EE359 – Lecture 13 Outline Adaptive MQAM: optimal power and rate Finite Constellation Sets Practical Constraints Update rate Estimation error Estimation delay
Dec 14, 2015
EE359 – Lecture 13 Outline
Adaptive MQAM: optimal power and rate
Finite Constellation SetsPractical Constraints
Update rateEstimation errorEstimation delay
Review of Last Lecture
Maximal Ratio Combining
MGF Approach for Performance of MRC
EGCHarder to analyze than MRC; lose ~1 dB
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
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
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)]
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
)(
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).
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,
…,NPower control maintains target BER
M(g)=g/gK*
gg0 g1=M1gK* g2 g3
0
M1
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
0
0,)/()1()(
jKM
P
P jjjj
)(log 11
2
jj
N
jj pM
B
R
Efficiency in Rayleigh Fading
Sp
ectr
al
Eff
icie
ncy
(bp
s/H
z)
Average SNR (dB)
Practical ConstraintsConstellation 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
regionin fademax at ratecrossinglevel
regionin fademin at ratecrossinglevel
spreaddelay
AFRD
1
j
j
M
j
N
N
T
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