JAIST Repository: Turbo Equalization: Fundamentals, Information Theoretic Considerations, and Extensions

(1)

Japan Advanced Institute of Science and Technology

JAIST Repository

https://dspace.jaist.ac.jp/

Title Turbo Equalization: Fundamentals, Information Theoretic Considerations, and Extensions

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

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

(2)

Turbo Equalization: Fundamentals, Information

Theoretic 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

(3)

Part II

Chained Turbo Equalization (CHATUE) for Block

Transmission without Guard Interval

Application to Uplink SCFDMA

-Khoirul Anwar

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

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

(4)

Outline of Presentation

1

Motivations

2

Basic Principle

1

System Model

2

The Concept of CHATUE Algorithm

3

Performance Evaluation

3

Applications

1

Uplink SC-FDMA

2

Mathematical Formulation

3

Performance Evaluation

4

Conclusions

(5)

General Problem of Wireless Communications

+ noise Rx= Tx= + Time L Symbol Duration T 䍃䍃䍃䍃䍃䍃 1G 䍃䍃䍃䍃䍃䍃 First path Last Path 2G 䍃䍃䍃䍃 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”

(6)

Motivation

Conventional:

Block 1 GI Block 2 GI Block 3

Proposed

Length of desired current block

Interference from the future Interference

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

(7)

The Standard Technique

Fourier Transform Time Frequency L 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

(8)

The Benefit of Guard Interval Removal

With Guard Interval:

K L K L Desired K Desired K

Rate Loss: YES

S N = E_b N0 · R · K (K+L) · M

Power Loss: YES

R = _NS · N0 E_b · (K+L) K · 1 M

Without Guard Interval:

K K Desired K Desired K Rate Loss: NO S N = E_b N0 · R · K (K+0) · M Power Loss: NO R = _NS · N0 E_b · (K+0) K · 1 M Notation: S

N : Signal-to-Noise Power Ratio, R: Coding rate,

E_b

N0: Energy bit per

(9)

CHATUE Algorithm: The Basic Principle

Khoirul Anwar

(10)

References (Suggested for Further Reading):

1 K. Anwar, H. Zhou, and T. Matsumoto, ”Chained Turbo Equalization

for Block Transmission without Guard Interval”, 2010 IEEE 71st Vehicular Technology Conference (VTC 2010-Spring), pp.1-5, May 2010, Taiwan.

2 K. Anwar and T. Matsumoto, ”Low Complexity Time-Concatenated

Turbo 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 MMSE

MIMO Turbo Equalizer EXIT Chart Computation”, IEEE Transaction

(11)

System Models

C Mod + !" -D-ACC-1 P D-ACC BCJR s_t = [s[0]_t , s[1]_t , · · · , s_t[k] · · · s[K−1]_t ]T ∈ CK×1. (1) y_t = 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

(12)

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        

(13)

Avoiding the Confusion on the Channel Models

time

Length of desired current block Interference

from the past block

Interference

from the future block

K K K

H_t−1 : A Past channel matrix

H′_t₋₁ : A Past channel matrix with the past form

H′′_t₋₁ : A Past channel matrix with the future form

H_t : A Current channel matrix

H′_t _{: A Current channel matrix with the past form}

(14)

Channel Model: Examples

Given the channel responses of the past, the current, and the future blocks, 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−1 2 H′′ t 3 H′′ t+1 4 H′ t

(15)

Solution by the CHATUE Algorithm

E1&D1 E2&D2 E3&D3

L_a,E1 L_p,D1=L_a,E2 L_a,E1=L_p,D2 L_a,E3 L_p,D2=L_a,E3 L_a,E2=L_p,D3 EQ’ EQ EQ’’ C-1_’ C-1 C-1_’’ y’’ y y’ FD SC/MMSE Decoder Block 1 Block 2 Block 3

me

Length of detected Block 2 Interference

from the past

Interference from the future

K K K 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 Guard} Interval”, 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).

