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
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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.
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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]
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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)
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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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