1

Interleave Division Multiple Access (IDMA)

Lihai Liu, Raymond Leung and Li Ping Department of Electronic and Engineering

City University of Hong Kong

2

Outline

• Introduction • Iterative detection• Performance evaluation• Multi-user gain in fading channels• Other applications• Conclusions

3

Outline

• Introduction • Iterative detection• Performance evaluation• Multi-user gain in fading channels• Other applications• Conclusions

4

The Focus of this Talk

We will mostly focus on up-link multiple access channels(MAC), although the results can be applied to down-link broadcasting channels (BC).

For detail, seeLi Ping, Lihai Liu, K. Y. Wu and W. K. Leung, "Interleave-division multiple-

access," IEEE Trans. on Wireless Commun, pp. 938-947, April 2006.

5

Desired Features of a Good Up-link Scheme

• low receiver cost• de-centralized (i.e., asynchronous) control• simple treatment of ISI• cross-cell interference mitigation• diversity against fading• high power efficiency • high spectral efficiency• suitable for both wide or narrow band transmission• flexible rate adaptation• multi-user gain (detailed tomorrow).

A conventional method (such as TDMA, FDMA, CDMA etc) cannot provide all these features simultaneously. Is there a unified solution? Yes!

6

Problems with TDMA, FDMA and CDMATDMA and FDMA require centralized control and strict synchronization. They are not flexible in many situations. For example, it is quite difficult to synchronize an ad hoc network.

TDMA and FDMA are strictly sub-optimal in fading environments. In particular, TDMA and FDMA (and OFDMA) can be seriously inferior in MIMO channels. This is related to multi-user gain.

CDMA is flexible regarding synchronization. However, CDMA is a low-rate scheme by nature. It is difficult to provide high single-user throughput with CDMA.

7

Multi-User Gain (MUG)From information theory, allowing multiple users to transmit simultaneously can lead to significantly power reduction. This advantage is referred to as multi-user gain.

See:

Peng Wang, Jun Xiao, and Li Ping, "Comparison of orthogonal and non-orthogonal approaches to future wireless cellular systems," IEEE Vehicular Technology Magazine, vol. 1, no. 3, pp. 4-11, Sept. 2006.

8

Multi-User Gain in Fading ChannelsUp-link, sum-rate = 8 bits/chip, Pout = 0.01

about 12dB

channel capacity

9

An Example of Multi-User Gain

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

10

The Problem with CDMA

0

0.5

1

1.5

2

2.5

3

3.5

4

-2 0 2 4 6 8 10 12 14

Eb/N0 (dB)

Spec

tral e

ffic

ienc

y (b

its/c

hip)

Matched Filter

Optimal

xxx

Multi-user detection is necessary to get into this range.

11

Shannon showed in 1940’s that optimal communication systems can be built using randomly generated signals.

However, random coding has long been regarded as genius theoretical concept, rather than a practical method. The advent of turbo coding showed that Shannon’s is actually very “practical”, at least for binary error correction codes.

Turbo and LDPC codes have solved the problem for random binary code design. How about other applications?

It turns out that it is very easy to achieve random signaling in a multi-user environment.

What is an Optimal System

t

12

Here is an engineering approach to random coding based on interleaving

13

IDMA System Model

h1

hk

hK n

1d

kd

Kd

Transmitter for user-1

1ENC1

Transmitter for user-k

kENCk

Transmitter for user-K

. .

KENCK

......

∑=

+=K

kkkh

1nxr

x1

xk

xK

14

CDMA System Model

h1

hk

hK n

1d

kd

Kd

Transmitter for user-1

ENC1

Transmitter for user-1

ENCk

Transmitter for user-K

ENCK

. ... ..

∑=

+=K

kkkh

1nxr

x1

xk

xK

s1

sk

sK

15

Comparison of IDMA and CDMA

h1

hk

hK n

1d

kd

Kd

Transmitter for user-1

ENC1

Transmitter for user-1

ENCk

Transmitter for user-K

ENCK

.... ..

x1

xk

xK

π1

πk

πK

h1

hk

hK n

1d

kd

Kd

Transmitter for user-1

ENC1

Transmitter for user-1

ENCk

Transmitter for user-K

ENCK

.... ..

x1

xk

xK

s1

sk

sK

IDMA CDMAInterleaving in IDMA does not incur rate loss, but spreading in CDMA incurs rate loss.

16

A Factor Graph for a LDPC Code

17

A Factor Graph for a CDMA System

User 1 information bits

User 2 information bits

18

A Factor Graph for an IDMA SystemUser 1 information bits

User 2 information bits

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Outline

• Introduction • Iterative detection• Performance evaluation• Multi-user gain in fading channels• Other applications• Conclusions

20

The Iterative Principle

The optimal approach is to consider two constraints jointly.

A sub-optimal approach is to handle one constraint at a time using an iterative process.

User 1:

User 2:

coding constraintt

User 3:

ReceivedSignal:

superpositionconstraint

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IDMA System Model

h1

hk

hK n

1d

kd

Kd

user-1

ENC1

user-k

ENCk

user-K

ENCK

......