(16)

Two Key Principles

1 Retrieval of Circularity: Matrix J

J =   0_{(K−L+1)×(L−1)} I_K_×K I_{(L−1)×(L−1)}   ∈ C K×(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 0 1 0 0 1 0 0 1 0 0 1   , JHt =   h₂ h₁ h₀ h0 h2 h1 h₁ h₀ h₂   (5)

(17)

Modified SC-MMSE for CHATUE: ISI and IBI Removal

H Est.

w

_MMSE LLR H’ 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” IFFT J J J FFT L_a;D L_e;D

(18)

Soft Canceller MMSE for Chained Equalization

J n s0_{; s; s}00 H0; H; H00 y r ø N(0; û2) Receive signal y_t = Htst + H′_t₋₁s_t′₋₁ + H′′_t₊₁s′′_t₊₁ + n (6)

Restore the circularity of the channel

r_t = Jy,

= JHtst+JH′_t₋₁s_t′₋₁+JH′′_t₊₁s′′_t₊₁+Jn (7)

Soft Replica

ˆrt = JHtˆst + JH′_t₋₁ˆs′_t₋₁ + JH′′_t₊₁ˆs′′_t₊₁ (8)

Cancellation ˜rt = rt − ˆrt. To simplify the expression, subscribe notation t may be removed.) Minimize the error:

w(k) = arg min

w(k)H |w(k)

H

(19)

Modified SC-MMSE for CHATUE: Time Domain

The Wiener-Hopft Solution

E ∂|w(k) H_[˜_{r + h(k)ˆ}_{s(k)] − s(k)|}2 ∂w(k)H = 0 (10) MMSE Weight w(k) = E[˜r˜rH + h(k)|ˆs(k)|2h(k)H−1 h(k), = JHΛHHJH + JH′Λ′H′HJH + JH′′Λ′′H′′HJH σ2JJH + h(k)|ˆs(k)|2h(k)H−1 h(k), = Σ + h(k)|ˆs(k)|2h(k)H−1 h(k) (11) where Λ = diag 1 − |ˆs(0)|2, 1 − |ˆs(1)|2, · · · , 1 − |ˆs(K − 1)|2 , (12) Λ′ _{= diag} _{0, · · · , 0}_{, 1 − |ˆs(L − 1)|}2_{, · · · , 1 − |ˆs(−1)|}2 , ₍₁₃₎ Λ′′ = diag 1 − |ˆs(K)|2, · · · , 1 − |ˆs(K + L − 1)|2, 0, · · · , 0 (14)

(20)

Output of CHATUE SC/MMSE

w(k)H = h(k)H Σ + h(k)|ˆs(k)|2h(k)H−1 ,

(a)

= 1 + γ(k)|ˆs(k)|2−1 h(k)HΣ−1 (15)

Therefore, time domain final output:

z(k) = 1 + γ(k)|ˆs(k)|2−1 h(k)HΣ−1 (˜r(k) + h(k)ˆs(k)) (16)

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

z = (IK + ΓS)−1 Γˆs + HHJHΣ˜r , (17)

S = diag |ˆs|2 , (18)

Γ = diag HHJH JHΛ(JH)H + JH′Λ′(JH′)H

(21)

Output of Block-Wise Processing CHATUE

Σ = JHΛHHJH + JH′Λ′H′HJH + JH′′Λ′′H′′HJH, (20) Γ _{= diag} HHJHΣ−1JH , ₍₂₁₎ S = diag(|ˆs|2) (22) Lemma: JH _{= F}HΦF _{→ H}HJH _{= F}HΦF 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 Γˆs + HHJHΣ−1˜r , (b) = [IK + Γs]−1 Γˆs + FHΦHX−1F˜r (25) Note: (a). X = FΣFH, (b). X−1 still require simplification.

(22)

Approximation to Diagonal

I JJ I J H JH I J H JH X H K H H K H H K H ) tr( ) '' '' '' tr( ) ' ' ' tr( 1 1 2 1 _Λ ₊ _Λ ₊ _σ + ΦΛΦ ≈ H H H H H H H H H H F JJ F F J H FJH F J H FJH F F X = Φ Λ Φ + _'Λ_' _' + _''Λ _'' _'' + σ 2 Index of P as t S ymbols In d e x o f P a s t S ym b o ls 10 20 30 40 50 60 10 20 30 40 50 60

Index of F uture S ymbols

In d e x o f F ut ure S ym b o ls 10 20 30 40 50 60 10 20 30 40 50 60

Index of nois e s amples

In d e x o f n o is e s a m p le s 10 20 30 40 50 60 10 20 30 40 50 60

Index of C urrent S ymbols

In d e x o f C u rr e n t S ym b o ls 10 20 30 40 50 60 10 20 30 40 50 60 Index of P as t S ymbols In d e x o f P a s t S ym b o ls 10 20 30 40 50 60 10 20 30 40 50 60

