turbo equalization: fundamentals, information …...turbo equalization: fundamentals, information...

Japan Advanced Institute of Science and Technology

JAIST Repositoryhttps://dspace.jaist.ac.jp/

TitleTurbo Equalization: Fundamentals, Information

Theoretic Considerations, and Extensions

Author(s) Matsumoto, Tad; Anwar, Khoirul; Ahmad, Norulhusna

CitationA Tutorial on the 75th IEEE Vehicular Technology

Conference (VTC-Spring 2012)

Issue Date 2012-05-06

Type Presentation

Text version author

URL http://hdl.handle.net/10119/10523

Rights

Copyright © 2012 Authors. Tad Matsumoto, Khoirul

Anwar and Norulhusna Ahmad, Turbo Equalization:

Fundamentals, Information Theoretic

Considerations, and Extensions, A Tutorial on the

75th IEEE Vehicular Technology Conference (VTC-

Spring 2012), Tutorial Handout ; Place :

Yokohama, Japan ; Date : 6 - 9 May, 2012.

Description

IEEE Vehicular Technology Conference （電気電子学

会移動体技術国際学会）VTC 2012-SpringでのTutorial

Handout

Turbo Equalization: Fundamentals, InformationTheoretic Considerations, and Extensions

A Tutorial on IEEE VTC-Spring 2012

Tad Matsumoto, Khoirul Anwar and Norulhusna Ahmad

Information Theory and Signal Processing Lab., School of Information Science,Japan Advanced Institute of Science and Technology (JAIST),

1-1 Asahidai, Nomi, Ishikawa, 923-1211 JAPAN,E-mail: {matumoto,anwar-k}@jaist.ac.jp

Yokohama, 6 May 2012

(IEEE VTC-Spring 2012) Tutorial on Turbo Equalizations 1 / 40

Part IIChained Turbo Equalization (CHATUE) for Block

Transmission without Guard Interval- Application to Uplink SC-FDMA -

Khoirul Anwar

Japan Advanced Institute of Science and Technology (JAIST)e-mail: [email protected]

1-1 Asahidai, Nomi-shi, Ishikawa, 923-1292, JAPANhttp://www.jaist.ac.jp/is/labs/matsumoto-lab


Outline of Presentation

1 Motivations2 Basic Principle

1 System Model2 The Concept of CHATUE Algorithm3 Performance Evaluation

3 Applications1 Uplink SC-FDMA2 Mathematical Formulation3 Performance Evaluation

4 Conclusions


General Problem of Wireless Communications

+ noiseRx=

Tx=

+

TimeL

Symbol Duration T

1G

First path

Last Path

2G

3G

<<T No inter-symbol interference (ISI)

T only minor ISI >>T Severe ISI

“0” “1” “1” “0”

“0” “1” “1” “0”

“0” “1” “1” “0”

“0” “1” “1” “0”


Motivation

Conventional:

Block 1 Block 2 Block 3GI GI

Proposed

Length of desired

current block

Interference

from the futureInterference

from the past

Block 1 Block 2 Block 3

Saving the Time:

Advantage of CP removal

Normal Guard Interval (GI) (cyclic prefix): 4.69 µs ( Cover 1.4km )

LTE-Advanced SC-FDMA symbol length= 66.7 µs

Data rate loss 4.69/66.7=7.03%

GSM: 3.69 µs

W-CDMA : 0.69 µs


The Standard Technique

Fourier

Transform

TimeFrequencyL

Rx:

Tx:

H

Rx:

Tx:

H

CP CP

CP CP

CP

CP

CP

CP

Desired

K

Desired

K

Desired

K

Desired

K

Desired

K

Desired

K

CP: Cyclic Pre x

L L


The Benefit of Guard Interval Removal

With Guard Interval:

K KLL

Desired

K

Desired

K

Rate Loss: YESSN

= Eb

N0·R · K

(K+L) ·M

Power Loss: YESR = S

N· N0

Eb· (K+L)

