[SOLVED] CS Note: We will start at 12:53 pm ET

Note: We will start at 12:53 pm ET
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18-441/741: Computer Networks Lectures 4: Physical Layer II
Swarun Kumar
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Physical Layer: Outline
Digitalnetworks
ModulationFundamentals
CharacterizationofCommunicationChannels
FundamentalLimitsinDigitalTransmission
DigitalModulation
LineCoding
PropertiesofMediaandDigitalTransmission Systems
ErrorDetectionandCorrection
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Transferring Information
Information transfer is a physical process
In this class, we generally care about
Electrical signals (on a wire or wireless) Optical signals (in a fiber)
More broadly, EM waves
Information carriers can be very diverse:
Sound waves, quantum states, proteins, ink & paper, etc.
Quote (usually attributed to Einstein):
You see, wire telegraph is a kind of a very, very long
cat. You pull his tail in New York and his head is meowing in Los Angeles.
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Modulation
Changing a signal to convey information
Ways to modulate a sinusoidal wave
Amplitude Modulation (AM) Frequency Modulation (FM) Phase Modulation (PM)
In music:
Volume Pitch Timing
In our case, modulate signal to encode a 0 or a 1. (multi-valued signals sometimes)
Analog is the same value just changes continuously
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Modulation Examples
Amplitude
001100 1100011100011000 1110
Frequency
Phase
0110110001
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Why Different Modulation Methods?
Offerschoiceswithdifferenttradeoffs: Transmitter/Receiver complexity
Power requirements
Bandwidth
Medium (air, copper, fiber, ) Noise immunity
Range
Multiplexing
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Physical Layer: Outline
Digitalnetworks
ModulationFundamentals
CharacterizationofCommunicationChannels
FundamentalLimitsinDigitalTransmission
DigitalModulation
LineCoding
PropertiesofMediaandDigitalTransmission Systems
ErrorDetectionandCorrection
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Questions of Interest
How long will it take to transmit a message?
How many bits are in the message (text, image)?
How fast does the network/system transfer information?
Can a network/system handle a voice (video) call?
How many bits/second does voice/video require? At what quality?
How long will it take to transmit a message without errors?
How are errors introduced?
How are errors detected and corrected?
What transmission speed is possible over radio, copper cables, fiber, infrared, ?
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Transmitter
Receiver
A Communications System
Communication channel
Transmitter
Converts information into a signal suitable for transmission
Injects energy into communications medium or channel
Telephone converts voice into electric current
Wireless LAN card converts bits into electromagnetic waves
Receiver
Receives energy from medium
Converts received signal into a form suitable for delivery to user
Telephone converts current into voice
Wireless LAN card converts electromagnetic waves into bits
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Digital Binary Signal
101101 +A
0 T 3T 4T 6T -A
Here, Bit Rate = 1 bit / T seconds
For a given communications medium:
How do we increase the bit rate (speed) ?
How do we achieve reliable communications?
Are there limits to speed and reliability?
2T
5T
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Bandwidth
Bandwidth is width of the frequency range in which the Fourier transform of the signal is non-zero.
Sometimes referred to as the channel width
Or, where it is above some threshold value (Usually, the half power threshold, e.g., -3dB)
dB short for decibel
Defined as 10 * log10(P1/P2)
When used for signal to noise: 10 * log10(S/N)
Also: dBm power relative to 1 milliwatt Defined as 10 * log10(P/1 mW)
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Signal = Sum of Waves

