superposition coded modulation (scm), scm-ofdm, and ofdm

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

3


Overview

4

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

8

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

9

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


11

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

12

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:

13

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:

14

Overview


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))}

16

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:

17

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.

18

ESE… …

APP DEC-k

kπ

1kπ−r={r(j)}

…

APP DEC-1

1π

11π−

…

……

The Iterative Detection Principle

19

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

20

Overview


21

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

22

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

22

2 2 21

log (1 )CNρρ

= ++

2 21 2

2log (1 )totalCN

ρ ρ+= +

21

1 2log (1 )CNρ

= +

1 2totalC C C= +?

For details, seeT. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley 1992

23

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

+= +

⎛ ⎞+ += ⎜ ⎟

⎝ ⎠⎛ ⎞+ + +

= ⋅⎜ ⎟+⎝ ⎠

+ + + = ++

24

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

25

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

≠

=+∑

26

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

27

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.

28

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

29

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

30

Overview


31

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:

32

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

33

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.

34

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

35

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

36

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.)

37

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))}


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

38

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

39

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)

40

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

41


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))}


FFT

r

43

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.

44


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

45

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


BICM-OFDM SP mapping

SCM-OFDM


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


BICM-OFDM SP mapping

SCM-OFDM


47

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.

48

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


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.

superposition coded modulation (scm), scm-ofdm, and ofdm

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