∑=

+=K

kkkh

1nxr

x1

xk

xK

s1

sk

sK

22

Message Passing at Channel NodesUser 1 information bits

User 2 information bits

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Gaussian Approximation Detection

Path model and Gaussian approximation

Estimation:

( ) ( )k k kh x j jζ+=

1( ) ( ) ( )

K

k kk

r j h x j n j=

= +∑

( )

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 j hx j j h r j j

r j j hx j jj

− ζ −−

= + ζ= ⋅ − ζ

− ζ += − ζ−

ζ

Gaussian

( ) ( )2( ) = ( ) E( ( ))Var( ( ))

kk k

k

he x j r j jj

⋅ − ζζ

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 h x jζ = −

( ) ( )1

E ( ) E ( )K

k kk

r j h x j=

=∑

( ) ( )2( ) ( ) E( ( ))Var( ( ))

kk k

k

he x j r j jj

= ⋅ − ζζ

( ) ( )2

1Var ( ) Var ( )

K

k kk

r j h x j=

=∑

( ) ( ) ( )2 ( )Var ( ) Var Var ( )k k kr jj h x jζ = −

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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A Factor Graph for an IDMA SystemUser 1 information bits

User 2 information bits

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Chip-by-Chip Multiuser Detection

Chip-by-ChipProcessing

… …

APP DEC-k

kπ

1−kπ

r={r(j)}…

APP DEC-1

1π

11−π

…

……

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Complexity

6 additions and 6 multiplications per chip per iteration per user.

Complexity (per user) is independent of user number K .

Comparison: To achieve good performance, the cost for MMSE CDMA multi-user detection is O(K2) due to matrix operations.

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Un-coded IDMA

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10 12 14 16 18 20 22 24

Average Eb/N0 (dB)

BER

8 users 64 users

single-user

Rate-1/8 repetition coding

29

Convolutional-Repetition Coded IDMA

(a)(b)

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10 12 14 16 18 20 22

Average Eb/N0 (dB)

BER

IDMA8 users

IDMA16 users

IDMA32 users

IDMA64 users

CDMA 6 usersmatched filter

capacities

Rate ½ and rate ¼ repetition coding. Overall rate =1/8.

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Outline

• Introduction • Iterative detection• Performance evaluation• Multi-user gain in fading channels• Other applications• Conclusions

31

The Basic Principle

The analysis of an iterative decoder or iterative multi-user detector is usually a difficult task. For example, for an iterative CDMA multi-user detector, the impact of spreading sequences are a complicated issue.

However, for IDMA, it is quite straightforward. This is because the operation is at the chip level. We detect a chip a time, which is very easy to analyze.

For Detail, seeLihai Liu, Jun Tong, and Li Ping, "Analysis and optimization of CDMA systems with chip-level interleavers," IEEE J. Select. Areas Commun., pp. 141-150, January 2006.

32

IDMA Performance Evaluation

)()()(

)()()(1

jnjxhpjxhp

jnjxhpjr

kiiiikkk

K

kkkk

+∑+=

+∑=

≠

=

( )∑≠

+=

ki

oldiiii

kknewk SNRfhp

hpSNR 2)(2

2)(

||||

σ

Gaussian

kSNR k ∀= ,0)0(

Received chip:

SNR evolution:

Initialization:

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SNR Evolution for an IDMA 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

34

SNR Evolution for an IDMA DecoderThe iterative detector can be characterized by the following SNRevolution process:

This is much simpler and faster than simulation.

2( )

2 ( ) 2

| || | ( )

new k kk old

i i i ii k

h pSNRh p f SNR σ

≠

=+∑

ESE

… …

f(·)1

kπ−

r={r(j)}

f(·)

… …

SNR1

SNRk

kπ

11π−

1πVariance1

Variancek

Evolutionprocess

Evolutionformula

35

IDMA Performance Evaluation

DECkSNRk

f(SNRk)

f-function of a rate R=1/2 ideal code

⎩⎨⎧

−<−≥

=12,112,0

)( 2

2

R

R

xx

xf

-20 -15 -10 -5 0 5 1010

-6

10-4

10-2

100

SNR (dB)

Var

ianc

e

36

Performance Evaluation

DECkSNRk

f(SNRk)

-20 -15 -10 -5 0 5 1010

-6

10-4

10-2

100

SNR (dB)

Var

ianc

e

f-function of a rate-1/2 convolutional code with generator: (23, 35)8

It can be obtained by the Monte-Carlo method

37

minimize

subject to performance requirement

where

with initial conditions

kSNR kL

k ∀Γ≥ ,)(

kSNRk ∀= ,0)0(

The Power Optimization Problem

∑k

kp

( ) LlkSNRfhphpSNR

ki

liiii

kklk L,2,1,,

||||

2)1(2

2)( =∀

+=∑≠

− σ

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 4 5 6 7 8 9 10 11 12user k

Power optimization results

38

Un-coded IDMA with Power Optimization

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 2 4 6 8 10 12 14 16 18 20 22 24

Average Eb/N0 (dB)

BER

8 users 64 users

single-user

Rate-1/8 repetition coding

Simulation software is available at my web site.

