveform will have infinite bandwidth
– BUT the transmission system will limit the bandwidth that can be transmitted
– AND, for any given medium, the greater the bandwidth transmitted, the greater the cost
– HOWEVER, limiting the bandwidth creates distortions
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Summary
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Can you ‘hear’ light or ‘see’ sound? Why? How?
SIGNALS
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ANALOG AND DIGITAL DATA TRANSMISSION
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Data Communication Terms
• Data:entitiesthatconveymeaning,orinformation
• Signals:electricorelectromagneticrepresentationsofdata
• Transmission:communicationofdatabythepropagationand processing of signals
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• Analog – Video – Audio
• Digital – Text
– Integers
Examples of Analog and Digital Data
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Analog Signals
• Acontinuouslyvaryingelectromagneticwavethatmaybepropagated over a variety of media, depending on frequency
• Examplesofmedia:
– Copper wire media (twisted pair and coaxial cable) – Fiber optic cable
– Atmosphere or space propagation
• Analogsignalscanpropagateanaloganddigitaldata
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Digital Signals
• Asequenceofvoltagepulsesthatmaybetransmittedoveracopper wire medium
• Generallycheaperthananalogsignaling
• Lesssusceptibletonoiseinterference
• Suffermorefromattenuation
• Digitalsignalscanpropagateanaloganddigitaldata
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Analog Transmission
• Transmitanalogsignalswithoutregardtocontent
• Attenuationlimitslengthoftransmissionlink
• Cascadedamplifiersboostsignal’senergyforlongerdistancesbut cause distortion
– Analog data can tolerate distortion – Introduces errors in digital data
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Digital Transmission
• Concernedwiththecontentofthesignal
• Attenuationendangersintegrityofdata
• DigitalSignal
– Repeaters achieve greater distance
– Repeaters recover the signal and retransmit
• Analogsignalcarryingdigitaldata
– Retransmission device recovers the digital data from analog signal – Generates new, clean analog signal
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Voltage at transmitting end
Voltage at receiving end
Attenuation of Digital Signals
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DIGITAL SIGNAL PROCESSING ...
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Putting everything you learned so far together...
• Checkoutthisvideo(Length20:11)- https://www.youtube.com/watch?v=WgJMjDh0nLU
• Whatdidyouget?
– Summarise your learning and share
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CHANNEL CAPACITY
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About Channel Capacity
• Impairments,suchasnoise,limitdataratethatcanbeachieved
• Fordigitaldata,towhatextentdoimpairmentslimitdatarate?
• ChannelCapacity:themaximumrateatwhichdatacanbetransmitted over a given communication path, or channel, under given conditions
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Effect of Noise on Digital Signal
Data
transmittted: 101001100110101
Signal:
Noise:
Signal plus noise:
Sampling times:
Data received: Original data:
101001000110111
1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 Bits in error
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Concepts Related to Channel Capacity • Datarate:rateatwhichdatacanbecommunicated(bps)
• Bandwidth:thebandwidthofthetransmittedsignalasconstrainedby the transmitter and the nature of the transmission medium (Hertz)
• Noise:averagelevelofnoiseoverthecommunicationspath
• Errorrate:rateatwhicherrorsoccur
– Error = transmit 1 and receive 0; transmit 0 and receive 1
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Nyquist Bandwidth
• Forbinarysignals(twovoltagelevels) – C = 2B
• Withmultilevelsignaling
– C=2Blog2 M
• M = number of discrete signal or voltage levels
• C = Capacity of the channel • B = Bandwidth
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Signal-to-Noise Ratio
• Ratioofthepowerinasignaltothepowercontainedinthenoisethat’s present at a particular point in the transmission
• Typicallymeasuredatareceiver
• Signal-to-noiseratio(SNR,orS/N)
(SNR) = 10 log signal power dB 10 noise power
• AhighSNRmeansahigh-qualitysignal,lownumberofrequired intermediate repeaters
• SNRsetsupperboundonachievabledatarate
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Shannon Capacity Formula
• Equation:
• Representstheoreticalmaximumthatcanbeachieved
• Inpractice,onlymuchlowerratesachieved
– Formula assumes white noise (thermal noise)
– Impulse noise is not accounted for
– Attenuation distortion or delay distortion not accounted for
C = Blog2(1+SNR)
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Example of Nyquist and Shannon Formulations
• Spectrumofachannelbetween3MHzand4MHz;SNRdB=24dB
B = 4 MHz - 3 MHz = 1 MHz SNRdB =24dB=10log10(SNR) SNR = 251
• UsingShannon’sformula
• logb(xy) = logbx + logby. • logb(x/y) = logbx - logby. • logb(xn) = n logbx.
