Slide 1 Digital Communications Aspects of Physical Layer Radio Systems Michael Fitz [email protected]
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Slide 1 U n W i R e D L a b UCLA Wireless Research and Development Digital Communications Aspects of Digital Communications Aspects of Physical Layer Radio Systems Physical Layer Radio Systems Michael Fitz [email protected]
Slide 1 Digital Communications Aspects of Physical Layer Radio Systems Michael Fitz [email protected]
Slide 3 You control the flow of the class. If you ask no
questions I will proceed linearly through the slides and the notes.
Background Material Digital Modulations Wireless Channels Diversity
Multiple Antennas Modems Radio ImpairmentsOverview
Slide 4
Slide 4 OSI Network Model
Slide 5
Slide 5 Physical Layer Abstraction
Slide 6
Slide 6 Bandpass Signals Two important characteristics of
bandpass signals Non-zero center frequency Energy spectrum does not
extend to DC
Slide 7
Slide 7 Bandpass Signal Representation I and Q form Amplitude
and Phase form Transformations
Slide 8
Slide 8 Bandpass Signal Characteristics There are two degrees
of freedom in bandpass signals Two low pass signals Communication
engineers use two representations In-phase and quadrature Amplitude
and phase
Slide 9
Slide 9 Complex Envelope Complex envelope Representing two
signals as a complex vector
Slide 10
Slide 10 Analogous to Fourier Transform Complex valued
analytical function Fourier transform is a function of frequency
Complex envelope is a function of time Mathematical concepts are
all the same Amplitude, phase, real, and imaginary for FT
Amplitude, phase, in-phase, and quadrature for CE
Slide 11
Slide 11 Conversion
Slide 12
Slide 12 Visualizing and Testing The complex envelope is a
three dimensional signal I-Q and time Amplitude, phase, and
time
Slide 13
Slide 13Example
Slide 14
Slide 14 2D Representation of CE As humans we can absorb 2D
information better I versus time - standard time plot Q versus time
- standard time plot I versus Q - vector diagram
Slide 15
Slide 15 Time Plots
Slide 16
Slide 16 New Tool - Vector Diagram A plot of the in-phase
signal versus the quadrature signal Originated in two channel
oscilloscopes
Slide 17
Slide 17 Example Vector Diagram
Slide 18
Slide 18 Bandpass/Baseband Spectrum There is a simple mapping
from baseband spectrum to bandpass spectrum
Slide 19
Slide 19Comparison
Slide 20
Slide 20Conclusions All wireless communications use bandpass
signals The complex envelope is a two dimensional analytical
representation of a bandpass signal All information about the
bandpass signal is contained in the complex envelope except the
carrier frequency A tool to characterize the complex envelope is
the vector diagram
Slide 21
Slide 21 You control the flow of the class. If you ask no
questions I will proceed linearly through the slides and the notes.
Background Material Digital Modulations Wireless Channels Diversity
Multiple Antennas Modems Radio ImpairmentsOverview
Slide 22
Slide 22 Digital Transmission Binary data source to be
transmitted
Slide 23
Slide 23 Digital Modulation Convert bits into waveforms
Slide 24
Slide 24 Digital Demodulation
Slide 25
Slide 25 Limits on Performance of Digital Communications
Shannon capacity of the AWGN channel Spectral efficiency
Slide 26
Slide 26 Our Benchmark Curve
Slide 27
Slide 27 Digital Communication Goals Achieve Shannons curve at
a complexity that is linear in the number of bits to be sent
Slide 28
Slide 28 Transmitting K b Bits K b bits M=2 K b waveforms on
[0, T p ] Bit rate W b =K b /T p
Slide 29
Slide 29 Examples- Frequency shift keying Signals
Slide 30
Slide 30 BFSK Vector Diagram
Slide 31
Slide 31 BFSK Bandpass Signals
Slide 32
Slide 32 Spectral Characteristics of BFSK
Slide 33
Slide 33 Example - Phase shift keying Signals
Slide 34
Slide 34 BPSK Vector Diagram
Slide 35
Slide 35 BPSK Bandpass Signal
Slide 36
Slide 36 Spectral Characteristics
Slide 37
Slide 37 Review of Binary Detection Problem formulation
Statistics are the digital communication engineers friend
Slide 38
Slide 38 Maximum A Posterior Word Demodulation MAPWD
Slide 39
Slide 39 Block Diagram
Slide 40
Slide 40 Maximum Likelihood Word Demodulation Equal priors
produce Matched filter and energy correction Complexity exponential
in the number of bits being transmitted
Slide 41
Slide 41Performance
Slide 42
Slide 42 Where Are We With Respect to Shannon?