39

Outline

• Introduction • Iterative detection• Performance evaluation• Multi-user gain in fading channels• Other applications• Conclusions

40

Multi-User Gain in Fading Channels

1 2 3 4 5 6 7 815

20

25

30

35

The number of users K

Ave

rage

tran

smitt

ed p

ower

(dB

)

TDMA capacity

Capacity

Sum-rate = 8 bits/chip, Pout = 0.01

about 12dB

channel capacity

41

1 2 3 4 5 6 7 815

20

25

30

35

The number of users K

Ave

rage

tran

smitt

ed p

ower

(dB

)

TDMA capacity

Capacity

IDMA, Convolutional coding

TDMA, Assumed performance

Sum-rate = 8 bits/chip, Pout = 0.01

about 12dB

about 12dB

Simulated IDMA

Simulated TDMA

channel capacity

Multi-User Gain in Fading Channels

42

IDMA-OFDM

Basic Principle:

• Randomly distribute information on the sub-carriers on frequency- time.

• Multi-layer structure using superposition coding.• Iterative detection.

This is proposed by Zhou et al and by Mahafeno et al. It has been considered as an option in 3GPP LTE.

IDMA IFFT FFT CBCchannel

43

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

44

Outline

• Introduction • Iterative detection• Performance evaluation• Multi-user gain in fading channels• Other applications• Conclusions

45

Extensions of IDMA Principles

As we have seen, IDMA is an engineering approach to realizing random signaling. This same principle is not limited to multiple-access. It can be extended to many other applications, such as

- coded modulation for high throughput single user transmission,- space-time coding,- relay and adhoc transmission,- MIMO

We will briefly explain these applications below.

46

IDMA

h1

hk

hK n

1d

kd

Kd

user-1

1ENC1

user-k

kENCk

user-K

. .

KENCK

......

∑=

+=K

kkkh

1nxr

x1

xk

xK

47

Superposition Coded Modulation (SCM)

1

K

k kk

h=

= ∑y x

layer-1

ENC1

layer-k

ENCk

layer-K

.

KENCK

......

x1

xk

xKK

K K

K K

dS/P

All the resources are given to a single user for high throughput.

48

Comparison between SCM and BICM

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.

49

IDM Space-Time Coding

Antenna 1

Antenna m

Antenna M

layer-1

ENC1

layer-k

ENCk

layer-K

.ENCK

. ... ..

x1

xk

xK

dS/P

π1

πk

πK

ρ1

ρk

ρK

S/P

S/P

S/P

......

50

IDM Space-Time Coding Performance

1.E-04

1.E-03

1.E-02

1.E-01

10 15 20 25 30E b /N 0 (dB)

FER

IDM-ST Codes

Outage capacity

4x1

2x1

Overall rate = 4 bits/symbol

51

Application in Relay Networks

sourcedestination

in the above relay network scenario, we can apply space-time coding across multiple relay nodes for space-time diversity. The synchronization requirement makes it difficult for such a schemebased on a conventional space-time code, because we have to coordinate different nodes and the number of active node may vary. For a IDM space-time code, it is quite straightforward.

52

Application in Ad Hoc NetworksAnother interesting application is proposed by S. M. Perlaza in his MSc thesis (Eurocom) “Decentralized Power Allocation in Interleaving Division Multiple Access (IDMA) Networks.”

Perlaza shows that the effect of delay on an interleaved signal is similar to different interleaving. Thus one interleaver can be used for the entire network. This is a very interesting concept for user separation in adhok networks.

delay by t1delay by t2

delay by t3

delay by t1

delay by t2

delay by t3

53

Application in Ad Hoc NetworksAnother interesting application is proposed by S. M. Perlaza in his MSc thesis (Eurocom) “Decentralized Power Allocation in Interleaving Division Multiple Access (IDMA) Networks.”

Perlaza shows that the effect of delay on an interleaved signal is similar to different interleaving. Thus one interleaver can be used for the entire network. This is a very interesting concept for user separation in adhok networks.

delay by t1delay by t2

delay by t3

delay by t1

delay by t2

delay by t3

54

Multi-user SIMO with IDMA.

Application in Multi-user MIMO Systems

Single user MIMO.

55R (bits/symbol)

MSP

(dB

)

0 1 2 3 4 5 6 7 8

-5

0

5

10

15

20

25

Rate

AveragePower

1×4 single user 4 ×4 single user

4 ×4 multi-user

Comparisons

1 ×4 multi user

56

Conclusions: Features of IDMA

• low receiver cost• de-centralized (i.e., asynchronous) control,• simple treatment of ISI,• cross-cell interference mitigation,• diversity against fading,• power efficiency • easy for adaptive rate control• high user number and high spectral efficiency• suitable for wide or narrow band transmission