Post on 12-Sep-2021
1
Superposition Coded Modulation (SCM),SCM-OFDM,
and OFDM-IDMA
Jun Tong and Li PingDepartment of Electronic Engineering
City University of Hong Kong
2
Overview
• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
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• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
Overview
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Coded modulation delivers high throughput using a large constellation of signaling points. TCM and BICM are two conventional coded modulation techniques. Different mapping rules are usually used for different constellations.
Coded Modulation
64 QAM constellation
5
0
0.5
1
1.5
2
2.5
3
3.5
4
-2 3 8 13Eb/N0 (dB)
Spec
tral e
ffic
ienc
y (b
its/c
hip)
capacity
A 32-QAM TCM delivers a rate of 4 b/s. If Eb/No < 8dB, errors will cause frequent re-transmission and then throughput drops seriously. On the other hand, even if Eb/No is very high, throughput is still limited by 5 b/s.
32-QAM TCM-ARQ Performance
32-QAM TCM-ARQ
8
6
4
2
0
6
0
0.5
1
1.5
2
2.5
3
3.5
4
-2 3 8 13Eb/N0 (dB)
Spec
tral e
ffic
ienc
y (b
its/c
hip)
capacity
Rate adaptation can be used to maximize throughput. However, with conventional methods, different rates involve different encoders and decoders. This is a quite cumbersome approach.
Rate Adaptation8
6
4
2
0
128-QAM TCM-ARQ64-QAM TCM-ARQ
32-QAM TCM-ARQ16-QAM TCM-ARQ
8-PSK TCM-ARQ
7
• A high rate scheme.• An alternative to TCM and BICM.• Simple, effective and flexible.
Superposition Coded Modulation (SCM)
SCM constellation
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A characteristic property of SCM is its randomness. We can see this from its constellation. Later we will see that the simplicity, performance and flexibility of the SCM scheme is closely associated to this randomness.
Quasi-Random Constellation of SCM
64 QAM constellation SCM constellation
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Features of SCM• Very simple• On-shelf binary encodes and decoders• Flexible rate adaptation• Capacity-approaching performance• A unified solution to
- the PAPR problem- the ISI problem, and - the multiple access problem
10
Overview
• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
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SCM Encoding Principles
π1
πK
C
C
layer-1
layer-K
… ……
πkClayer-k
… ……
ρ1
ρK
…
ρk…
1
K
k kk
ρ=
=∑r x
• Parallel transmission for high rate.• Layer separation using interleavers {πk}.• Performance optimization using power control factors {ρk}.
x1
xk
xK
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Superimposed Signals and Interference
A fundamental problem in communication is how to separate several signal after they are superimposed. Traditionally this is a very complicated problem. The key here is how to handle the interference among different signals.
Signal 1:
Signal 2:
coding constraint t
Signal 3:
SuperimposedSignal:
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Iterative Processing
The interference problem can be efficiently resolved by the detector below. In the ESE, we only consider superposition constraint. In the DECs, we only consider coding constraint. The results are combined iteratively.
ESEr={r(j)}
DEC-11
1π−
1π
DEC-2
DEC-3
12π−
2π1
3π−
3π
coding constraint
t
Superpositionconstraint:
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Overview
• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
15
ESE… …
APP DEC-k
kπ
1kπ−r={r(j)}
…
APP DEC-1
1π
11π−
…
……
Iterative Detection Principles
{e(x1(j))}
{E(x1(j))}
{e(xk(j))}
{E(xk(j))}
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Gaussian Approximation Detection
Path model and Gaussian approximation
Estimation:
( ) ( )k k kx j jρ ζ+=
1( ) ( ) ( )
K
k kk
r j x j n jρ=
= +∑
( )
2
2
( ( ) E( ( )) )exp( )Pr( ( ) 1) 2Var( ( )) 2log = log ( ) E( ( ))
( ( ) E( ( )) )Pr( ( ) 1) Var( ( ))exp( )2Var( ( ))
k k
k k kk
k kk k
k
r j jx j j r j j
r j jx j jj
ρρ
ρ
− ζ −−
= + ζ= ⋅ − ζ
− ζ += − ζ−
ζ
Gaussian
( ) ( )2( ) = ( ) E( ( ))Var( ( ))
kk k
k
e x j r j jj
ρ⋅ − ζ
ζ
Some details:
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Chip-by-Chip (CBC) Detection Algorithm
Step 1.
Step 2.
Step 3.