+ 1.3 X + 0.56 X + 1.15 X
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Closer look at waves
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The Frequency Domain
A (periodic) signal can be viewed as a sum of sine waves of different strengths.
Corresponds to energy at a certain frequency
Every signal has an equivalent representation in the frequency domain.
What frequencies are present
and what is their strength (energy)
E.g., radio and TV signals,
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Spectrum of a signal: measures power of signal as function of frequency
x1(t) varies faster in time & has more high frequency content than x2(t)
Bandwidth Ws is defined as range of frequencies where a signal has non-negligible power, e.g. range of band that contains 99% of total signal power
Mini Quiz: Between [A] x1 and
[B] x2, which has more bandwidth?
Spectrum of x1(t)
Spectra & Bandwidth
1.2 1 0.8 0.6 0.4 0.2 0
Spectrum of x2(t)
frequency (kHz)
1.2 1 0.8 0.6 0.4 0.2 0
frequency (kHz)
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0
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Transmission Channel Considerations
Every medium supports transmission in a certain frequency range.
Outsidethisrange,effectssuchas attenuation, .. degrade the signal too much
Transmission and receive hardware will try to maximize the useful bandwidth in this frequency band.
Tradeoffsbetweencost,distance,bit rate
As technology improves, these parameters change, even for the same wire.
Good Bad
Frequency
Signal

Attenuation & Dispersion
Notnicelowpassfilters Whydowecare?
Good Bad
+
= ???
Frequency
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Limits to Speed and Distance
Noise: random energy is added to the signal.
Attenuation: some of the energy in the signal leaks away.
Dispersion: attenuation and propagation speed are frequency dependent.
(Changes the shape of the signal)
Effects limit the data rate that a channel can sustain. But affects different technologies in different ways
Effects become worse with distance. Tradeoff between data rate and distance

Pulse Transmission Rate
Objective: Maximize pulse rate through a channel, that is, make T as small as possible
Channel
t
l If input is a narrow pulse, then typical output is a spread-out pulse with ringing
l Question: How frequently can these pulses be transmitted without interfering with each other?
l 2Wc pulses/sec with binary amplitude encoding where Wc is the bandwidth of the channel
T
t
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Bandwidth of a Channel
X(t) = a cos(2pft) Channel Y(t) = A(f) a cos(2pft)
If input is sinusoid of frequency f, then
output is a sinusoid of same frequency f
A(f)
Output is attenuated by an amount A(f) that depends on f
A(f)1, then input signal passes readily
A(f)0, then input signal is blocked
Bandwidth Wc is range of frequencies passed by channel
1
0
W f c
Ideal lowpass channel
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Multi-level Pulse Transmission
Assume channel of bandwidth Wc, and transmit 2Wc pulses/sec (without interference)
If pulses amplitudes are either -A or +A, then each pulse conveys 1 bit, so
Bit Rate = 1 bit/pulse x 2Wc pulses/sec = 2Wc bps
If amplitudes are from {-A, A/3, +A/3, +A}, then bit rate is 2x2Wc bps
By going to M=2m amplitude levels, we achieve
Bit Rate = m bits/pulse x 2Wc pulses/sec = 2mWc bps
In the absence of noise,
the bit rate can be increased without limit by increasing m
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Noise & Reliable Communications
All physical systems have noise
Electrons always vibrate at non-zero temperature
Motion of electrons induces noise
Presence of noise limits accuracy of measurement of received signal amplitude
Errors occur if digital signal separation is comparable to noise level
Thus, noise places a limit on how many amplitude levels can be used in pulse transmission
Bit Error Rate (BER) increases with decreasing signal-to- noise ratio
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Signal-to-Noise Ratio (SNR)
Signal
Noise
Signal + noise
t
No errors Signal + noise
t
error
High SNR
t
t
Low SNR
Signal
t
SNR =
Noise
t
Average signal power Average noise power
SNR (dB) = 10 log10 SNR
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Physical Layer: Outline
Digitalnetworks
ModulationFundamentals
CharacterizationofCommunicationChannels
FundamentalLimitsinDigitalTransmission
DigitalModulation
LineCoding
PropertiesofMediaandDigitalTransmission Systems
ErrorDetectionandCorrection
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The Nyquist Limit
AnoiselesschannelofwidthHcanatmost transmit a binary signal at a rate 2 x H.
Assumes binary amplitude encoding
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The Nyquist Limit
A noiseless channel of width H can at most transmit a binary signal at a rate 2 x H.
Assumes binary amplitude encoding
E.g. a 3000 Hz channel can transmit data at a rate of at most 6000 bits/second
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Sample Quiz Question
[True / False] The bandwidth of Wi-Fi (802.11ac, first-gen) is 80 MHz. So by
Nyquist theorem, its max speed is 160 Mbps
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Past the Nyquist Limit
More aggressive encoding can increase the bandwidth
Example: modulate multi-valued symbols
Modulate blocks of digital signal bits, e.g, 3 bits = 8 values Often combine multiple modulation techniques
PSK
PSK+AM
Problem? Noise!
The signals representing two symbols are less distinct
Noise can prevent receiver from decoding them correctly
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Example: Modem Rates
100000 10000 1000 100
1975 1980 1985 1990 1995 2000
15-441 2008-10
Year
Lecture 30
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Modem rate

