Digital Communications Aspects of Physical Layer Radio Systems

1
Digital Communications Aspects of Physical Layer
Radio Systems Michael Fitz fitz_at_ee.ucla.edu
2
UnWiReD Laboratory (http//www.ee.ucla.edu/unwire
d/)
3
Overview

• Background Material
• Digital Modulations
• Wireless Channels
• Diversity
• Multiple Antennas Modems
• Radio Impairments

You control the flow of the class. If you ask no
questions I will proceed linearly through the
slides and the notes.
4
OSI Network Model
5
Physical Layer Abstraction
6
Bandpass Signals

• Two important characteristics of bandpass signals
• Non-zero center frequency
• Energy spectrum does not extend to DC

7
Bandpass Signal Representation

• I and Q form
• Amplitude and Phase form
• Transformations

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

9
Complex Envelope

• Complex envelope
• Representing two signals as a complex vector

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

11
Conversion
12
Visualizing and Testing

• The complex envelope is a three dimensional
  signal
• I-Q and time
• Amplitude, phase, and time

13
Example
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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

15
Time Plots
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New Tool - Vector Diagram

• A plot of the in-phase signal versus the
  quadrature signal
• Originated in two channel oscilloscopes

17
Example Vector Diagram
18
Bandpass/Baseband Spectrum

• There is a simple mapping from baseband spectrum
  to bandpass spectrum

19
Comparison
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Conclusions

• 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

21
Overview

• Background Material
• Digital Modulations
• Wireless Channels
• Diversity
• Multiple Antennas Modems
• Radio Impairments

You control the flow of the class. If you ask no
questions I will proceed linearly through the
slides and the notes.
22
Digital Transmission

• Binary data source to be transmitted

23
Digital Modulation

• Convert bits into waveforms

24
Digital Demodulation
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Limits on Performance of Digital Communications

• Shannon capacity of the AWGN channel
• Spectral efficiency

26
Our Benchmark Curve
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Digital Communication Goals

• Achieve Shannons curve at a complexity that is
  linear in the number of bits to be sent

28
Transmitting Kb Bits

• Kb bits
• M2 Kb waveforms on 0, Tp
• Bit rate WbKb/Tp

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Examples- Frequency shift keying

• Signals

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BFSK Vector Diagram
31
BFSK Bandpass Signals
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Spectral Characteristics of BFSK
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Example - Phase shift keying

• Signals

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BPSK Vector Diagram
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BPSK Bandpass Signal
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Spectral Characteristics
37
Review of Binary Detection

• Problem formulation
• Statistics are the digital communication
  engineers friend

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Maximum A Posterior Word Demodulation

• MAPWD

39
Block Diagram
40
Maximum Likelihood Word Demodulation

• Equal priors produce
• Matched filter and energy correction
• Complexity exponential in the number of bits
  being transmitted

41
Performance
42
Where Are We With Respect to Shannon?
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

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
• Kb independent bit decisions

45
Orthogonal Modulation Demodulation

• Conditions for orthogonal modulations
• Orthogonality implies each bit is decoded
  independently

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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

47
Example - OFDM

• Orthogonal frequency division multiplexing
• Send each bit on an orthogonal subcarrier
• Signal model
• Orthogonality condition
• Used in wireless LANs (802.11a)

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Temporal Characteristics of OFDM

• K4 bits

Vector Diagram
Amplitude Plot
49
Demodulator for OFDM
Fourier transform of the channel output
evaluated at f_i
50
Spectrum Plots
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Vector Diagram of Matched Filter Output

• Orthogonality ensures that each symbol can be
  decoded optimally and separately

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

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Example - OCDM

• Orthogonal code division multiplexing
• Each bit sent on a different spreading waveform
• Signal model
• Orthogonality condition
• Used in cellular/mobile telephony

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Example Spreading Waveforms
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Temporal Characteristics of OCDM

• K4 bits

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Demodulator for OCDM
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Spectrum Plots
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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

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Example - OTDM

• Orthogonal time division multiplexing
• Bits modulated on time shifted pulses
• Stream modulation
• Signal model
• Orthogonality condition
• Used in all wireless systems

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Temporal Characteristics of Stream Modulations

• K4 bits

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Demodulator
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Matched Filter Output
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Spectrum Plots
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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

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Where Are We With Respect to Shannon?

• With linear complexity we can now achieve

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Can we get closer to Shannon?

• Orthogonal modulations
• Orthogonal modulations with memory

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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)

68
Where We Are At Today!
69
Overview

• Background Material
• Digital Modulations
• Wireless Channels
• Diversity
• Multiple Antennas Modems
• Radio Impairments

You control the flow of the class. If you ask no
questions I will proceed linearly through the
slides and the notes.
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..