Index of F uture S ymbols

In d e x o f F u tu re S ym b o ls 10 20 30 40 50 60 10 20 30 40 50 60

Index of nois e s amples

In d e x o f n o is e s a m p le s 10 20 30 40 50 60 10 20 30 40 50 60 Index of C urrent S ymbols

In d e x of C urre n t S ym b o ls 10 20 30 40 50 60 10 20 30 40 50 60

Note: The mutual information (MI) of the past, the current, and the

(23)

Extrinsic LLR Formulation

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

z_t = µtst + vt ∈ CK×1 (26)

µt = E[zt · s∗_t ] =

1

K tr{Γ(IK + ΓSt)

−1_}, ₍₂₇₎

where vt is the equivalent noise vector with variance being

σ_t2 = µt(1 − µt). In (27), we used the approximation,

S_t = diag{|ˆs_t|2} ≈ 1 K K X k=1 |ˆs[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_t[k]|s[k]_t = +1) Pr(z_t[k]|s[k]_t = −1) = 4ℜ(z_t[k]) 1 − µt , (29)

with z_t[k] being the k-th component of zt and ℜ(z_t[k]) denoting the real

(24)

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 1 0 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 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

64-path Rayleigh Fading BPSK, FFT: 512, GI: 0 Interleaver: 512 Eb/N0= 4dB, With ACC P = 1:8

(25)

The Advantage of GI/CP Removal

0 1 2 3 4 5 6 7 8 9 10 10-5 10-4 10- 3 10-2 10-1 100 Eb/N0(dB) A v e ra ge B E R R=2/3, CP:25% R=1/2, CHATUE

64-path Rayleigh Fading BPSK, K=256

Interleaver: 256, CC-3[7,5] Truncation Length = 1 block

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

ℓ=0 |hℓ|2 = 1. The block

length is kept by K_CHATUE = K_SCCP + L with advantage of

N

RCHATUE =

N

(26)

BER Performances

1 2 3 4 5 6 7 8 9 10 10-5 10-4 10-3 10-2 10-1 100 Eb /N0[dB] A v e ra g e B E R

64-path Rayleigh Fading 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 10 10-5 10-4 10-3 10-2 10-1 100 Eb/N0 (dB) A ve ra g e B E R

64-path Rayleigh Fading 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 with

(27)

How to Solve the Channel Variation?

hö_` H ¯ hℓ = _K1 PK_k₌₀−1 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 .. . h¯₀ ¯ hL−1 ... . .. ¯ hL−1 ... ¯h0 . .. .._. 0 h¯L−1            t = ¯H_t ∈ C(K+L−1)×K

(28)

Performances Evaluation

10-5 10-4 10-3 10-2 10-1 100 Av er a ge B E R

w/o ACC (Lower Bound) w/o ACC (Truncation) w/ ACC (Lower Bound) w/ ACC (Truncation) 1 0.1 0.01 0.001 0.0001 0.00001 0.000001 E_b/N₀= 6 dB E_b/N₀= 4 dB

Truncation Length = 3 Blocks Lower Bound:

f_dT_s

Block length, K = 512

Ia;E= I0a;E= I00a;E= 1

Normalized Doppler Spread ( ) over single carrier symbol duration

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

Highway speed: 100 km/h at 3.5 GHz (WiMAX)

(29)

CHATUE Algorithm: Application to

SC-FDMA Systems

Khoirul Anwar

(30)

References (Suggested for Further Reading):

1 H. Zhou, K. Anwar, and T. Matsumoto, ”Chained Turbo Equalization

for 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 Complexity

Time-Concatenated Turbo Equalization for Block Transmission

without Guard Interval: Part 2 – Application to SC-FDMA,” Wireless

Personal Communications, Springer, Sept. 2011 (DOI:

(31)

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.,

(32)

SC-FDMA: A Review

K -D F T Source _S/P Subcarrier Mapping P/S ChannelHi M -ID F T i_{-th User} User 1 User 2

User i Base Staon

Subcarrier Allocaon: Localized Distributed : User 1 : User 2 : User 3 SM

(33)

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

r_t = I X i=1 r_i,t + Jn, (30) where

(34)

Matrix D for Subcarrier Allocations: Example

D_i is a M × K matrix for the i-th user, by which, the κ-th sub-carrier

component of the K-point Discrete Fourier Transform (DFT) is mapped to the m-th sub-carrier of the M -point DFT, where 0 ≤ κ ≤ K − 1, and 0 ≤ m ≤ M − 1.