K· 1M

Without Guard Interval:

K K

Desired

K

Desired

K

Rate Loss: NOSN

= Eb

N0·R · K

(K+0) ·M

Power Loss: NOR = S

N· N0

Eb· (K+0)

K· 1M

Notation:SN: Signal-to-Noise Power Ratio, R: Coding rate, Eb

N0: Energy bit per

noise, M : Number of bits per symbol, K: Block length, L: GI length


CHATUE Algorithm: The Basic Principle

Khoirul Anwar

E-mail: [email protected]


References (Suggested for Further Reading):

1 K. Anwar, H. Zhou, and T. Matsumoto, ”Chained Turbo Equalizationfor Block Transmission without Guard Interval”, 2010 IEEE 71stVehicular Technology Conference (VTC 2010-Spring), pp.1-5, May2010, Taiwan.

2 K. Anwar and T. Matsumoto, ”Low Complexity Time-ConcatenatedTurbo Equalization for Block Transmission without Guard Interval:Part 1– The Concept”, Wireless Pers. Commun., Springer, DOI:10.1007/s11277-012-0563-0 (Online: 24 March 2012).

3 K. Kansanen and T. Matsumoto, ”An Analytical Method for MMSEMIMO Turbo Equalizer EXIT Chart Computation”, IEEE Transaction

on Wireless Communications, Vol. 6, No. 1, pp. 59–63.


System Models

C Mod

+

!"

-

D-ACC-1

P

D-ACC

BCJR

st = [s[0]t , s

[1]t , · · · , s

[k]t · · · s

[K−1]t ]T ∈ C

K×1. (1)

yt = Htst +H′t−1s′t−1 +H′′t+1s

′′t+1 + n ∈ C

(K+L−1)×1, (2)

Block 1 Block 2 Block 3

�me

Length of detected

Block 2

Interference

from the past

Interference

from the future

K KK


Channel Model

Ht=

h[0]0 0... h

[1]0

h[0]L−1

.... . .

h[1]L−1

... h[K−1]0

. . ....

0 h[K−1]L−1

∈ C(K+L−1)×K , (3)

H′t−1=

h[K−L+1]L−1 · · · h

[K−1]1

. . ....

h[K−1]L−1

0

, H′′t+1=

0

h[0]0...

. . .

h[0]L−2 · · · h

[L−2]0


Avoiding the Confusion on the Channel Models

time

Length of desired

current blockInterference

from the past block

Interference

from the future block

K KK

Ht−1 : A Past channel matrixH′t−1 : A Past channel matrix with the past formH′′t−1 : A Past channel matrix with the future formHt : A Current channel matrixH′t : A Current channel matrix with the past formH′′t : A Current channel matrix with the future form


Channel Model: Examples

Given the channel responses of the past, the current, and the futureblocks, respectively, as

ht−1 = [1, 0.7],ht = [1, 0.5],ht+1 = [1, 0.3],

and block length K = 4, write the channels of:

1 H′t−12 H′′t

3 H′′t+1

4 H′t


Solution by the CHATUE Algorithm

E1&D1 E2&D2 E3&D3

La,E1 Lp,D1=La,E2

La,E1=Lp,D2 La,E3

Lp,D2=La,E3

La,E2=Lp,D3

EQ’

EQ

EQ’’

C-1’

C-1

C-1’’y’’

y

y’

FD SC/MMSE DecoderBlock 1 Block 2 Block 3

me

Length of detected

Block 2

Interference

from the past

Interference

from the future

K KK

m

e

Chained Equaliza on

With GI Without GI

1 2

1 [1] K. Anwar, Z. Hui, and T. Matsumoto, ”Chained Turbo Equalization for Block Transmission without GuardInterval”, in IEEE VTC-Spring 2010, Taiwan, May 2010.2 [2] K. Anwar and T. Matsumoto, ”Low-complexity Time-concatenated Turbo Equalization for Block Transmission:Part 1 – The Concept”, Wireless Personal Comm., Springer, March 2012 (DOI 10.1007/s11277-012-0563-0).