( ) ( ) ( ) ( ) E ( ) E E ( )k k kr jj x jζ ρ= −
( ) ( )1
E ( ) E ( )K
k kk
r j x jρ=
=∑
( ) ( )2( ) ( ) E( ( ))Var( ( ))
kk k
k
e x j r j jj
ρ= ⋅ − ζ
ζ
( ) ( )2
1Var ( ) Var ( )
K
k kk
r j x jρ=
=∑
( ) ( ) ( )2 ( )Var ( ) Var Var ( )k k kr jj x jζ ρ= −
Notes:(1) There is no matrix operation.(2) E(xk(j) and Var(xk(j)) are the feedback from the decoders.
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ESE… …
APP DEC-k
kπ
1kπ−r={r(j)}
…
APP DEC-1
1π
11π−
…
……
The Iterative Detection Principle
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SCM Performance: K=5, R=5 b/s
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
7 8 9 10 11 12Eb/N0(dB)
BER
Frame length: 105; IT = 6; See:Xiao Ma and Li Ping, "Coded modulation using superimposed binary codes," IEEE Trans. Inform. Theory, Dec. 2004.
SCM Performance
Shannon limit
64 QAM capacity
1
2
3
4
5
6
7
8
0 2 4 6 8 10 12 14 16 18
Eb/N0(dB)
I(X;
Y) (b
its/s
ymbo
l)
64-QAMcapacity
Shannon limit by Gaussiansignaling
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Overview
• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
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Stripping Detection of a Two-Layer System
(1) Decode x2 by treating x1 as noise.(2) Assume (1) successful. Strip off x2 from r. (3) Decode x1 .
This principle can be applied to systems with more layers.
1 1 2 2ρ ρ= + +r x x ηπ1Clayer-1
π2Clayer-2
ρ1
ρ2
x1
x2
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Capacity Analysis of Stripping Decoding
Decode x2 by treating x1 as noise.
Decoding x1 :
Overall capacity:
1 1 2 2ρ ρ= + +r x x ηπ1Clayer-1
π2Clayer-2
ρ1
ρ2
x1
x2
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2 2 21
log (1 )CNρρ
= ++
2 21 2
2log (1 )totalCN
ρ ρ+= +
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1 2log (1 )CNρ
= +
1 2totalC C C= +?
For details, seeT. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley 1992
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SCM Is Capacity Achieving (Tom Cover)Here is an interesting property of the Shannon formula.
This says that stripping decoding is indeed capacity achieving. However, This applies only to ideal coding and decoding. How about practical coding and decoding?
2 21 2
2
2 21 2
2
2 2 21 2 1
2 21
2 22 1
2 2 1 221
log (1 )
log
log
= log (1 ) log (1 )
CN
NN
N NN N
C CN N
ρ ρ
ρ ρ
ρ ρ ρρ
ρ ρρ
+= +
⎛ ⎞+ += ⎜ ⎟
⎝ ⎠⎛ ⎞+ + +
= ⋅⎜ ⎟+⎝ ⎠
+ + + = ++
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SNR Evolution for an SCM Detector
ESE… …
APP DEC-k
1kπ−
r={r(j)}
APP DEC-1
… …kπ
11π−
1π
{e(x1(j))}
{E(x1(j))}
{e(xk(j))}{E(xk(j))}
Iterativedetector
ESE
…
f(·)
r={r(j)}
f(·)
…
SNR1
SNRk
Variance1
Variancek
Evolutionprocess
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1( ) ( ) ( )
( ) ( ) ( )
K
k kk
k k i ii k
r j x j n j
x j x j n j
ρ
ρ ρ
=
≠
= +∑
= + +∑
Gaussian
kSNR k ∀= ,0)0(
Received signal:
SNR evolution:
Initialization:
Evolution Process
For details, seeLihai Liu, Jun Tong, and Li Ping, "Analysis and optimization of CDMA systems with chip-level interleavers," IEEE J. Select. Areas Commun. vol. 24, no. 1, pp. 141-150, Jan. 2006.
)2( )
2(
2 ( )oldi i
new kk
ii k
SNRf SNR
ρρ σ
≠
=+∑
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SNR Evolution for an SCM DecoderThe iterative detector can be characterized by the following SNRevolution process:
This is much simpler and faster than simulation.
2( )
2 ( ) 2( )new k
k oldi i i
i k
SNRf SNR
ρρ σ
≠
=+∑
ESE
… …
f(·)1
kπ−
r={r(j)}
f(·)
… …
SNR1
SNRk
kπ
11π−
1πVariance1
Variancek
Evolutionprocess
Evolutionformula
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Examples of f(·)
- 2 0 - 1 5 - 1 0 - 5 0 5 1 01 0
- 6
1 0- 4
1 0- 2
1 00
S N R ( d B )
Var
ianc
e a rate 1/2 convolutional code obtained by Monte-Carlo method
f(·)SNR
Variance
Decoder
a rate 1/2ideal code
The f-function is the transfer function of an APP decoder in terms of variance vs SNR.