• logbx = logax / logab
•𝑌=𝑙𝑜𝑔!𝑥→ 𝑥=𝑎"
C=106 ́log (1+251)»106 ́8=8Mbps 2
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Scientific Calculatoris required? CLICK HERE
• Howmanysignalinglevelsarerequired? C = 2Blog2M
8 ́106 =2 ́(106) ́log M 2
4=log2 M M =16
Note: If M is a fraction, round up, as we cannot have a fraction of a signal. Ex.: if M = 31.7 then 32 signaling levels are required
Example of Nyquist and Shannon Formulations
•𝑌=𝑙𝑜𝑔!𝑥→ 𝑥=𝑎"
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Challenge 1
• Whatisthecapacityofachannelwitha1000Hzbandwidthanda signal-to-noise ratio of 30 dB? Hint: Use Shannon's equation. [Stallings,
Prob 2.9]
C = log2 (1+
)
(SNR)dB =10log10
1. B = 1000 Hz
2. SNR dB
= 30 -> SNR?
3. () C=Blog2 1+SNR
• C = 1000 x log2 (1+1000)
• C=1000×9.967
• C=9967
• Add unit – bps
• C = 10kbps
• SNRdB = 10 x log10(SNR)
• 30 = 10 x log10(SNR)
• log10(SNR) = 3
• SNR=103 =1000
signal power noise power
B
SNR
𝑌=𝑙𝑜𝑔!𝑥→ 𝑥=𝑎”
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Challenge 2
You are using Channel 11 (with spectrum from 2.45GHz to 2.47GHz) for your WiFi Network at home. And you have a SNRdB of 40. What is your Channel Capacity?
signal power noise power
C = Blog2(1+SNR) B = 2.47GHz – 2.45GHz = 0.02GHz
=20MHz=20×106 Hz 40 = 10log10 SNR
SNR = 104
C = 20 x 106 x log2(1+ 104) = 20Mx13.288
= 265760000
= 265.76Mbps
(SNR)
dB
= 10 log 10
Reflection
1. Why do we need to know this calculation? 2. SNRdB = 40 OR SNR = 10000 Is it good?
3. What is the threshold SNR value for WiFi? 4. How to improve SNR?
5. Given a SNR, how to improve the performance of data transmission?
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MULTIPLEXING
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Multiplexing (1)
• Capacityoftransmissionmediumusuallyexceedscapacityrequiredfor transmission of a single signal
• Multiplexing-carryingmultiplesignalsonasinglemedium – More efficient use of transmission medium
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Multiplexing (2)
n inputs MUX 1 link, n channels DEMUX n outputs
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Reasons for Widespread Use of Multiplexing
• Costperkbpsoftransmissionfacilitydeclineswithanincreaseinthe data rate
• Costoftransmissionandreceivingequipmentdeclineswithincreased data rate
• Mostindividualdatacommunicatingdevicesrequirerelativelymodest data rate support
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Multiplexing Techniques
• Frequency-divisionmultiplexing(FDM)
– Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal
– Use guard bands to avoid interference • Time-divisionmultiplexing(TDM)
– Takes advantage of the fact that the achievable bit rate of the medium exceeds the required data rate of a digital signal
f f6 f f4 5
(a) Frequency division multiplexing
f f2 3 1
(b) Time division multiplexing
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Channel 1
Channel 5
Channel 4
Channel 3
Channel 2
Channel 5
Channel 4
Channel 3
Channel 2
Channel 1
Channel 6
etc.
Channel 1 Channel 2
Channel 3 Channel 4
Channel 5 Channel 6
Frequency
Frequency
Time
Time
• GuardBand
Guard Band
– A guard band is a narrow frequency range that separates two ranges of wider frequency. This ensures that simultaneously used communication channels do not experience interference, which would result in decreased quality for both transmissions.
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Housekeeping
• Hands-onTutorial1–dueonthedayfollowingthetutorialclass.You need to complete the attendance test for week 2 before you can submit
• Tutorial1nextweek–tutorialquestionsaremadeavailableinModule2 folder on vUWS
• Thetutorialhasthreeparts
– Non-assessed questions
– Assessed questions – due on the day following the tutorial class – Supplementary questions
It’s hard… I know and I am with you… but did we learn something useful? To relax your brain – check this video out: https://youtu.be/9vJRopau0g0
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Sources for this lecture
Cory Beard, William Stallings. Wireless Communication Networks and Systems, 1st edition. Pearson Higher Education, 2016
(Chapter 2)
All material copyright 2016
Cory Beard and William Stallings, All rights reserved
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