Capacity of a Noisy Channel
Places upper bound on channel capacity, while considering noise
Shannons theorem:
C = B x log2(1 + S/N)
C: maximum capacity (bps)
B: channel bandwidth (Hz)
S/N: signal to noise ratio of the channel
Often expressed in decibels (db) ::= 10 log(S/N)
Example:
Local loop bandwidth: 3200 Hz (old school dialup) Typical S/N: 1000 (30db)
What is the upper limit on capacity?
C = 3200 x log2(1 + 1000) = 31.9 Kbps
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Shannons Channel Capacity Theorem
C=W log (1+SNR) bps c2
Arbitrarily-reliable communications is possible if the transmission rate R < C If R > C, then arbitrarily-reliable communications is not possible
Arbitrarily-reliable means the BER can be made arbitrarily small through sufficiently complex coding
C can be used as a measure of how close a system design is to the best achievable performance
Bandwidth Wc & SNR determine C
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Sample Quiz Question
FindtheShannonchannelcapacityforaWiFi channel with Wc = 80 MHz and SNR = 40 dB
SNR (dB) = 40 dB corresponds to SNR = 10^(40/10) = 10000
C = 80 log2 (1 + 10000) Mbps
= 80 log10 (10001)/log102 = 1063 Mbps
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Physical Layer: Outline
Digitalnetworks
ModulationFundamentals
CharacterizationofCommunicationChannels
FundamentalLimitsinDigitalTransmission
DigitalModulation
LineCoding
PropertiesofMediaandDigitalTransmission Systems
ErrorDetectionandCorrection
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From Signals to Packets
Analog Signal
Digital Signal
BitStream 00101110001
Packets
Packet Transmission
0100010101011100101010101011101110000001111010101110101010101101011010111001
Header/Body
Sender
Header/Body
Header/Body
Receiver
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Baseband versus Carrier Modulation
Basebandmodulation:sendthebaredigital signal
Channel must be able to transmit low frequencies For example, copper media
Carriermodulation:usethesignalto modulate a higher frequency signal, called a carrier
Can send the signal in a particular part of the spectrum
Can modulate the amplitude, frequency or phase
For example, wireless and optical
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Bandpass Channels
fcWc/2 fc fc+Wc/2
Bandpass channels pass a range of frequencies around
some center frequency fc
Radio channels, telephone & DSL modems
Digital modulators embed information into waveform with frequencies passed by bandpass channel
Sinusoid of frequency fc is centered in middle of bandpass channel
Modulators embed information into a sinusoid
0
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Amplitude Carrier Modulation
Signal
Carrier Modulated Frequency Carrier
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Amplitude
Amplitude

Signaling rate and Transmission Bandwidth
Frommodulationtheory:
If
Baseband signal x(t) with bandwidth B Hz
then
Modulated signal x(t)cos(2pfct) has bandwidth 2B Hz
B
f
f

If bandpass channel has bandwidth Wc Hz,
Then baseband channel has Wc/2 Hz available, so modulation system supports Wc/2 x 2 = Wc pulses/second That is, Wc pulses/second per Wc Hz = 1 pulse/Hz
Recall baseband transmission system supports 2 pulses/Hz
f
fc-B c fc+B