Two Key Principles

1 Retrieval of Circularity: Matrix J

J =

0(K−L+1)×(L−1) IK×KI(L−1)×(L−1)

∈ CK×(K+L−1) (4)

2 ISI and IBI Removal: Modified FD/SC-MMSE

Example of Matrix J with L = 3,K = 3 and ht = [h0, h1, h2]

J =

0 0 1 0 01 0 0 1 00 1 0 0 1

, JHt =

h2 h1 h0h0 h2 h1h1 h0 h2

(5)


Modified SC-MMSE for CHATUE: ISI and IBI Removal

H Est.

wMMSE

LLRH’ Est.H’’ Est.

Channel

Decoder -1

tanh(*/2)tanh(*/2)

input-

+

+

-

La

Future

Block

Past

Block

So Es!ma!on

MMSE Filter

tanh(*/2)

FFT

La’La”

IFFTJ J J

FFT

La;D

Le;D


Soft Canceller MMSE for Chained Equalization

J

n

s0; s; s00

H0; H;H00

yr

ø N(0; û2)

Receive signal

yt = Htst +H′t−1s′t−1 +H′′t+1s

′′t+1 + n (6)

Restore the circularity of the channel

rt = Jy,

= JHtst+JH′t−1s

′t−1+JH

′′t+1s

′′t+1+Jn (7)

Soft Replica

rt = JHtst + JH′t−1s′t−1 + JH′′t+1s

′′t+1 (8)

Cancellation rt = rt − rt. To simplify the expression, subscribe notation t may be removed.)

Minimize the error:

w(k) = arg minw(k)H

|w(k)H [r + h(k)s(k)]− s(k)|2 (9)

with h(k) is the k-th column of matrix JH.(IEEE VTC-Spring 2012) Tutorial on Turbo Equalizations 17 / 40

Modified SC-MMSE for CHATUE: Time Domain

The Wiener-Hopft Solution

E

[

∂|w(k)H [r + h(k)s(k)]− s(k)|2

∂w(k)H

]

= 0 (10)

MMSE Weight

w(k) =(

E[rrH + h(k)|s(k)|2h(k)H)−1

h(k),

=(

JHΛHHJH + JH′Λ′H′HJH + JH′′Λ′′H′′HJH

σ2JJH + h(k)|s(k)|2h(k)H)−1

h(k),

=(

Σ+ h(k)|s(k)|2h(k)H)−1

h(k) (11)

where

Λ = diag(

1− |s(0)|2, 1− |s(1)|2, · · · , 1− |s(K − 1)|2)

, (12)

Λ′ = diag(

0, · · · , 0, 1− |s(L− 1)|2, · · · , 1− |s(−1)|2)

, (13)

Λ′′ = diag(

1− |s(K)|2, · · · , 1− |s(K + L− 1)|2, 0, · · · , 0)

(14)


Output of CHATUE SC/MMSE

w(k)H = h(k)H[

Σ+ h(k)|s(k)|2h(k)H]−1

,

(a)=

(

1 + γ(k)|s(k)|2)−1

h(k)HΣ−1 (15)

Therefore, time domain final output:

z(k) =(

1 + γ(k)|s(k)|2)−1

h(k)HΣ−1 (r(k) + h(k)s(k)) (16)

By performing block-wise processing, symbol wise inversion is not required:

z = (IK + ΓS)−1(

Γs+HHJHΣr)

, (17)

S = diag[

|s|2]

, (18)

Γ = diag[

HHJH(

JHΛ(JH)H + JH′Λ′(JH′)H

+JH′′Λ′′(JH′′)H + σ2JJH)−1

JH]

(19)

Note: (a). γ(k) = h(k)HΣ−1h(k)(IEEE VTC-Spring 2012) Tutorial on Turbo Equalizations 19 / 40