Slide 43
Slide 43 Standard Modulation Conclusions One matched filter for
each possible word Complexity scales exponentially with the number
of bits to be transmitted This is not acceptable in practice Goal
would be to have a complexity that is linear in the number of bits
to be sent Spectral efficiency can be set at whatever value you
need depending on modulation Performance can achieve a variety of
levels depending on the modulation
Slide 44
Slide 44 Independent Bit Decisions The goal is to be able to
design signals such that individual optimum bit decisions are
independent of all the other bits that were transmitted Making
optimal independent bit decisions gives linear complexity K b
independent bit decisions
Slide 45
Slide 45 Orthogonal Modulation Demodulation Conditions for
orthogonal modulations Orthogonality implies each bit is decoded
independently
Slide 46
Slide 46 Orthogonal Modulations Examples Orthogonal in
frequency Orthogonal in waveform (code) Orthogonal in time This
orthogonality condition was first identified by Nyquist in 1928
Will assume each bit sent on a separate orthogonal waveform but
generalizations are possible
Slide 47
Slide 47 Example - OFDM Orthogonal frequency division
multiplexing Send each bit on an orthogonal subcarrier Signal model
Orthogonality condition Used in wireless LANs (802.11a)
Slide 49 Demodulator for OFDM Fourier transform of the channel
output evaluated at f_i
Slide 50
Slide 50 Spectrum Plots
Slide 51
Slide 51 Vector Diagram of Matched Filter Output Orthogonality
ensures that each symbol can be decoded optimally and
separately
Slide 52
Slide 52 Conclusions - OFDM Orthogonality gives linear
complexity Same BEP performance as BPSK Spectral efficiency is
about 1 bit/s/Hz with binary modulations per subcarrier OFDM has
peak-to-average power issues Demodulator is implemented by using a
Fourier transform to get the matched filter FFT is used in practice
for implementation efficiency
Slide 53
Slide 53 Example - OCDM Orthogonal code division multiplexing
Each bit sent on a different spreading waveform Signal model
Orthogonality condition Used in cellular/mobile telephony
Slide 54
Slide 54 Example Spreading Waveforms
Slide 55
Slide 55 Temporal Characteristics of OCDM K=4 bits
Slide 56
Slide 56 Demodulator for OCDM
Slide 57
Slide 57 Spectrum Plots
Slide 58
Slide 58 Conclusions - OCDM Orthogonality gives linear
complexity OCDM is most general form of orthogonal modulation Same
BEP performance as BPSK Spectral efficiency is about 1 bit/s/Hz
Transmitted signal has peak to average power issues
Slide 59
Slide 59 Example - OTDM Orthogonal time division multiplexing
Bits modulated on time shifted pulses Stream modulation Signal
model Orthogonality condition Used in all wireless systems
Slide 60
Slide 60 Temporal Characteristics of Stream Modulations K=4
bits
Slide 61
Slide 61Demodulator
Slide 62
Slide 62 Matched Filter Output
Slide 63
Slide 63 Spectrum Plots
Slide 64
Slide 64 Conclusions - Stream Orthogonality gives linear
complexity Same performance as bits sent in isolation Spectral
efficiency is about 1 bit/s/Hz Stream modulations give better
control on peak to average power of the transmitted signal Almost
all communications systems use the idea of time orthogonality and
stream bits in time
Slide 65
Slide 65 Where Are We With Respect to Shannon? With linear
complexity we can now achieve
Slide 66
Slide 66 Can we get closer to Shannon? Orthogonal modulations
Orthogonal modulations with memory
Slide 67
Slide 67 Example Modulations with Memory Error control codes
Line codes (spectral shaping) Convolutional codes Trellis coded
modulation Turbo codes Low density parity check codes Continuous
phase modulation (Peak power control)
Slide 68
Slide 68 Where We Are At Today!
