short course: wireless communications : lecture 2
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Short Course: Wireless Communications : Lecture 2. Professor Andrea Goldsmith. UCSD March 22-23 La Jolla, ca. Course Outline. Overview of Wireless Communications Path Loss, Shadowing, and WB/NB Fading Capacity of Wireless Channels Digital Modulation and its Performance - PowerPoint PPT PresentationTRANSCRIPT
Short Course:Wireless Communications: Lecture 2
Professor Andrea Goldsmith
UCSDMarch 22-23La Jolla, ca
Course Outline Overview of Wireless Communications Path Loss, Shadowing, and WB/NB
Fading Capacity of Wireless Channels Digital Modulation and its
Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications &
Wireless Networks Future Wireless Systems
Lecture 1
Lecture 2
Lecture 1 Summary
Future Wireless Networks
Wireless Internet accessNth generation CellularWireless Ad Hoc NetworksSensor Networks Wireless EntertainmentSmart Homes/SpacesAutomated HighwaysAll this and more…
Ubiquitous Communication Among People and Devices
• Hard Delay/Energy Constraints• Hard Rate Requirements
Signal Propagation
Path LossShadowingMultipath
d
Pr/Pt
d=vt
Statistical Multipath Model
Random # of multipath components, each with varying amplitude, phase, doppler, and delay
Narrowband channelSignal amplitude varies randomly
(complex Gaussian).2nd order statistics (Bessel function), Fade
duration, etc. Wideband channel
Characterized by channel scattering function (Bc,Bd)
Capacity of Flat Fading Channels
Three casesFading statistics knownFade value known at receiverFade value known at receiver and
transmitterOptimal Adaptation
Vary rate and power relative to channel
Optimal power adaptation is water-filling
Exceeds AWGN channel capacity at low SNRs
Suboptimal techniques come close to capacity
Modulation Considerations
Want high rates, high spectral efficiency, high power efficiency, robust to channel, cheap.
Linear Modulation (MPAM,MPSK,MQAM)Information encoded in amplitude/phase More spectrally efficient than nonlinearEasier to adapt.Issues: differential encoding, pulse shaping,
bit mapping.
Nonlinear modulation (FSK)Information encoded in frequency More robust to channel and amplifier
nonlinearities
Linear Modulation in AWGN
ML detection induces decision regionsExample: 8PSK
Ps depends on# of nearest neighborsMinimum distance dmin (depends on gs)
Approximate expression sMMs QP g
dmin
Linear Modulation in Fading
In fading gs and therefore Ps random
Metrics: outage, average Ps , combined outage and average.Ps
Ps(target)
Outage
Ps
Ts
Ts
sssss dpPP ggg )()(
Delay spread exceeding a symbol time causes ISI (self interference).
ISI leads to irreducible error floorIncreasing signal power increases ISI
power
Without compensation, requires Ts>>Tm Severe constraint on data rate
(Rs<<Bc)
ISI Effects
0 Tm
1 2 3 4 5
Ts
Main TakeawayNarrowband wireless channel
characterized by random flat-fading (Bu<<Bc)
Wideband wireless channel characterized by random frequency-selective fading (ISI)
Need to combat flat and frequency-selective fading
Focus of this section of short course
Course Outline Overview of Wireless Communications Path Loss, Shadowing, and Fading
Models Capacity of Wireless Channels Digital Modulation and its
Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications &
Wireless Networks Future Wireless Systems
Adaptive Modulation Change modulation relative to
fading
Parameters to adapt:Constellation sizeTransmit power Instantaneous BERSymbol timeCoding rate/scheme
Optimization criterion:Maximize throughputMinimize average powerMinimize average BER
Only 1-2 degrees of freedom needed for good performance
Variable-Rate Variable-Power MQAM
UncodedData Bits Delay Point
SelectorM(g)-QAM ModulatorPower: P(g)
To Channel
g(t) g(t)
log2 M(g) Bits One of theM(g) Points
BSPK 4-QAM 16-QAM
Goal: Optimize P(g) and M(g) to maximize R=Elog[M(g)]
Optimization Formulation
Adaptive MQAM: Rate for fixed BER
Rate and Power Optimization
Same maximization as for capacity, except for K=-1.5/ln(5BER).