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Wireless Channels as Linear Time-Varying Systems
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Free Space Propagation

• Characterized by free space radio wave
  propagation
• Time delay produces a phase shift

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Free Space Model - No Mobility

• The channel is linear and time-invariant

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Free Space with Mobility

• Doppler shift determines the speed of the fading

an
?
v
A1
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Free Space Model - Mobility

• Channel becomes linear but time-varying

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Multipath Model
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Multipath Signals

• Recall a single path of a transmitted carrier
  will have
• This is represented with

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Model for Course - No Mobility

• mp is the number of paths
• Hn is the path gain (complex number)
• tn is the propagation delay

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Impulse Response - No Mobility

• The wireless channel in this case is a linear
  time--invariant system

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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

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Transmitting a Tone

• The resultant received signal is the vector sum
  of the multipath signals

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

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Terminology

• Rayleigh fading
• Delay spread
• Frequency selective fading
• Time varying fading
• Rich scattering environments
• Spatially independent fading
• Etc.

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Amplitude Models I

• Rayleigh fading is a model where
• HI and HQ 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

85
Measurements on Real Channels
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Amplitude Models II

• Ricean fading is a model where
• HI and HQ are zero mean jointly Gaussian
  independent random variables
• A good model where many paths exist and a single
  path dominates

87
Graphical Channel Representation
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Transmitting an Impulse
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Transfer Function
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Example -1
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Delay Spread

• The delay spread, td, is the time between the
  first multipath delay and the last multipath
  delay.
• A delay spread causes the channel to be frequency
  selective

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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

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Example 2 - 802.11a
Transmitted
Received
94
Video Example
95
Frequency Flat Models

• When (BW of signal)Td 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

96
Examples
97
Angle of Arrival-Tone Transmission
A1
Path n

• Position A1 has

98
Spatial Separate Antennas

• What happens when I move the antenna?

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Notation for Second Antenna
an
?
D
A1
A2
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Spatial Diversity
an
?
D
A1
A2

• Antenna displacement is
• Position A2 path length has changed

101
Change in Phase for Path

• The new phase shift relative to A1 is
• The new multiplicative distortion is

102
A Spatial Standing Wave
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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

104
Terminal Mobility

• If the antennas moves through the spatial
  standing wave then the received signal will vary
  with time
• Example

105
Issues for Mobility

• Doppler shift determines the speed of the fading
  and angle of arrival determines the Doppler shift

an
?
v
A1
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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

107
Isotropic Scattering

• Doppler spectrum - fD0.01

108
Small Angle Spread

• Doppler Spectrum - fD0.01
• Where is the mean angle of arrival?

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Example Time Waveforms
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Final Mathematical Model

• Multipath, delay spread, Doppler spread, angle of
  arrival
• Hn is the channel response at a reference antenna

111
Conclusions

• Wireless channels are
• Frequency selective
• Spatially selective
• Time selective
• The details of these characteristics are
  determined by the geometry of the wireless channel

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

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

114
Overview

• Background Material
• Digital Modulations
• Wireless Channels
• Diversity
• Multiple Antennas Modems
• Radio Impairments

You control the flow of the class. If you ask no
questions I will proceed linearly through the
slides and the notes.
115
Wireless Communication
X(t)
Y(t)
Mod
I(l)
Demod
116
Wireless Packet Data

• Orthogonal modulation
• Transmitting frames of data
• Frames include coding for reliability, redundancy
  for synchronization
• Typical frame

Preamble
Payload
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 SNREH2/N0

118
A Communications Model
Encoder
Channel
Decoder
TCSI
RCSI
PH(h)
119
Common Modeling Assumptions

• Perfect channel information
• Known channel at the receiver
• Unknown channel

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

121
Information Theory Says?

• Conditioned on Hh this is a standard Gaussian
  channel
• Shannons formula

122
Some Questions

• Assume you wanted to communicate at R2 bits per
  symbol.
• Could you always communicate reliably at R2?
• Clearly no since H2 can be very small
• Could you sometimes communicate reliably at R2?
• Clearly yes since H2 is often very large

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

124
Average Capacity

• Averaged over the random channel realization
  produced by the placement of the antenna within
  the spatial standing wave

125
Average Capacity-Rayleigh
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Outage Probability

• How often is a channel bad enough to not support
  communication of a certain rate?