Slide 69
Slide 69 You control the flow of the class. If you ask no
questions I will proceed linearly through the slides and the notes.
Background Material Digital Modulations Wireless Channels Diversity
Multiple Antennas Modems Radio ImpairmentsOverview
Slide 70
Slide 70 Overview-Wireless Review Free Space Propagation
Multipath Propagation Channel Modeling Frequency Selectivity
Spatial Characteristics Time Selectivity This is a systems
engineering point of view Characterize what makes wireless
different than wired Simplify the model compared to the EM
folks..
Slide 71
Slide 71 Wireless Channels as Linear Time-Varying Systems
Slide 72
Slide 72 Free Space Propagation Characterized by free space
radio wave propagation Time delay produces a phase shift
Slide 73
Slide 73 Free Space Model - No Mobility The channel is linear
and time-invariant
Slide 74
Slide 74 Free Space with Mobility Doppler shift determines the
speed of the fading A1A1 nn v
Slide 75
Slide 75 Free Space Model - Mobility Channel becomes linear but
time-varying
Slide 76
Slide 76 Multipath Model
Slide 77
Slide 77 Multipath Signals Recall a single path of a
transmitted carrier will have This is represented with
Slide 78
Slide 78 Model for Course - No Mobility m p is the number of
paths H n is the path gain (complex number) n is the propagation
delay
Slide 79
Slide 79 Impulse Response - No Mobility The wireless channel in
this case is a linear time--invariant system
Slide 80
Slide 80 Important Factors Path gains are a function of path
length, path geometry, reflection/diffraction characteristics. Path
delays are only a function of the path length Radio waves travel at
the speed of light Path delays induce a phase shift in a carrier
modulated signal
Slide 81
Slide 81 Transmitting a Tone The resultant received signal is
the vector sum of the multipath signals
Slide 82
Slide 82 Fading and Diversity Note it is possible for all the
multipath vectors to be relatively large and the resultant signal
to be small This is denoted a fade Wireless communications is about
trying to transmit information over redundant channels to mitigate
fades This is denoted diversity
Slide 83
Slide 83Terminology Rayleigh fading Delay spread Frequency
selective fading Time varying fading Rich scattering environments
Spatially independent fading Etc.
Slide 84
Slide 84 Amplitude Models I Rayleigh fading is a model where H
I and H Q are zero mean jointly Gaussian independent random
variables A good model where many paths exist and no path dominates
Often considered a worst case channel
Slide 85
Slide 85 Measurements on Real Channels
Slide 86
Slide 86 Ricean fading is a model where H I and H Q are zero
mean jointly Gaussian independent random variables A good model
where many paths exist and a single path dominates Amplitude Models
II
Slide 87
Slide 87 Graphical Channel Representation
Slide 88
Slide 88 Transmitting an Impulse
Slide 89
Slide 89 Transfer Function
Slide 90
Slide 90 Example -1
Slide 91
Slide 91 Delay Spread The delay spread, d, is the time between
the first multipath delay and the last multipath delay. A delay
spread causes the channel to be frequency selective
Slide 92
Slide 92 Sum of Sinusoids The transfer function is a sum of
sinusoids The larger the delay spread the larger the difference
between the smallest and largest frequency the faster the channel
changes with frequency
Slide 93
Slide 93 Example 2 - 802.11a Transmitted Received
Slide 94
Slide 94 Video Example
Slide 95
Slide 95 Frequency Flat Models When (BW of signal)*T d is much
less than unity then the channel can be modeled as frequency flat
All multipaths arrive at roughly the same time compared to the time
variations of the transmitted signal
Slide 96
Slide 96Examples
Slide 97
Slide 97 Angle of Arrival-Tone Transmission Position A 1 has
A1A1 Path n
Slide 98
Slide 98 Spatial Separate Antennas What happens when I move the
antenna? Channel 1 Channel 2
Slide 99
Slide 99 Notation for Second Antenna A1A1 A2A2 nn
Slide 100
Slide 100 Spatial Diversity Antenna displacement is Position A
2 path length has changed A1A1 A2A2 nn
Slide 101
Slide 101 Change in Phase for Path The new phase shift relative
to A 1 is The new multiplicative distortion is
Slide 102
Slide 102 A Spatial Standing Wave
Slide 103
Slide 103 Conclusion on Spacing Spacing should be proportional
to wavelength A wide angle spread scattering environment allows
more decorrelation per unit of spacing A narrow angle spread
scattering environment decorrelates less per unit of spacing Mean
angle of arrival is also important An array deployed parallel to
the angle of arrival will produce less variability than an array
deployed broadside to the angle of arrival
Slide 104
Slide 104 Terminal Mobility If the antennas moves through the
spatial standing wave then the received signal will vary with time
Example
Slide 105
Slide 105 Issues for Mobility Doppler shift determines the
speed of the fading and angle of arrival determines the Doppler
shift A1A1 nn v
Slide 106
Slide 106 Issues for Time-Varying Fading Doppler spectrum due
to a set of discrete frequencies due to each multipath Doppler
spectrum is strictly limited by vehicle speed Spectral distribution
of the multipaths is a function of the angle of arrival of the
multipath and the vehicle driving direction
Slide 107
Slide 107 Isotropic Scattering Doppler spectrum - f D
=0.01
Slide 108
Slide 108 Small Angle Spread Doppler Spectrum - f D =0.01 Where
is the mean angle of arrival?