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To minimize
subject to performance requirement
where
with initial conditions
This problem can be solved by linear programming. SeeLihai Liu, Jun Tong, and Li Ping, "Analysis and optimization of CDMA
systems with chip-level interleavers," IEEE JSAC, Jan. 2006.
kSNR kL
k ∀Γ≥ ,)(
kSNRk ∀= ,0)0(
Power Optimization
2k
k
ρ∑
2( )
2 ( 1) 2 , ,( )
l kk l
i i ii k
SNR k lf SNR
ρρ σ−
≠
= ∀+∑
SCM performance can be optimized by searching minimizing total transmission power. The problem can be formulated as follows
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Comparisons of Evolution and Simulation
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
10.0 11.0 12.0 13.0 14.0Eb/No(dB)
BER
Evolution
Simulation
R=4 b/s, K=16, convolutional code, frame length=16348, frequency selective fading
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Overview
• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
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The PAPR Problem• SCM has a relatively high PAPR.• This may be a disadvantage for a straightforward SCM.• However, it actually implies a unique advantage for SCM-
OFDM, as will be explained later.
SCM constellation
π1
πK
C
C
layer-1
layer-K
… ……
πkClayer-k
… ……
ρ1
ρK
…ρk…
SuperimposedSignal:
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A simple PAPR reduction method.
Induces non-linear distortion.
PAPR Reduction by Clipping
, | |
, | || |
x x Ax A x x Ax
≤⎧⎪≡⎨ >⎪⎩
z x x= −Amplitude clipper
xRe
xIm
A
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33.5
44.5
55.5
66.5
7
4 6 8 10 12 14Eb/N0(dB)
I(X;
Y) (
bits
/sym
bol)
Loss of Mutual Information Due to Clipping
Shannon limit, PAPR = ∞
64-QAM capacity, PAPR = 3.68 dB
5 layer clipped SCM, PAPR = 3.68 and 2.65 dB
Theoretically, performance loss due to clipping is marginal.
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1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
7 8 9 10 11 12Eb/N0(dB)
BER
The Impact of Clipping
Clipping may seriously affect BER performance. (K=5, R=5 b/s)
no clippingPAPR = 5.39 dB
Clipped, PAPR = 3.68 dB
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Basic SCM Principle Again
SCM with K-layers
π1
πK
C
C
layer-1
layer-K
… ……
πkClayer-k
… ……
ρ1
ρK
…ρk…
1
K
k kk
ρ=
=∑r x
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Gaussian Assumption Again
( ) ( ) ( ) k k kr j x j jρ ξ= +
No clipping: Interference
Clipping distortion.With Clipping:
( ) ( ) ( ) ( ) k k kr j x j j z jρ ξ= + +
∑≠
=K
kiiik xρξ
Based on the feedback from the decoder, we can also estimate theclipping distortion and compensate it iteratively. (How? If we know the transmitted signal, of cause we also know the clipping distortion.)
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Iterative Clipping Compensation
Signal estimation
&clipping
compensation … …
APP DEC-k
1kπ−
r={r(j)}
APP DEC-1
… …kπ
11π−
1π
{e(x1(j))}
{E(x1(j))}
{e(xk(j))}{E(xk(j))}
We can estimate the clipping distortion z(j) using decode feedbacks.
( ) ( ) ( ) ( ) k k kr j x j j z jρ ξ= + +
clipping thresholds
z(j)
A-A 0
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Estimation of Clipping Noise
Based on the DEC feedbacks, we can then approximately estimate E(z(j)) and Var(z(j)) using Gaussian approximation.
For details, seeJun Tong, Li Ping, and Xiao Ma, "Superposition coding with peak-power limitation," in Proc. IEEE Int. Conf. on Commun., ICC'06, Istanbul, Turkey, 11-15 June 2006.
clipping thresholds
z(j)
A-A 0
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Gaussian Approximation Detection
( ) ( )2( ) = ( ) E( ( ))Var( ( ))
kk k
k
e x j r j jj
ρ⋅ − ζ
ζ
( ) ( ) ( ) ( ) k k kr j x j j z jρ ξ= + +
Gaussian approximation
Estimation:
Gaussian ζk(j)
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1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
7 8 9 10 11 12Eb/N0(dB)
BER
Soft Clipping Effect Compensation
No clipping,PAPR = 5.39 dB
With soft compensation, PAPR = 3.68 dB
Without soft compensation, PAPR = 3.68 dB
K=5, R=5 b/s; Frame length: 105; IT = 6.
Shannon limit
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• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
Overview
42
SCM-OFDM Features
• Robust against frequency-selective fading.• Robust against amplitude clipping.• Flexible rate adaptation.