PPK
PP
BERM )(1)(
)5ln(5.11)( ggggg
PPKEME
PP
)(1logmax)]([logmax 2)(2)(
ggggg
Optimal Adaptive Scheme
Power Adaptation
Spectral Efficiency
else0
)( 0
0
11KKK
PP ggg g
gg
g
1
0g
1gK
gk g
RB
p dK K
log ( ) .2
g
gg
g g
Equals capacity with effective power loss K=-1.5/ln(5BER).
Spectral Efficiency
K1
K2
K=-1.5/ln(5BER)
Can reduce gap by superimposing a trellis code
Constellation Restriction
Restrict MD(g) to {M0=0,…,MN}. Let M(g)=g/gK
*, where gK* is later
optimized. Set MD(g) to maxj Mj: Mj M(g). Region boundaries are gj=MjgK*, j=0,
…,N Power control maintains target BER
M(g)=g/gK*
gg0 g1=M1gK* g2 g3
0M1
M2
OutageM1
M3
M2
M3
MD(g)
Power Adaptation and Average Rate
Power adaptation: Fixed BER within each region
Es/N0=(Mj-1)/K Channel inversion within a region
Requires power increase when increasing M(g)
Average Rate
1
1
00,)/()1()(
ggggggg jKM
PP jjjj
)(log 11
2
jj
N
jj pM
BR ggg
Efficiency in Rayleigh Fading
Spec
tral
Eff
icie
ncy
(bps
/Hz)
Average SNR (dB)
Constellation Restriction
M(g)=g/gK*
gg0 g1=M1gK* g2 g3
0M1
M2
OutageM1
M3
M2
M3
MD(g)
Power adaptation:
Average rate:
1
1
00,)/()1()(
ggggggg jKM
PP jjjj
)(log 11
2
jj
N
jj pM
BR ggg
Efficiency in Rayleigh Fading
Spec
tral
Eff
icie
ncy
(bps
/Hz)
Average SNR (dB)
Practical Constraints Constellation updates: fade region
duration
Error floor from estimation errorEstimation error at RX can cause error in
absence of noise (e.g. for MQAM)Estimation error at TX causes mismatch
of adaptive power and rate to actual channel
Error floor from delay: let r(t,t)=g(t-t)/g(t).Feedback delay causes mismatch of
adaptive power and rate to actual channel
Mjj
jj TT
NN
1
t
regionin fademax at ratecrossinglevel
regionin fademin at ratecrossinglevel
spreaddelay
AFRD
1
j
j
M
j
N
N
T
t
Detailed Formulas Error floor from estimation error
(gg)
Joint distribution p(g,g) depends on estimation: hard to obtain. For PSAM the envelope is bi-variate Rayleigh
Error floor from delay: let =g[i]/g[i-id].p(|g) known for Nakagami fading
ggggg
g
ddpBERP yb
K
ˆ)ˆ,(]5[2. ˆ/
0target
^
^
ggg ddppBERPb )()|(]5[2.0 0
target
Main Points Adaptive modulation leverages fast
fading to improve performance (throughput, BER, etc.)
Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K.Comes within 5-6 dB of capacity
Discretizing the constellation size results in negligible performance loss.
Constellations cannot be updated faster than 10s to 100s of symbol times: OK for most dopplers.
