1

Adaptive Modulation

2OutlineAdaptive MQAM: optimal power and rateFinite Constellation SetsUpdate rateEstimation errorEstimation delayPractical Considerations in Adaptive Modulation

3Adaptive ModulationChange modulation relative to fading

Parameters to adapt: Constellation size Transmit power Instantaneous BER Symbol time Coding rate/scheme

Optimization criterion: Maximize throughput Minimize average power Minimize average BER

Only 1-2 degrees of freedom needed for good performance

Adaptive Technologies Rate Control

Fixing symbol rate， using multiple modulation schemes or constellation sizes• Fairly easy, used in current systems, such as GSM, IS-136 EDGE or 802.11a,

et. al. Fixing the modulation, changing the symbol rate

• Varying signal bandwidth is impractical and complicates bandwidth sharing.

Power Control Adapting the transmit power alone is generally used to compensate

for SNR variation due to fading. To maintain a fixed bit error probability, or a constant received SNR. The power adaptation thus inverts the channel fading so that the

channel appears as an AWGN channel to the modulator and demodulator.

Adaptive Technologies (cont) Error Control

Adapt the instantaneous BER subject to an average BER constraint.• Not an adaptive technique, since the transmitter does not adapt to SNR.

Error probability is typically adapted along with some other form of adaption such as constellation size or modulation type.

Hybrid techniques Adapt multiple parameters of the transmission scheme, including rate,

power, coding, and instantaneous error probability. Joint optimization of the different techniques is used to meet a given

performance requirement. Rate adaption is often combined with power adaptation to maximize

spectral efficiency.

6Variable-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

The rate and power of MQAM are varied to maximize spectral efficiency while meeting a given instantaneous Pb target.

Goal: Optimize P(g) and M(g) to maximize R=Elog[M(g)]

7Optimization FormulationAdaptive 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

8Optimal Adaptive SchemePower Adaptation

Spectral Efficiency

0

0

1 1( )0 else

K KKPP

gg g g gg

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).

9Spectral Efficiency

K1

K2

K=-1.5/ln(5BER)

Can reduce gap by superimposing a trellis code

10Constellation RestrictionRestrict 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

0M1

M2

OutageM1

M3

M2

M3

MD(g)

11Power 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

12Efficiency in Rayleigh Fading

13Practical 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 channelError 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

14Detailed FormulasError 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

ˆ/target

0

ˆ ˆ.2[5 ] ( , )K

bP BER p d dg g

g

g g g g

^

^

ggg ddppBERPb )()|(]5[2.0 0

target

15Main 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 and delay lead to irreducible error floors in adaptive MQAM