Slide 109
Slide 109 Example Time Waveforms
Slide 110
Slide 110 Final Mathematical Model Multipath, delay spread,
Doppler spread, angle of arrival H n is the channel response at a
reference antenna
Slide 111
Slide 111Conclusions Wireless channels are Frequency selective
Spatially selective Time selective The details of these
characteristics are determined by the geometry of the wireless
channel
Slide 112
Slide 112 Conclusions II Geometry is determined by Power delay
profile Mean angles of arrival/departure Angle spreads of
arrival/departure Motion of the antennas at transmitter/receiver
Antenna array geometry
Slide 113
Slide 113 Wireless Channels and Data Communications Fading is a
major issue Multipath destructively interferes at points in time,
space, or frequency Wireless channels are frequency selective Radio
frequencies must be used to transmit information
Slide 114
Slide 114 You control the flow of the class. If you ask no
questions I will proceed linearly through the slides and the notes.
Background Material Digital Modulations Wireless Channels Diversity
Multiple Antennas Modems Radio ImpairmentsOverview
Slide 115
Slide 115 Wireless Communication Mod I(l) X(t) Demod Y(t)
Slide 116
Slide 116 Wireless Packet Data Orthogonal modulation
Transmitting frames of data Frames include coding for reliability,
redundancy for synchronization Typical frame PreamblePayload
Slide 117
Slide 117 Matched Filter Processing In frequency flat channels
the matched filter output is a sufficient statistic The matched
filter form is k represents time/frequency/code index Noise is
white if pulse shape satisfies Nyquist criterion Average SNR=E[|H|
2 ]/N 0
Slide 118
Slide 118 A Communications Model EncoderChannelDecoder P H (h)
TCSIRCSI
Slide 119
Slide 119 Common Modeling Assumptions Perfect channel
information Known channel at the receiver Unknown channel
Slide 120
Slide 120 Common Communication Paradigms Optimize throughput by
varying transmission rate depending on the channel Adaptive
modulation Communicate at some fixed rate on the channel Voice
systems
Slide 121
Slide 121 Conditioned on H=h this is a standard Gaussian
channel Shannons formula Information Theory Says?
Slide 122
Slide 122 Some Questions Assume you wanted to communicate at
R=2 bits per symbol. Could you always communicate reliably at R=2?
Clearly no since |H| 2 can be very small Could you sometimes
communicate reliably at R=2? Clearly yes since |H| 2 is often very
large
Slide 123
Slide 123 Two Parameters to Characterize Wireless Channels
Average capacity What is the average instantaneous capacity Measure
capacity in bits per channel use Outage probability For a fixed
rate (bits/channel use) how often will operation be above
capacity
Slide 124
Slide 124 Average Capacity Averaged over the random channel
realization produced by the placement of the antenna within the
spatial standing wave
Slide 125
Slide 125 Average Capacity-Rayleigh
Slide 126
Slide 126 Outage Probability How often is a channel bad enough
to not support communication of a certain rate?