Course Outline Overview of Wireless Communications Path Loss, Shadowing, and WB/NB
Fading Capacity of Wireless Channels Digital Modulation and its
Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications &
Wireless Networks Future Wireless Systems
Introduction to Diversity
Basic IdeaSend same bits over independent
fading paths Independent fading paths obtained by
time, space, frequency, or polarization diversity
Combine paths to mitigate fading effects
Tb
tMultiple paths unlikely to fade simultaneously
Combining Techniques
Selection CombiningFading path with highest gain used
Maximal Ratio CombiningAll paths cophased and summed with
optimal weighting to maximize combiner output SNR
Equal Gain CombiningAll paths cophased and summed with
equal weighting
Array/Diversity gainArray gain is from noise averaging
(AWGN and fading)Diversity gain is change in BER slope
(fading)
Selection Combining Analysis and Performance
Selection Combining (SC)Combiner SNR is the maximum of the
branch SNRs.CDF easy to obtain, pdf found by
differentiating.Diminishing returns with number of
antennas.Can get up to about 20 dB of gain.
OutageProbability
MRC and its Performance
With MRC, gS=Sgi for branch SNRs giOptimal technique to maximize output
SNRYields 20-40 dB performance gainsDistribution of gS hard to obtain
Standard average BER calculation
SSSS
MMMs
MMsss
dddpppP
dpppPdpPP
gggggggg
ggggggggg
...)()...()()...(...
)(...)()()...()()(
21211
**2*11
Integral hard to obtain in closed form and often diverges
MMx
s dddpppdxePM
gggggg
gg
...)()...()(2
... 2121)...(
2/
1
2
dxeQP xs
2/2
21)(
g
gRecall
MGF Approach Use alternate form of Q function
Define the MGF of gi as
Laplace transform of distributionOften simple closed form expressions
Rearranging order of integration, we get
dgPM
iis
5.
0 12sin
1 M
MMs dddpppdeP M gggggg
gg ...)()...()(... 2121
2/
0
)/(sin)...( 221
is
ii deps i gg g)()(0
M
g depends on modulation (,)
EGC and Transmit Diversity
EGQ simpler than MRCHarder to analyzePerformance about 1 dB worse
than MRC
Transmit diversityWith channel knowledge, similar
to receiver diversity, same array/diversity gain
Without channel knowledge, can obtain diversity gain through Alamouti scheme: works over 2 consecutive symbols
Main Points Diversity typically entails some penalty
in terms of rate, bandwidth, complexity, or size.
Techniques trade complexity for performance.MRC yields 20-40 dB gain, SC around 20 dB.
Analysis of MRC simplified using MGF approach
EGC easier to implement than MRC: hard to analyze.Performance about 1 dB worse than MRC
Transmit diversity can obtain diversity gain even without channel information at transmitter.
Course Outline Overview of Wireless Communications Path Loss, Shadowing, and Fading
Models Capacity of Wireless Channels Digital Modulation and its
Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications &
Wireless Networks Future Wireless Systems
MIMO Systems and their Decomposition
MIMO (multiple-input multiple-output) systems have multiple transmit and receive antennas
Decompose channel through transmit precoding (x=Vx) and receiver shaping (y=UHy)
Leads to RHmin(Mt,Mr) independent channels with gain si (ith singular value of H) and AWGN
Independent channels lead to simple capacity analysis and modulation/demodulation design
H=USVHy=Hx+n y=S x+n~ ~
yi=six+ni~ ~ ~
~
~ ~
Capacity of MIMO Systems
Depends on what is known at TX and RX and if channel is static or fading
For static channel with perfect CSI at TX and RX, power water-filling over space is optimal:In fading waterfill over space (based on
short-term power constraint) or space-time (long-term constraint)
Without transmitter channel knowledge, capacity metric is based on an outage probabilityPout is the probability that the channel
capacity given the channel realization is below the transmission rate.
Beamforming Scalar codes with transmit precoding
1x
2x
tMxx
1v
tMv
• Transforms system into a SISO system with diversity.• Array and diversity gain• Greatly simplifies encoding and decoding.• Channel indicates the best direction to beamform• Need “sufficient” knowledge for optimality of beamforming
y=uHHvx+uHn
2v 1u
rMu
2u y
Optimality of Beamforming
Mean Information Covariance Information
Diversity vs. Multiplexing
Use antennas for multiplexing or diversity
Diversity/Multiplexing tradeoffs (Zheng/Tse)
Error Prone Low Pe
r)r)(M(M(r)d rt*
rSNRlog
R(SNR)lim SNR
dSNRlog
P log e
)(lim SNRSNR
Best usedependson the
application
How should antennas be used?