Output of Block-Wise Processing CHATUE

Σ = JHΛHHJH + JH′Λ′H′HJH + JH′′Λ′′H′′HJH , (20)

Γ = diag[

HHJHΣ−1JH]

, (21)

S = diag(|s|2) (22)

Lemma: JH = FHΦF→ HHJH = FHΦF

Σ = FHΦFΛFHΦHF+ JH′Λ′H′HJH + JH′′Λ′′H′′HJH , (23)

Γ = diag[

FHΦHFΣ−1FHΦF] (a)= diag

[

FHΦHX−1ΦF]

(24)

Finally, output of z:

z = [IK + Γs]−1[

Γs+HHJHΣ−1r]

,

(b)= [IK + Γs]−1

[

Γs+ FHΦHX−1Fr]

(25)

Note: (a). X = FΣFH , (b). X−1 still require simplification.(IEEE VTC-Spring 2012) Tutorial on Turbo Equalizations 20 / 40

Approximation to Diagonal

IJJIJHJHIJHJHXH

K

HH

K

HH

K

H )tr()''''''tr()'''tr( 2111 σ+Λ+Λ+ΦΛΦ≈

HHHHHHHHHHFJJFFJHFJHFJHFJHFFX

2''''''''' σ+Λ+Λ+ΦΛΦ=

Index of P ast S ymbols

Ind

ex

of

Pa

st

Sym

bo

ls

10 20 30 40 50 60

10

20

30

40

50

60

Index of F uture S ymbols

Ind

ex

of

Fu

ture

Sym

bo

ls

10 20 30 40 50 60

10

20

30

40

50

60

Index of noise samples

Ind

ex

of

no

ise

sa

mp

les

10 20 30 40 50 60

10

20

30

40

50

60

Index of C urrent S ymbols

Ind

ex

of

Cu

rre

nt

Sym

bo

ls

10 20 30 40 50 60

10

20

30

40

50

60

Index of P ast S ymbols

Ind

ex

of

Pa

st

Sym

bo

ls

10 20 30 40 50 60

10

20

30

40

50

60

Index of F uture S ymbols

Ind

ex

of

Fu

ture

Sym

bo

ls

10 20 30 40 50 60

10

20

30

40

50

60

Index of noise samples

Ind

ex

of

no

ise

sa

mp

les

10 20 30 40 50 60

10

20

30

40

50

60

Index of C urrent S ymbols

Ind

ex

of

Cu

rre

nt

Sym

bo

ls

10 20 30 40 50 60

10

20

30

40

50

60

Note: The mutual information (MI) of the past, the current, and thefuture blocks are I ′a,Et

= Ia,Et= I ′′a,Et

= 0.5.


Extrinsic LLR Formulation

zt can be expressed as being equivalent to a Gaussian channel output as,

zt = µtst + vt ∈ CK×1 (26)

µt = E[zt · s∗t ] =

1

Ktr{Γ(IK + ΓSt)

−1}, (27)

where vt is the equivalent noise vector with variance beingσ2t = µt(1− µt). In (27), we used the approximation,

St = diag{|st|2} ≈

1

K

K∑

k=1

|s[k]t |

2 · IK ∈ CK×K . (28)

Finally, the extrinsic LLR of the transmitted binary symbol is

Le,Et[s

[k]t ] = ln

Pr(z[k]t |s

[k]t = +1)

Pr(z[k]t |s

[k]t = −1)

=4ℜ(z

[k]t )

1− µt

, (29)

with z[k]t being the k-th component of zt and ℜ(z

[k]t ) denoting the real

part of the complex z[k]t .


EXIT Chart Analysis

Eb/N0 = 4 dB

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

A

B

64-path Rayleigh Fading

BPSK, FFT: 512, GI: 0

Interleaver: 512

Eb/N0=4dB, Without ACC

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


BPSK, FFT: 512, GI: 0

Interleaver: 512

Eb/N0 = 4dB, With ACC P = 1:8

Note: EXIT analysis of the CHATUE Algorithm without and with dopedaccumulator (D-ACC) with P = 8.