SCM encoder
OFDM transmitter
OFDM receiver
ISIchannel
SCM detector
ESE
… …
APP DEC-k
1−kπ
r={r(j)}
APP DEC-1
… …kπ
11π−
1π
{e(x1(j))}
{E(x1(j))}
{e(xk(j))}{E(xk(j))}
FFT
r
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Robust against Frequency Selective Fading
π1
πK
C
C
layer-1
layer-K
… ……
πkClayer-k
… ……
ρ1
ρK
…
ρk…
1
K
k kk
ρ=
=∑r x
We can use relatively low-rate code for each layer so that the scheme becomes very robust against frequency-selective fading. This is due to the spreading effect introduced by low-rate coding. However, note that the overall rate can be maintained the same by increasing layer number K.
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Robust against Frequency Selective Fading
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
5.0 6.0 7.0 8.0Eb/No(dB)
BER
SCM-OFDM
BICM-OFDM (SP mapping)
SCM-OFDM vs BICM-OFDM over fading channels, with and without clipping; R = 2 b/s, clipping ratio = 3 dB
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1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
8 9 10 11 12
Eb/No(dB)
BER
Robust against Frequency Selective Fading
BICM-OFDM SP mapping
SCM-OFDM
SCM-OFDM vs BICM-OFDM over fading channels, with and without clipping; R = 3 b/s, clipping ratio = 3 dB
46
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
13 14 15 16 17 18 19 20 21 22
Eb/No(dB)
BER
Robust against Frequency Selective Fading
BICM-OFDM SP mapping
SCM-OFDM
SCM-OFDM vs BICM-OFDM over fading channels, with and without clipping; R = 5 b/s, clipping ratio = 3 dB
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Overall Trend
SCM with clipping BICM with clippingSCM without clipping BICM without clipping
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
13 14 15 16 17 18 19 20 21 22
Eb/No(dB)
BER
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
5.0 6.0 7.0 8.0Eb/No(dB)
BER
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
8 9 10 11 12
Eb/No(dB)
BER
R=2 R=3 R= 5
The advantage of SCM become more noticeable at higher rate.
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Robust against Clipping• PAPR is a serious problem for OFDM, regardless of coding
(TCM, BICM of SCM).
• However, for SCM-OFDM, PAPR can be reduced by clipping. The clipping distortion can be alleviated by iterative compensation.
• This makes SCM an attractive solution to the PAPR problem in OFDM.
• Iterative clipping compensation is a more complicated problem for BICM.
49
Flexible Rate Adaptation
0
0.5
1
1.5
2
2.5
3
3.5
4
-2 3 8 13
Eb/N0 (dB)
Spec
tral e
ffici
ency
(bits
/chi
p)
Optimal
QPSK
8
6
4
2
8 PSK16 QAM
32 QAM
SCM rate 1/3 per layer
64 QAM
128 QAM
SCM is very flexible since different rate can be realized by different K. It is much more complicated for other coded modulation methods.
50
• Introduction• Superposition coded modulation (SCM)• Iterative decoding• Performance analysis and performance optimization• The PAPR problem• SCM-OFDM• OFDM-IDMA• Conclusions
Overview
51
OFDM-IDMA
SCM encoder IFFT
SCM encoder IFFT FFT
ISIchannel
Jointmulti-user
SCM detector
SCM encoder IFFT
User 1
User 2
User 3
An OFDM-IDMA system is almost the same as SCM-OFDM, except different layers are transmitted by different users.
Therefore the detection principles are almost the same.
52
OFDM-IDMA
An OFDM-IDMA system is almost the same as SCM-OFDM, except layers may belong to different users. This does not affect the receiver function, so the detection principles are almost the same.
ESE
DEC-2-11
2 1π −−
r={r(j)}DEC-1-2
2 1π −
11 2π −−
1 2π −
FFT
DEC-1-11
1 1π −−
1 1π −
DEC-2-21
2 2π −−
2 2π −
User 1
User 2
53
Advantages of OFDM-IDMA
• ISI suppression by OFDM.
• Robust against frequency-selective fading.
• Robust against PAPR clipping.
• Flexible rate adaptation.
• Multi-user gain. (This topic will be discussed in detail later.)
54
OFDM-IDMA vs BICM-OFDM
For details, seeLi Ping, Qinghua Guo, and Jun Tong, “The OFDM-IDMA approach to wireless communication systems,” IEEE Wireless Commun. Mag., June 2007.
Multi-user gain
OFDM-IDMA
OFDMA
Average transmission power
55
Conclusions
• SCM is a high performance and flexible approach to coded modulation.
• Gaussian approximation plays a crucial role in iterative SCM detection.
• Clipping can be applied to SCM to reduce PAPR. The related distortion can be compensated by an iterative technique. This is particularly attractive in OFDM applications.
• Very simple and flexible design strategies.
• A very large range of rate can be supported.