Use antennas for multiplexing:
Use antennas for diversity
High-RateQuantizer
ST CodeHigh Rate Decoder
Error Prone
Low Pe
Low-RateQuantizer
ST CodeHigh
DiversityDecoder
Depends on end-to-end metric: Solve by optimizing app. metric
MIMO Receiver Design
Optimal Receiver: Maximum likelihood: finds input symbol most likely
to have resulted in received vector Exponentially complex # of streams and
constellation size Decision-Feedback receiver
Uses triangular decomposition of channel matrix Allows sequential detection of symbol at each
received antenna, subtracting out previously detected symbols
Sphere Decoder: Only considers possibilities within a sphere of
received symbol.
Space-Time Processing: Encode/decode over time & space
Other MIMO Design Issues
Space-time coding: Map symbols to both space and time via
space-time block and convolutional codes.
For OFDM systems, codes are also mapped over frequency tones.
Adaptive techniques: Fast and accurate channel estimationAdapt the use of transmit/receive
antennas Adapting modulation and coding.
Limited feedback: Partial CSI introduces interference in
parallel decomp: can use interference cancellation at RX
TX codebook design for quantized channel
Main Points MIMO systems exploit multiple
antennas at both TX and RX for capacity and/or diversity gain
With TX and RX channel knowledge, channel decomposes into independent channels Linear capacity increase with number of
TX/RX antennasWith TX/RX channel knowledge, capacity
vs. outage is the capacity metric Beamforming provides diversity gain in
direction of dominent channel eigenvectors
Fundamental tradeoff between capacity increase and diversity gain: optimization depends on application
Main Points
MIMO RX design trades complexity for performanceML detector optimal; exponentially complexDF receivers prone to error propagationSphere decoders allow performance tradeoff
via radiusSpace-time processing (i.e. coding) used in
most systems
Adaptation requires fast/accurate channel estimation
Limited feedback introduces interference between streams: requires codebook design
ISI Countermeasures Equalization
Signal processing at receiver to eliminate ISI, must balance ISI removal with noise enhancement
Can be very complex at high data rates, and performs poorly in fast-changing channels
Not that common in state-of-the-art wireless systems
Multicarrier ModulationBreak data stream into lower-rate
substreams modulated onto narrowband flat-fading subchannels
Spread spectrumSuperimpose a fast (wideband)
spreading sequence on top of data sequence, allows resolution for combining or attenuation of multipath components.
Course Outline Overview of Wireless Communications Path Loss, Shadowing, and Fading
Models Capacity of Wireless Channels Digital Modulation and its
Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications &
Wireless Networks Future Wireless Systems
Multicarrier Modulation
Breaks data into N substreams Substream modulated onto separate
carriersSubstream bandwidth is B/N for B total
bandwidthB/N<Bc implies flat fading on each
subcarrier (no ISI)
x
cos(2f0t)
x
cos(2fNt)
SR bps
R/N bps
R/N bps
QAMModulator
QAMModulator
Serial To
ParallelConverter
Overlapping Substreams
Can have completely separate subchannelsRequired passband bandwidth is B.
