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