Download - EE359 – Lecture 13 Outline
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EE359 – Lecture 13 Outline
AnnoucementsMidterm announcementsNo HW this week (study for MT; HW due
next week)
Midterm reviewIntroduction to adaptive
modulationVariable-rate variable-power
MQAMOptimal power and rate adaptationFinite constellation sets
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Midterm Announcements
Midterm Tues Nov. 4, 6-8pm, Shriram104Open book/notes (bring
textbook/calculators)Covers Chapters 1-7
Extra OHs next two daysMon (today) 1-3pm, and Tues 11am-1pmTAs (Tentative): Mon 11:30-1:30, 5-7, Tue
11:30-12:30, 2-4No HW due this week, new HW
posted Thu.Midterms from past 3 MTs posted
10 bonus points for “taking” a practice exam
Solns for all exams given when you turn in practice exam
Can turn it in at the exam and get the points
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Review of Last Lecture
Maximal Ratio Combining
MGF Approach for Performance of MRC
Transmit diversityWith channel knowledge, similar to
receiver diversity, same array/diversity gain
Without channel knowledge, can obtain diversity gain through Alamouti scheme over 2 consecutive symbols
MMbbb dddpppPdpPP ...)(...)()()(...)()( 21**2*1
dg
PM
iiib
5.
0 12
;sin
1M
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Adaptive ModulationChange modulation relative to
fading
Parameters to adapt:Constellation sizeTransmit powerInstantaneous BERSymbol timeCoding rate/scheme
Optimization criterion:Maximize throughputMinimize average powerMinimize average BER
Only 1-2 degrees of freedom needed for good performance
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Variable-Rate Variable-Power MQAM
UncodedData Bits Delay
PointSelector
M(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)]
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Optimization Formulation
Adaptive MQAM: Rate for fixed BER
Rate and Power Optimization
Same maximization as for capacity, except for K=-1.5/ln(5BER).
P
PK
P
P
BERM
)(1
)(
)5ln(
5.11)(
P
PKEME
PP
)(1logmax)]([logmax 2
)(2
)(
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Optimal Adaptive Scheme
Power Adaptation
Spectral Efficiency
else0
)( 0
0
11KKK
P
P
g
1
0
1
Kgk g
R
Bp d
K K
log ( ) .2
Equals capacity with effective power loss K=-1.5/ln(5BER).
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Spectral Efficiency
K1
K2
K=-1.5/ln(5BER)
Can reduce gap by superimposing a trellis code
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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,
…,NPower control maintains target BER
M(g)=g/gK*
gg0 g1=M1gK* g2 g3
0
M1
M2
OutageM1
M3
M2
M3
MD(g)
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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
0
0,)/()1()(
jKM
P
P jjjj
)(log 11
2
jj
N
jj pM
B
R
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Efficiency in Rayleigh Fading
Sp
ectr
al
Eff
icie
ncy
(bp
s/H
z)
Average SNR (dB)
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Practical ConstraintsConstellation updates: fade region
duration
Estimation error Estimation error at RX can cause error in
absence of noise (e.g. for MQAM)Estimation error at TX can be caused by
estimator and/or delay in the feedback path
Causes mismatch of adaptive power and rate to actual channel
Can lead to large errors
Mjj
jj TT
NN
1
regionin fademax at ratecrossinglevel
regionin fademin at ratecrossinglevel
spreaddelay
AFRD
1
j
j
M
j
N
N
T
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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.
Estimation error/delay causes error floor