For localized sub-carrier mapping,

Di =

(

1, m = Ru · K + κ

0, otherwise (31)

and for distributed sub-carrier mapping,

D_i =

(

1, m = Ru + M_K · κ

0, otherwise (32)

with Ru indicating the resource unit allocation, which is subjected to

(35)

Soft Cancellation in CHATUE-SC-FDMA

J n Soft Cancellation ˜rt = rt − ˆrt Soft Replica ˆr_t = I X i=1 JH_i,tFH_MD_iF_Kˆsi,t + I X i=1 JH′_i,t₋₁FH_MD_iF_Kˆs′_i,t−1 + I X i=1 JH′′_i,t₊₁FH_MD_iF_Kˆs′′_i,t₊₁ (33)

Soft Symbol Estimates ˆ

si,t(k) = E[si,t(k)|L_e,C−1

i ] = tanh{Le,Ci−1[si,t(k)]/2}, (34)

ˆ

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) ˆ

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

(36)

CHATUE-SC-FDMA Output

z_i,t = (Ik + Γi,tSi,t)−1[Γi,tˆsi,t + FH_KΦH_i,tFKΣ−1_i,t ˜ri,t]

= (Ik + Γi,tSi,t)−1[Γi,tˆsi,t + F_KHΦH_i,tX−1FK˜ri_,t] ∈ CK×1, (37)

where the Γi,t can be expressed as

Γ_i,t = diag[ ¯HH_i,tΣi_,t−1H¯ _i,t]

= diag[FH_KΦH_i,tF_KΣi_,t−1FH_KΦ_i,tF_K]

= diag[FH_KΦH_i,tX−1Φ_i,tF_K] ∈ CK×K (38)

with X being the frequency domain covariance matrices given by

X = FKΣi_,tFKH = Φ_i,tF_KΛ_i,tFH_KΦH_i,t+F_Kσ_i2DT_i JJHD_iFH_K

+FKH¯′_i,t₋₁Λ_i,t′ ₋₁H¯ ′H_i,t₋₁FH_K

+FKH¯′′_i,t+1Λ′′_i,t+1H¯ ′′H_i,t+1FH_K ∈ CK×K (39)

(37)

Approximation for Computational Complexity Reduction

Based on FΛFH ≈ _K1 tr[Λ]IK, we can perform:

X ≈ Φi,tΛi,tΦH_i,t+ diag(FKσ_i2DT_i JJHDiFH_K + FKH¯′_i,t−1Λ′_i,t−1H¯′H_i,t−1FH_K

+FKH¯′′_i,t+1Λ_i,t+1′′ H¯′′H_i,t+1FH_K)

≈ Φi,tΛi,tΦH_i,t+

1

K tr

h

σ_i2DT_i JJHD_i_{+ ¯}H′_i,t−1Λ′_i,t−1H¯′H_i,t−1_{+ ¯}H′′_i,t+1Λ′′_i,t+1H¯′′H_i,t+1i I_K (40)

Residual IBI from past and future Noise ICI 50 100 150 200 250 50 100 150 200 250 0 0 50 100 150 200 250 50 100 150 200 250 0 0 50 100 150 200 250 50 100 150 200 250 0 0

(38)

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 1 0 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 Equalizer, when MI from Past/Future = 1 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) Equalizer, when MI from Past/Future = 0 Equalizer, when MI from Past/Future = 1 Trajectory Q P 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 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

(39)

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 E_b/N₀_{(dB) for user 1} _E b/N0(dB) for user 1 A v er ag e BE R 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 with

(40)

CHATUE-SC-FDMA: Performance of Multiple Users

0 10 20 30 40 50 60 10-6 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-FrameCHATUE-SC-FDMA

Block Length, M = 512 Multi-path L = 64 Conv. Code: Memory 2 Iteration = 5 G = [7, 5]₈ Eb=N0= 6dB A v er ag e BE R / U se r

It is found that the BER performance is not significantly affected, even when the 512 sub-carriers are shared by 64 users.

(41)

Conclusions

GI causes power loss or total rate-loss with a factor of K/(K + L). CHATUE Algorithm can excellently improve the performance of

transmission without GI with low computational complexity (it is also applicable for system with insufficient GI).

Better performance (ICI, ISI, IBI Removal) can be achieved as demonstrated by: BER performance & Trajectory Analysis of the EXIT 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 4G systems is possible without cyclic prefix/guard interval.

A comparison of CHATUE SC-FDMA with the conventional

SC-FDMA with GI/CP-Transmission verifies that the performance is almost similar, but CHATUE SC-FDMA has a better spectral