The Advantage of GI/CP Removal

0 1 2 3 4 5 6 7 8 9 1010

-5

10-4

10- 3

10-2

10-1

100

Eb/N0(dB)

Avera

ge B

ER

R=2/3,

CP:25%

R=1/2,

CHATUE


BPSK, K=256

Interleaver: 256, CC-3[7,5]

Truncation Length = 1 block

Note: The total power (over all path) is∑L−1

ℓ=0 |hℓ|2 = 1. The block

length is kept by KCHATUE = KSCCP + L with advantage ofN

RCHATUE= NRSCCP

+ 1.


BER Performances

1 2 3 4 5 6 7 8 9 1010

-5

10-4

10-3

10-2

10-1

100

Eb /N0[dB]

Avera

ge B

ER


BPSK, K = 512, GI: 0

Interleaver: 512, CC-3[7,5]

Lower Bound:

Coded, AWGN,

K=512, GI=0

Truncation Length = 3 Blocks,

1 2 3 4 5 6 7 8 9 1010

-5

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

Avera

ge B

ER


BPSK, K = 512, GI: 0

ACC P=8, Interleaver: 512, CC-3[7,5]

Truncation: 1 Block

Truncation Length = 3 Blocks,

Note: BER performances of the CHATUE Algorithm without and withdoped accumulator (D-ACC) with P = 8.


How to Solve the Channel Variation?

hö`

H

hℓ =1K

∑K−1k=0 h

[k]ℓ ,

Ht =

h[0]0 0... h

[1]0

h[0]L−1

.... . .

h[1]L−1

... h[K−1]0

. . ....

0 h[K−1]L−1

t

≈

h0 0... h0

hL−1...

. . .

hL−1... h0. . .

...0 hL−1

t

= Ht ∈ C(K+L−1)×K


Performances Evaluation

10-5

10-4

10-3

10-2

10-1

100

Av

erage

BE

R

w/o ACC (Lower Bound)

w/o ACC (Truncation)

w/ ACC (Lower Bound)

w/ ACC (Truncation)

10.10.010.0010.00010.000010.000001

Eb/N0= 6 dB

Eb/N0= 4 dB

Truncation Length = 3 Blocks

Lower Bound:

fdTs

Block length, K = 512

Ia;E = I0

a;E= I

00

a;E= 1

Normalized Doppler Spread ( ) over single carrier symbol duration

In general, broadband communication (e.g. 4G) is sensitive toDoppler shift.

Highway speed: 100 km/h at 3.5 GHz (WiMAX)→ fdTs = 0.00162/512 = 0.0000031


CHATUE Algorithm: Application to

SC-FDMA Systems

Khoirul Anwar

E-mail: [email protected]


References (Suggested for Further Reading):

1 H. Zhou, K. Anwar, and T. Matsumoto, ”Chained Turbo Equalizationfor SC-FDMA Systems without Cyclic Prefix”, IEEE Globecom 2010

Workshop on Broadband Single Carrier and Frequency Domain

Communications, pp.1318-1322, Dec. 2010, USA.

2 H. Zhou, K. Anwar, and T. Matsumoto, ”Low ComplexityTime-Concatenated Turbo Equalization for Block Transmissionwithout Guard Interval: Part 2 – Application to SC-FDMA,” Wireless

Personal Communications, Springer, Sept. 2011 (DOI:10.1007/s11277-011-0409-1).


Application to (4G) Uplink SC-FDMA without GI

Ref.: H. Zhou, K. Anwar and T. Matsumoto, ”Low Complexity

Time-Concatenated Turbo Equalization for Block Transmission without Guard

Interval: Part 2. Application to SC-FDMA”, Wireless Personal Commun.,

Springer, DOI 10.1007/s11277-011-0409-1, Pub. online: 25 Sept. 2011.