Slide 127
Slide 127 Example - R=2 Rayleigh
Slide 128
Slide 128Insights-Rayleigh Average capacity goes up with the
log of average SNR. Outage probability goes as Wireless system
performance is dominated by antenna locations corresponding to a
deep fade
Slide 129
Slide 129 How to Improve Performance? Pre-1990s the design
practice was to add diversity Diversity is the reception of
redundant versions channel distorted transmitted waveform Goal is
to have versions reasonably independent Diversity achieved with
multiple receive antennas, transmission on different frequencies,
transmission at different times Redundancy added efficiently with
coding
Slide 130
Slide 130 Example-Multiple Receive Antennas Mod I(l) X(t) Demod
Y 1 (t) Y Lr (t) L r receive antennas Multiple receive antennas are
interesting because they cause no loss in throughput
Slide 131
Slide 131 For signal to be faded all antenna must be faded!
Demod
Slide 132
Slide 132 Channel Model-Quasi-static Vectorize the previous
model All vectors are L r x1 and noise is independent k represents
the time index Notation Vectors Matrices
Slide 133
Slide 133 Conditioned on channel this is a standard
multi-channel Gaussian problem Extension to Shannons formula
Information Theory Says?
Slide 134
Slide 134 Spatial Independence For this discussion we assume
each channel has a gain that is independent of the other channel
gains Dependency between the channels will reduce the average
capacity and diversity achieved Correlated channels can be
considered as well
Slide 135
Slide 135 Average Capacity-Rayleigh L r =1:16
Slide 136
Slide 136 Outage Probability-Rayleigh, R=1 L r =1:16
Slide 137
Slide 137Insight Average capacity increases with the log(L r )
Analogous to an increase in SNR Outage probability for a rate R
behaves as Diversity does not add much to achieved throughput but
greatly increases reliability
Slide 138
Slide 138 Average Capacity per Resource Each antenna added is a
resource that costs money so the question becomes how effectively
is that resource being used to increase the data rate
Slide 139
Slide 139 Average Capacity per Resource-Rayleigh L t =1:16
Slide 140
Slide 140 Capacity Conclusion With multiple receive antennas
Capacity gain per resource decreases with more receive antennas
Other methods might be equally effective More powerful amplifier
Frequency hopping and more powerful code Significant improvements
in reliability is achieved Gains after four antennas is diminishing
With other resources (frequency, time diversity) Reliability gain
is achieved usually at the cost of bandwidth Coding adds the
redundancy to achieve the diversity Pre-1996 the high performance
system used all of these ideas GSM - sophisticated error control
coding, frequency hopping, wideband transmission, multiple
antennas
Slide 141
Slide 141 You control the flow of the class. If you ask no
questions I will proceed linearly through the slides and the notes.
Background Material Digital Modulations Wireless Channels Diversity
Multiple Antennas Modems Radio ImpairmentsOverview
Slide 142
Slide 142 What Happened in the 1990s? Telatar and
Foschini&Gans asked the question what happens in a system with
multiple transmit and multiple receive antennas? Mod I(l) X 1 (t)
Demod Y 1 (t) Y Lr (t) L r receive antennas L t transmit antennas X
Lt (t)
Slide 143
Slide 143 Channel Model Multiple input-multiple output (MIMO)
model k represents time index Q(k) and N(k) are L r x1, [H] is L r
xL t, and D(k) is L t x1 There are now L r xL t independent channel
coefficients
Slide 144
Slide 144 Information Theory Says Conditional capacity (Telatar
1996)
Slide 145
Slide 145 Average Capacity- L t =L r Rayleigh L t =1:16
Slide 146
Slide 146Insights Capacity scales linearly with the min(L t, L
r ) Capacity scales logarithmically with the max(L t, L r ) Recall
L t =1
Slide 147
Slide 147 Capacity per Resource Capacity and complexity now
grow in direct proportion to each other Adding more bandwidth is
not so expensive as before! It is growing better than linearly with
the total number of antennas
Slide 148
Slide 148 Example L t =L r -Rayleigh L t =1:16
Slide 149
Slide 149 Outage Probability MIMO gives both improved capacity
and improved reliability min(L t, L r ) parallel channels with
max(L t, L r ) levels of diversity Insight only true at medium
SNR
Slide 150
Slide 150 Example L t =L r with R= L t -Rayleigh L t =1:16
Slide 151
Slide 151Conclusions MIMO radio potentially allows you to get
more bits communicated with a greater reliability Wireless spectrum
is limited/costly and so this has been very exciting for owners of
spectrum It is usually much cheaper to build more expensive radios
than it is to buy more spectrum A way to increase the spectral
efficiency of wireless communications without limit
Slide 152
Slide 152 You control the flow of the class. If you ask no
questions I will proceed linearly through the slides and the notes.
