Adaptive Modulation and Coding for OFDM Systemsfor OFDM Systems

Suk Chan KimDept. of Electronics EnginerringDept. of Electronics EnginerringPusan National University

ContentsContents

Introduction

Adaptive code-rate for OFDM system

Adaptive modulation for BICM-OFDM system

Conclusion

2

IntroductionIntroduction

Adaptive transmission techniques improve the performance of wireless communication system by adjusting transmission parameter like modulation code-rate and power depending on the channel statemodulation, code rate, and power depending on the channel state adaptively.

When adaptive transmission is applied to OFDM system, transmission parameters of each subcarrier are adapted to each subchannel. Adaptive

d l i f d d OFDM h b di d id lmodulation for uncoded OFDM system have been studied widely.

W t d d ti d t d d ti d d d l ti f OFDMWe study adaptive code-rate and adaptive coded modulation for OFDM system.

3

Adaptive code rate for OFDM systemAdaptive code-rate for OFDM system

Code-rate of each subcarrier is adapted to each subchannel optimally.

T bt i diff t d t f h b i t tibl t dTo obtain different code-rate for each subcarrier, rate-compatible punctured convolutional (RCPC) code is used

Received signal-to-noise ratio (SNR) is used for measure of subchannel state to select appropriate code-rate for each subcarrier.pp p

Transmission power and modulation for each subcarrier is fixed for simplication of the adaptation algorithm

4

Code rate selectionCode-rate selection

Code-rate for each subcarrier are selected according to switching levels.Received SNR and code-rate of each subcarrier is shown in figure. Th 6th b i l t th d t i th i d SNR iThe 6th subcarrier selects the code-rate r2 since the received SNR is between s2 and s3.

5

OptimizationOptimization

Our optimization problem is

max ( ) such that ( ) TR BER BERγ γ ≤s smax ( , ) such that ( , ) ,

: set of switching level,( ) d t

c TR BER BER

R

γ γ ≤s

s s

s( , ) : average code-rate,

( , ) : average BER,BER

cR

BERBER

γ

γ

s

s

To get optimal switching levels s Lagrange method is applied to the

: target BER.TBER

To get optimal switching levels s, Lagrange method is applied to the optimazation.

( ) ( ) ( )J R BER BERλ ⎡ ⎤( , ) ( , ) ( , )c TJ R BER BERγ γ λ γ⎡ ⎤= + −⎣ ⎦s s s

6

Performance AnalysisPerformance Analysis

Rayleigh fadingBPSK modulation.P l i l d K 4 (1 1 13)Parent convolutional code: K = 4, g = (15,17,13)8.RCPC code-rates: 8/9, 8/10, 8/14, 8/18, 8/22, 8/24.T t BER 10 4 10 6Target BER = 10-4 or 10-6.

7

Average code rateAverage code-rate

Average code-rate of adaptive code-rate OFDM system at BER = 10-4 and 10-6.

0.8

0.9

0 6

0.7

e-ra

te

0.5

0.6

Ave

rage

cod

e

0.3

0.4

A

Average BER = 10-4

0 5 10 15 200.2

Average SNR (dB)

g

Average BER = 10-6

8

g

Average BERAverage BER

Average BER of adaptive and fixed code-rate OFDM system.10

-2

1/3 adaptive

10-3

1/2 adaptive

2/3 adaptive

1/3 fixed

1/2 fixed

2/3 fixed

10-5

10-4

or P

roba

bilit

y

2/3 fixed

10-6

105

Ave

rage

Bit

Err

o

10-7

0 2 4 6 8 10 12 14 16 18 20

10-8

Es/No [dB]

9

ConclusionConclusion

Code-rate of each subcarrier was adapted to subchannel state to maximize data rate and to satisfy average BER.

To get different code-rate and to reduce complexity, RCPC code was used for each subcarrier. o eac subca e .

We showed that large SNR gain was achieved by adaptive code-rate g g y pOFDM system.

Since we use BPSK modulation, data rate is saturated at high SNR. If high level modulation is used, we can expect more increase of data rate at high SNRSNR.

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BICM OFDM systemBICM-OFDM system

OFDM system overcome ISI caused from multipath fading using large number of subcarrier and guard interval.

Channel coding is essential for OFDM system to cope with faded subcarriers.subca e s.

Bit-interleaved coded modulation (BICM) is widely used in broadband ( ) ywireless communication since it has high capacity in fading channel and it use bit-interleaver and simple encoder/decoder.

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Adaptive modulation for BICM-OFDM systemAdaptive modulation for BICM-OFDM system

Adaptive modulator choose modulation level for each subcarrier according to subchannel state and maps coded bits to QAM symbol using Gray labelinglabeling.Demodulator produces the bit metric using transmission mode of each subcarrier.