127
Example - R2 Rayleigh
128
Insights-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

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

130
Example-Multiple Receive Antennas

• Multiple receive antennas are interesting because
  they cause no loss in throughput

Y1(t)
Demod
X(t)
Mod
I(l)
YLr(t)
Lr receive antennas
131
For signal to be faded all antenna must be faded!
Demod
132
Channel Model-Quasi-static

• Vectorize the previous model
• All vectors are Lrx1 and noise is independent
• k represents the time index
• Notation
• Vectors
• Matrices

133
Information Theory Says?

• Conditioned on channel this is a standard
  multi-channel Gaussian problem
• Extension to Shannons formula

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

135
Average Capacity-Rayleigh
Lr116
136
Outage Probability-Rayleigh, R1
Lr116
137
Insight

• Average capacity increases with the log(Lr)
• 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

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

139
Average Capacity per Resource-Rayleigh
Lt116
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

141
Overview

• Background Material
• Digital Modulations
• Wireless Channels
• Diversity
• Multiple Antennas Modems
• Radio Impairments

You control the flow of the class. If you ask no
questions I will proceed linearly through the
slides and the notes.
142
What Happened in the 1990s?

• Telatar and FoschiniGans asked the question what
  happens in a system with multiple transmit and
  multiple receive antennas?

Y1(t)
Demod
X1(t)
Mod
I(l)
YLr(t)
XLt(t)
Lr receive antennas
Lt transmit antennas
143
Channel Model

• Multiple input-multiple output (MIMO) model
• k represents time index
• Q(k) and N(k) are Lrx1, H is LrxLt, and D(k) is
  Ltx1
• There are now LrxLt independent channel
  coefficients

144
Information Theory Says

• Conditional capacity (Telatar 1996)

145
Average Capacity- LtLr Rayleigh
Lt116
146
Insights

• Capacity scales linearly with the min(Lt, Lr)
• Capacity scales logarithmically with the max(Lt,
  Lr)
• Recall Lt 1

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

148
Example LtLr-Rayleigh
Lt116
149
Outage Probability

• MIMO gives both improved capacity and improved
  reliability
• min(Lt, Lr) parallel channels with max(Lt, Lr)
  levels of diversity
• Insight only true at medium SNR

150
Example LtLr with R Lt -Rayleigh
Lt116
151
Conclusions

• 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

152
Overview

• Background Material
• Digital Modulations
• Wireless Channels
• Diversity
• Multiple Antennas Modems
• Radio Impairments

You control the flow of the class. If you ask no
questions I will proceed linearly through the
slides and the notes.
153
Radio Impairments Important in Wireless

• Radio Channels are frequency selective
• Radio signal must use radio electronics
• Phase noise
• Nonlinearities
• Signal processing imperfections

154
Frequency Selective Channels

• For a general modulation this is not that
  difficult

• MAPWD

155
Orthogonal Modulations Lose Orthogonality!
156
Optimum Demodulation

• Because of loss of orthogonality the demodulation
  has complexity O(2Kb)
• This is not desirable hence we look at
• Suboptimal decoding algorithms
• Special cases having structure to enable optimal
  decoding with linear linear complexity

157
OCDM and Frequency Selective Channels

• Decoding structures are often referred to as
  multi-user detection
• No simplification for the general MLWD

158
Suboptimal Detectors for OCDM

• Linear Detectors - Complexity O(Kb2)
• Successive interference cancellation - Complexity
  O(Kb2)

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(Kb)
• 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

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

161
Result 2 - Integration in Demod is Finite

• If the complex sinusoid is constant over the
  integration time the spreading waveforms would
  remain orthogonal

162
Solution - Extend the Pulse in Time

• Transmitted pulse
• Received pulse
• Often denoted cyclic prefix

Channel Delay Spread
Integration Length
Transient Response
Constant or Steady State Response
Transient Response
163
Simple Example
164
Demodulator

• Demodulator is exactly the same as in frequency
  flat channel
• Gain and phase of the channel for each subcarrier
  needs to be compensated

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(Kb2Nu)

166
Linear Equalizers - O(Kb)
167
Decision Feedback Equalizer
168
Frequency Selective Conclusions

• Orthogonal modulations lose orthogonality in
  frequency selective channels
• Demodulation summary

169
Radio Frequency Distortions

• Radios have to be built with analog components
• Quantization noise, Phase noise, IQ imbalances,
  nonlinearities

Single Chip Analog GSM Radio
170
Electronic Measurement of Impairments

• Error vector magnitude.

171
Amplifier Nonlinearities
172
Continuous Phase Modulation

• Solution is to keep the amplitude constant and
  vary only the phase
• Used on GSM reverse link

QPSK
CPM
173
Conclusions

• 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