Background Material Digital Modulations Wireless Channels Diversity
Multiple Antennas Modems Radio ImpairmentsOverview
Slide 153
Slide 153 Radio Impairments Important in Wireless Radio
Channels are frequency selective Radio signal must use radio
electronics Phase noise Nonlinearities Signal processing
imperfections
Slide 154
Slide 154 Frequency Selective Channels For a general modulation
this is not that difficult MAPWD
Slide 156 Optimum Demodulation Because of loss of orthogonality
the demodulation has complexity O(2 K b ) This is not desirable
hence we look at Suboptimal decoding algorithms Special cases
having structure to enable optimal decoding with linear linear
complexity
Slide 157
Slide 157 OCDM and Frequency Selective Channels Decoding
structures are often referred to as multi-user detection No
simplification for the general MLWD
Slide 158
Slide 158 Suboptimal Detectors for OCDM Linear Detectors -
Complexity O(K b 2 ) Successive interference cancellation -
Complexity O(K b 2 )
Slide 159
Slide 159 OFDM in Frequency Selective Channels OFDM is a
special case of OCDM so all results apply OFDM has a suboptimal
demodulator that has complexity O(K b ) This suboptimal demodulator
is found by exploiting two ideas The spreading waveform is a
complex sinusoid The optimal demodulator in the time domain is an
integrator over a finite time interval
Slide 160
Slide 160 Result 1 - Complex Sinusoids and Linear Systems
Sinusoids are so important in engineering analysis because the are
the eigenfunctions of linears systems Input is a constant times the
input! Orthogonality would not be lost if pulses were infinite in
length
Slide 161
Slide 161 Result 2 - Integration in Demod is Finite If the
complex sinusoid is constant over the integration time the
spreading waveforms would remain orthogonal
Slide 162
Slide 162 Solution - Extend the Pulse in Time Channel Delay
Spread Integration Length Transmitted pulse Received pulse Often
denoted cyclic prefix Transient Response Constant or Steady State
Response Transient Response
Slide 163
Slide 163 Simple Example
Slide 164
Slide 164Demodulator Demodulator is exactly the same as in
frequency flat channel Gain and phase of the channel for each
subcarrier needs to be compensated
Slide 165
Slide 165 OTDM (Stream) and Frequency Selective Channels The
match filter output model is given as The optimal time recursive
was first proposed by Ungerboeck Complicated (cannot hope to do
justice in this introduction) If delay spread is Nu symbols than
demodulation complexity is O(K b 2 N u )
Slide 166
Slide 166 Linear Equalizers - O(K b )
Slide 167
Slide 167 Decision Feedback Equalizer
Slide 168
Slide 168 Frequency Selective Conclusions Orthogonal
modulations lose orthogonality in frequency selective channels
Demodulation summary ModulationOptimal Demod Complexity Suboptimal
Demod Complexity OCDMO(2 K b )O(K b 2 ) OFDMO(2 K b )O(K b )
StreamO(K b 2 N u )O(K b )
Slide 169
Slide 169 Radio Frequency Distortions Radios have to be built
with analog components Quantization noise, Phase noise, IQ
imbalances, nonlinearities Single Chip Analog GSM Radio
Slide 170
Slide 170 Electronic Measurement of Impairments Error vector
magnitude.
Slide 171
Slide 171 Amplifier Nonlinearities
Slide 172
Slide 172 Continuous Phase Modulation Solution is to keep the
amplitude constant and vary only the phase Used on GSM reverse link
CPM QPSK
Slide 173
Slide 173Conclusions 60 years and a lot of smart people has led
to many significant advances In wired channels we can meet Shannon
bounds Wireless is still an open problem Interaction between
networking and physical layers Complex signal processing Multiple
antennas solutions Managing on a finite energy budget