`

S/P IDFT P/STransmit

Binary data

OFDMBICM

Encoder Interleaver Modulator S/P, IDFT, P/SAdd CP

Multipath fadingChannel

y

S/P DFT P/S

Multipath fadingchannel

ChannelEstimation

AWGN

Transmission modefrom Transmitter

Receive Binary data

Decoder DeInterleaver Demodulator S/P, DFT, P/SRemove CP

y

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AdaptationAdaptation

Our adaptation policy is to minimize BER under the constant throughput.-1

min subject toN

BER m N=∑0 1

c,..., 0min subject to

: the number of coded bits for th subcarrierN

km m k

k

BER m N

m k− =

=∑

We obtain Chernoff bound for pairwise error probability of adaptive

c : the number of coded bits for a OFDM symbolN

We obtain Chernoff bound for pairwise error probability of adaptive OFDM-BICM system by assuming ideal bit interleaving.

d212

20

| |1( , , ) exp | | ()ˆ4

dN

kk

kc

hf d m E x zN

μ χσ

−

=

⎛ ⎞⎡ ⎤⎛ ⎞≤ − −⎜ ⎟⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦⎝ ⎠∑

⎝ ⎠

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ContCont.

Using Lagrange method, our adaptation problem is simplified by

min k kH mλ−

22

2| |where exp | | .ˆ4

kk km

k khH m E x z

⎡ ⎤⎛ ⎞= − −⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

Since m has discrete values such as {0 1 2 4 6 8} our optimization is

2p | |4k k σ⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

Since mk has discrete values such as {0,1,2,4,6,8}, our optimization is discrete resource allocation problem.

We find Lagrange multiplier λ that satisfy the given constraint Nc using iterative method.

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ContCont.

Example of finding λ iteratively given Nc = 256

iteration λ

0 1.000000 336 70.939687

1

0

Nkk

m−

=∑1

0

Nkk

H−

=∑

1 0.211130 214 4.676390

2 0 543142 281 29 2345502 0.543142 281 29.234550

3 0.366540 242 12.005676

4 0 441766 261 19 5455684 0.441766 261 19.545568

5 0.396836 256 17.418943

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Simulation parameterSimulation parameter

Coded bits per subcarrier mk = {0,1 2,4,6,8}.64 subcarrier, 4.0μs OFDM symbol duration. E ti ll d i lti th i t i filExponentially decaying multipath intensive profile.Delay spread of τrms= 0.2μs, τmax= 0.8μsC l ti l d ith K 7 (133 171 ) R 1/2 2/3 3/4Convolutional code with K=7, g=(1338,1718), Rc=1/2, 2/3, 3/4

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Simulation resultSimulation result

Bit allocation result for a realization of the multipath channel when SNR = 18 dB, Nc = 256.

1

1.5

of

|h|

0 10 20 30 40 50 600

0.5

1

Sq

uar

e o

0 10 20 30 40 50 60Subcarrier

4

6

d b

its/

arri

er

0 10 20 30 40 50 60012

b i

Co

ded

Su

bca

subcarrier

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Simulation result (2)Simulation result (2)

BER when Rc=1/2, Nc = 128, 256.10

0

Adaptive (N = 128)

10-1

Adaptive (Nc = 128)

Nonadaptive (Nc = 128)

Adaptive (Nc = 256)

Nondaptive (Nc = 256)

-3

10-2

R

c

10-4

103

BE

R

10-5

4 6 8 10 12 14 16 1810

-6

SNR (dB)

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Simulation result (3)Simulation result (3)

BER when Rc=2/3, Nc = 128, 256.10

0

Adaptive (N = 128)

10-1

Adaptive (Nc = 128)

Nonadaptive (Nc = 128)

Adaptive (Nc = 256)

Nonadaptive (Nc = 256)

3

10-2

R

p ( c )

10-4

10-3

BE

R

10-5

6 8 10 12 14 16 18 20 2210

-6

SNR (dB)

19

Simulation result (4)Simulation result (4)

BER when Rc=3/4, Nc = 128, 256.10

0

Adaptive (N = 128)

10-1

Adaptive (Nc 128)

Nonadaptive (Nc = 128)

Adaptive (Nc = 256)

Nonadaptive (Nc = 256)

10-3

10-2

R

c

10-4

103

BE

R

10-5

8 10 12 14 16 18 20 22 2410

-6

SNR (dB)

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ConclusionConclusion

Adaptive modulation for BICM-OFDM system was considered.

BER b d i i i i d d th t t th h tBER bound is minimized under the constant throughput.

C d d bit ll t d t h b i i di t LCoded bits were allocated to each subcarrier using discrete Lagrange optimization.

Simulation results show that adaptive BICM-OFDM system got large SNR gain over nonadaptive one.

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