SC-FDMA: A Review

K-D

FT

Source S/PSubcarrier

Mapping P/S ChannelHi

M-ID

FT

i-th User

User 1

User 2

User i Base Sta�on

Subcarrier Alloca�on:

Localized Distributed: User 1

: User 2

: User 3

SM


SC-FDMA: System Model

Subcar.De-Mapping/

CHATUE SC-FDMA J

Channel

H

Past LLR

Future LLR

Sub

Map.Mod

+-

+

--

Sub.

Map.

User i

-

J

P

Doped Accumulator

n

The received composite signal is

rt =I

∑

i=1

ri,t + Jn, (30)

where

ri,t=JHi,tFHMDiFKsi,t+JH

′

i,t−1FHMDiFKs

′

i,t−1+JH′′

i,t+1FHMDiFKs

′′

i,t+1


Matrix D for Subcarrier Allocations: Example

Di is a M ×K matrix for the i-th user, by which, the κ-th sub-carriercomponent of the K-point Discrete Fourier Transform (DFT) is mappedto the m-th sub-carrier of the M -point DFT, where 0 ≤ κ ≤ K − 1, and0 ≤ m ≤M − 1.For localized sub-carrier mapping,

Di =

{

1, m = Ru ·K + κ

0, otherwise(31)

and for distributed sub-carrier mapping,

Di =

{

1, m = Ru + MK· κ

0, otherwise(32)

with Ru indicating the resource unit allocation, which is subjected to0 ≤ Ru ≤

MK− 1.


Soft Cancellation in CHATUE-SC-FDMA

J

n Soft Cancellation rt = rt − rtSoft Replica

rt =I

∑

i=1

JHi,tFHMDiFK si,t +

I∑

i=1

JH′i,t−1FHMDiFK s

′i,t−1

+I

∑

i=1

JH′′i,t+1FHMDiFK s

′′i,t+1 (33)

Soft Symbol Estimates

si,t(k) = E[si,t(k)|Le,C−1i

] = tanh{Le,C−1

i[si,t(k)]/2}, (34)

s′i,t−1(k) = E[s′i,t−1(k)|L′p,C−1

i,t−1

] = tanh{L′p,C−1

i,t−1

[s′i,t−1(k)]/2}, (35)

s′′i,t+1(k) = E[s′′i,t+1(k)|L′′p,C−1

i,t+1

] = tanh{L′′p,C−1

i,t+1

[s′′i,t+1(k)]/2}. (36)


CHATUE-SC-FDMA Output

zi,t = (Ik + Γi,tSi,t)−1[Γi,tsi,t + FH

KΦHi,tFKΣ

−1i,t ri,t]

= (Ik + Γi,tSi,t)−1[Γi,tsi,t + FH

KΦHi,tX

−1FK ri,t] ∈ CK×1, (37)

where the Γi,t can be expressed as

Γi,t = diag[HHi,tΣi,t

−1Hi,t]

= diag[FHKΦ

Hi,tFKΣi,t

−1FHKΦi,tFK ]

= diag[FHKΦ

Hi,tX

−1Φi,tFK ] ∈ CK×K (38)

with X being the frequency domain covariance matrices given by

X = FKΣi,tFKH = Φi,tFKΛi,tF

HKΦ

Hi,t+FKσ2

iDTi JJ

HDiFHK

+FKH′i,t−1Λ

′i,t−1H

′Hi,t−1F

HK

+FKH′′i,t+1Λ

′′i,t+1H

′′Hi,t+1F

HK ∈ C

K×K (39)

and σ2i = K

Mσ2n for the i-th user.