OFDM overlaps substreamsSubstreams (symbol time TN)
separated in RXMinimum substream separation is
BN/(1+).Total required bandwidth is B/2 (for
TN=1/BN)f0 fN-1
B/N
Fading Across Subcarriers
Leads to different BERSCompensation techniques
Frequency equalization (noise enhancement)
PrecodingCoding across subcarriersAdaptive loading (power and rate)
FFT Implementation of OFDM
Use IFFT at TX to modulate symbols on each subcarrier
Cyclic prefix makes linear convolution of channel circular, so no interference between FFT blocks in RX processing
Reverse structure (with FFT) at receiverx
cos(2fct)
R bps QAMModulator
Serial To
ParallelConverter
IFFT
X0
XN-1
x0
xN-1
Add cyclicprefix and
ParallelTo SerialConvert
D/A
TX
x
cos(2fct)
R bpsQAMModulatorFFT
Y0
YN-1
y0
yN-1
Remove cyclic
prefix andSerial toParallelConvert
A/DLPFParallelTo SerialConvert
RX
OFDM Design IssuesTiming/frequency offset:
Impacts subcarrier orthogonality; self-interference
Peak-to-Average Power Ratio (PAPR)Adding subcarrier signals creates large
signal peaks
Different fading across subcarriersSame mitigation techniques as in MCM:
Precoding to invert fading, coding across subcarriers, and adaptative loading over time most common
MIMO/OFDMApply OFDM across each spatial
dimensionCan adapt across space, time, and
frequency
Main Points ISI can be mitigated through
equalization, multicarrier modulation (MCM) or spread spectrum Today, equalizers often too complex or can’t
track channel.
MCM splits channel into NB flat fading subchannelsFading across subcarriers degrades
performance. Compensate through coding or adaptation
OFDM efficiently implemented using FFTs
OFDM challenges are PAPR, timing and frequency offset, and fading across subcarriers
Course Outline Overview of Wireless Communications Path Loss, Shadowing, and WB/NB
Fading Capacity of Wireless Channels Digital Modulation and its
Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications &
Wireless Networks Future Wireless Systems
Introduction to Spread Spectrum
Modulation that increases signal BWMitigates or coherently combines
ISI Mitigates narrowband
interference/jammingHides signal below noise (DSSS) or
makes it hard to track (FH)Also used as a multiple access
techniqueTwo types
Frequency Hopping: Narrowband signal hopped over wide
bandwidthDirection Sequence:
Modulated signal multiplied by faster chip sequence
Direct Sequence Spread Spectrum
Bit sequence modulated by chip sequence
Spreads bandwidth by large factor (K)
Despread by multiplying by sc(t) again (sc(t)=1)
Mitigates ISI and narrowband interference
s(t) sc(t)
Tb=KTc Tc
S(f)Sc(f)
1/Tb 1/Tc
S(f)*Sc(f)
2
ISI and Interference Rejection
Narrowband Interference Rejection (1/K)
Multipath Rejection (Autocorrelation rt
S(f) S(f)I(f)S(f)*Sc(f)
Info. Signal Receiver Input Despread Signal
I(f)*Sc(f)
S(f) S(f)S(f)*Sc(f)[d(t)+(t-t)]
Info. Signal Receiver Input Despread Signal
rS’(f)
Pseudorandom Sequences
Autocorrelation determines ISI rejectionIdeally equals delta function
Maximal Linear CodesNo DC componentLarge period (2n-1)TcLinear autocorrelationRecorrelates every periodShort code for acquisition, longer for
transmissionIn SS receiver, autocorrelation taken
over TbPoor cross correlation (bad for MAC)
1
-12n-1 Tc -Tc
SynchronizationAdjusts delay of sc(t-t) to hit
peak value of autocorrelation.Typically synchronize to LOS
component
Complicated by noise, interference, and MP
Synchronization offset of Dt leads to signal attenuation by r(Dt)
1
-12n-1 Tc -Tc
DtrDt)
RAKE Receiver Multibranch receiver
Branches synchronized to different MP components
These components can be coherently combinedUse SC, MRC, or EGC
x
x
sc(t)
sc(t-iTc)
xsc(t-NTc)
Demod
Demod
Demod
y(t)
DiversityCombiner
dk̂
Main Points In DSSS, bit sequence modulated by
chip sequence
Spreads bandwidth by large factor (K) Despread by multiplying by sc(t) again
(sc(t)=1) Mitigates ISI and narrowband
interferenceISI mitigation a function of code
autocorrelation Must synchronize to incoming signal RAKE receiver used to combine
multiple paths
s(t) sc(t)
Tb=KTc Tc
S(f)Sc(f)
1/Tb 1/Tc
S(f)*Sc(f)
2