Frequency Division Multiplexing: Multiple Channels
Determines Bandwidth of Link
Determines Bandwidth of Channel
Different Carrier Frequencies
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Amplitude

Frequency Modulation
Information 1 0 1 1 0 1
+1
0
-1
Use two frequencies to represent bits 1sendfrequencyfc+d
0sendfrequencyfcd
Demodulator looks for power around fc + d or fc d
Frequency Shift Keying
T 2T 3T 4T 5T 6T
t
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Phase Modulation
Information 1 0 1 1 0 1
Phase Shift Keying
+1
-1
0 T 2T 3T 4T 5T 6T
t
Map bits into phase of sinusoid:
1 send A cos(2pft) , i.e. phase is 0 0 send A cos(2pft+p) , i.e. phase is p
Equivalent to multiplying cos(2pft) by +A or -A
1 send A cos(2pft) multiply by 1 0 send A cos(2pft+p) = A cos(2pft) multiply by -1
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Modulator & Demodulator
Modulate cos(2pfct) by multiplying by Ak for T seconds:
x cos(2pfct)
during kth interval
Demodulate (recover Ak) by multiplying by 2cos(2pfct)
for T seconds and lowpass filtering (smoothing):
Ak
Yi(t) = Ak cos(2pfct) Transmitted signal
Yi(t) = Akcos(2pfct)
Received signal during kth interval
x 2cos(2pfct)
Xi(t)
Lowpass Filter (Smoother)
2Ak cos2(2pfct) = Ak {1 + cos(2p2fct)}
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Example of Phase Modulation
Information
+A
-A
+A
-A
A cos(2pft)
101101
Baseband Signal
0 T
3T 4T 6T
2T
5T
Modulated Signal
x(t)
0 T
3T 4T 6T
-A cos(2pft)
2T
5T
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Example of Phase Demodulation
A {1 + cos(4pft)} +A
0 T
-A {1 + cos(4pft)}
After multiplication at receiver
x(t) cos(2pfct)
Baseband signal discernable after smoothing
Recovered Information
-A +A
-A
3T 4T 6T
2T
5T
0 T
3T 4T 6T
2T
101101
5T
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Quadrature Amplitude Modulation (QAM)
QAM uses two-dimensional signaling
Ak modulates in-phase cos(2pfct)
Bk modulates quadrature phase sin(2pfct)
Transmit sum of inphase & quadrature phase components
x
cos(2pfct) + Y(t)
Ak
Bk
Yi(t) = Ak cos(2pfct)
x Yq(t) = Bk sin(2pfct) sin(2pfct)
Transmitted Signal
l l
Yi(t) and Yq(t) both occupy the bandpass channel QAM sends 2 pulses/Hz
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QAM Demodulation
Lowpass filter (smoother)
Y(t)
x 2cos(2pfct)
x 2sin(2pfct)
Ak
2cos2(2pfct)+2Bk cos(2pfct)sin(2pfct)
= Ak {1 + cos(4pfct)}+Bk {0 + sin(4pfct)}
smoothed to zero
Bk
2Bk sin2(2pfct)+2Ak cos(2pfct)sin(2pfct)
= Bk {1 cos(4pfct)}+Ak {0 + sin(4pfct)} smoothed to zero
Lowpass filter (smoother)

Signal Constellations
Eachpair(Ak,Bk)definesapointintheplane Signalconstellationsetofsignalingpoints
Bk
(A, A)
(A,-A)
4 possible points per T sec. 2 bits / pulse
Bk
(-A,A)
(-A,-A)
Ak Ak
16 possible points per T sec. 4 bits / pulse
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Physical Layer: Outline
Digitalnetworks
CharacterizationofCommunicationChannels
FundamentalLimitsinDigitalTransmission
ModemsandDigitalModulation
LineCoding(nextlecture)
PropertiesofMediaandDigitalTransmission Systems
ErrorDetectionandCorrection
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