Approximation for Computational Complexity Reduction

Based on FΛFH ≈ 1Ktr[Λ]IK , we can perform:

X ≈ Φi,tΛi,tΦHi,t+ diag(FKσ2

iDTi JJ

HDiFHK + FKH

′

i,t−1Λ′

i,t−1H′Hi,t−1F

HK

+FKH′′

i,t+1Λ′′

i,t+1H′′Hi,t+1F

HK)

≈ Φi,tΛi,tΦHi,t+

1

Ktr

[

σ2iD

Ti JJ

HDi+H′

i,t−1Λ′

i,t−1H′Hi,t−1+H

′′

i,t+1Λ′′

i,t+1H′′Hi,t+1

]

IK

(40)Residual IBI from past and future NoiseICI

50 100 150 200 250

50

100

150

200

250

0

050 100 150 200 250

50

100

150

200

250

0

050 100 150 200 250

50

100

150

200

250

0

0


EXIT Chart Analysis for CHATUE-SC-FDMA

Eb/N0 = 5 dB

Q

P

IA-E, IE-D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Decoder (conv. constraint length 3, rate ½ code)

Equalizer, when MI from Past/Future = 0


Trajectory

Block Length, M=512

Path Length, L=64

Eb=N0 = 5 dB

IE-E

, IA

-D

IA-E,IE-D

Decoder (R=3/5 (punctured) , const. length =3)



Trajectory

Q

P

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Block Length, M=512

Multi-path Length, L=64

Eb=N0 = 5 dB

IE-E

,IA

-D

Note: EXIT analysis of the CHATUE Algorithm without and with dopedaccumulator (D-ACC) of foping rate P = 8.


BER Performances of CHATUE-SC-FDMA: User 1

Block Length, M = 512

CP Length = Multi-path L = 64

Conv. Code: Memory 2

G = [7, 5]8

0 1 2 3 4 5 6 7 8 9

Iter.1

AWGN (Coded)

Iter.5, Conv. CP.

Iter.2

Iter.5, CHATUE

Av

erag

e B

ER

Iter.0

10-5

10-4

10-3

10-2

10-1

100

Eb/N0

(dB) for user 1 Eb/N0 (dB) for user 1

Av

erag

e B

ER

Iter.1

MI past/future = 1

Iter.2

0 1 2 3 4 5 6 7 8 9 10

Block Length, M=512

CP Length = Multi-path L=64

Conv. Code: Memory 2,

G=[7, 5]8

Iter.5, Conv. CP-Trans.

Iter.5, CHATUE (DA)

10-5

10-4

10-3

10-2

10-1

100

Iter.0

Note: BER performances of the CHATUE Algorithm without and withdoped accumulator (D-ACC) with P = 8.


CHATUE-SC-FDMA: Performance of Multiple Users

0 10 20 30 40 50 6010

-6

10-5

10-4

10-3

10-2

10-1

100

Number of Users

CHATUE-SC-FDMA (Orthogonal sub-carrier

allocation in one frame)

Over-Frame CHATUE-SC-FDMA

Block Length, M = 512

Multi-path L = 64

Conv. Code: Memory 2

Iteration = 5

G = [7, 5]8

Eb=N0 = 6 dB

Av

erag

e B

ER

/U

ser

It is found that the BER performance is not significantly affected, even when the

512 sub-carriers are shared by 64 users.


Conclusions

GI causes power loss or total rate-loss with a factor of K/(K + L).

CHATUE Algorithm can excellently improve the performance oftransmission without GI with low computational complexity (it is alsoapplicable for system with insufficient GI).

Better performance (ICI, ISI, IBI Removal) can be achieved asdemonstrated by: BER performance & Trajectory Analysis of theEXIT chart

Further Advantages: (1) Lower Code Rate, (2) Turbo Cliff, (3)Multi-User Systems, (4) Uplink 4G SC-FDMA

Using the CHATUE Algorithm for SC-FDMA, the next generation 4Gsystems is possible without cyclic prefix/guard interval.

A comparison of CHATUE SC-FDMA with the conventionalSC-FDMA with GI/CP-Transmission verifies that the performance isalmost similar, but CHATUE SC-FDMA has a better spectralefficiency by eliminating the necessity of the GI/CP transmission.


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