SC-FDMA Oversampling MMSE Equalizer - …leoliuyunxiang.net/talks/SC_FDMA_oversampling_MMSE_equalizersli… · SC-FDMA Oversampling MMSE Equalizer YunXiang LIU, Leo INFINITUS, Nanyang

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SC-FDMA Oversampling MMSE Equalizer

YunXiang LIU, LeoINFINITUS, Nanyang Technological University

Yingcai Experimental School, University of Electronic Science and Technologyof China

[email protected]

May 14, 2013

YunXiang LIU, Leo ([email protected]) May 14, 2013 1 / 34

.. Outline

• Background

• Introduction to Oversampling MMSE Equalizer SC-FDMA System

• Simulation Results

• Conclusions

• Future Work


.. Outline

• Background



• Conclusions

• Future Work


.. Outline

• Background



• Conclusions

• Future Work


.. Outline

• Background



• Conclusions

• Future Work


.. Outline

• Background



• Conclusions

• Future Work


.. Outline

• Background



• Conclusions

• Future Work


.. Background

• SC-FDMA system is a Pre-DFT OFDM system, which is similar to OFDM

• SC-FDMA (Single Carrier FDMA) is an attractive alternative to OFDMAespecially in the uplink communications where lower PAPR (peak to averagepower ratio) greatly benefits the mobile terminal, in terms of transmit powerefficiency and terminal costs.

• SC-FDMA has been adopted as the uplink multiple access scheme in 3GPPLong Term Evolution (LTE), or Evolved UTRA

• SC-FDMA effectively copes with frequency-selective fading channels by usingsimple frequency-domain equalization


.. Background






.. Background






.. Background






.. Background

• However, SC-FDMA also suffers from carrier frequency offset, which iscaused by oscillator instability, Doppler effect

• CFO destoys the orthogonality among subcarriers

• Inter-carrier Interference is introduced

• Frequency offset estimation and compensation is critical


.. Background






.. Background






.. Background






.. Background

• Oversampling MMSE Equalization may be also an effective way to combatthe frequency offset

• It is clear by noting that a dual problem of frequency offset for multicarriersystems is timing jitter for signal-carrier systems, which is traditionally solvedvia time-domain-oversampling

• Frequency oversampling should be expected to be robust against frequencyoffset


.. Background





.. Background





.. Outline

• Background



• Conclusions

• Future Work


..Comparison between Conventional MMSE andOversampling MMSE


.. Mathmatical Model-Transmitter

• DFT operation

Xi = FMdi

wheredi = [di

1, di2, ......., di

M]T

[FM]p,q = (1/√

M)e−j2π(pq/M)

i = 1, 2, ...,Q,Q = N/M

• Subcarrier Mapping

XiN×1 = Mi

TXiM×1

where MiT is subcarrier mapping matrix



• DFT operation

Xi = FMdi

wheredi = [di

1, di2, ......., di

M]T

[FM]p,q = (1/√

M)e−j2π(pq/M)

i = 1, 2, ...,Q,Q = N/M


XiN×1 = Mi

TXiM×1




• DFT operation

Xi = FMdi

wheredi = [di

1, di2, ......., di

M]T

[FM]p,q = (1/√

M)e−j2π(pq/M)

i = 1, 2, ...,Q,Q = N/M


XiN×1 = Mi

TXiM×1




• IDFT operation

x = F−1N

Q∑i=1

MiTXi

• Add Guard Interval

x = PGIF−1N

Q∑i=1

MiTXi

wherePGI = [IT

N, 0TNg×N]

T



• IDFT operation

x = F−1N

Q∑i=1

MiTXi

• Add Guard Interval

x = PGIF−1N

Q∑i=1

MiTXi

wherePGI = [IT

N, 0TNg×N]

T


.. Mathmatical Model-Channel Model

• Channel Response

h =K−1∑k=0

hkδ(τ − τk)

whereK−1∑k=0

E[|hk|2

]= 1


.. Mathmatical Model-Channel and Receiver

• Receiver Signal after Zeros Padding

r = D (ε)PzpHx + n

wherePzp =

[ITP0

T(L−P)×P

]T

D (ε) = diag1, e−j 2π

N ε, ..., e−j 2πN (L−1)ε

and H is a P × P lower triangular Toeplitz matrix with the first column[h0, h1, ..., hK−1, 0, ..., 0]

T and ε is normalized by subcarrier spacing 1/T


.. Mathmatical Model-Receiver

• Channel Matrix Transformation

Hzp = PzpHPGI

By definingFL×L

∆=

1√L

exp(−j2πL np

)L×L

FL×N∆=

1√L

exp(−j2πL lp

)L×N

Hzp = FHL×LHFL×N

where H = diag H0,H1, ...,HL−1 and S = L/N, which is the oversamplingfactor

Hl∆= H

(l

ST

)=

K−1∑k=0

hk exp(−j2π[

lS

]τqT ), l = 0, 1, ...,L − 1.



• Channel Matrix Transformation

Hzp = PzpHPGI

By definingFL×L

∆=

1√L

exp(−j2πL np

)L×L

FL×N∆=

1√L

exp(−j2πL lp

)L×N

Hzp = FHL×LHFL×N

where H = diag H0,H1, ...,HL−1 and S = L/N, which is the oversamplingfactor

Hl∆= H

(l

ST

)=

K−1∑k=0

hk exp(−j2π[

lS

]τqT ), l = 0, 1, ...,L − 1.



• Receive Signal after L-point DFT

y = FL×LD (ε)PzpHPGIFHN×N

Q∑i=1

MiTXi + FL×LPzpn

= FL×LD (ε)FHL×LHFL×NFH

N×N

Q∑i=1

MiTXi + FL×Pn

= FL×LD (ε)FHL×LHΩΨ+ η

where

Ω = FL×NFHN×N,Ψ =

Q∑i=1

MiTXi, η = FL×Pn

Cη = E[ηηH] = σ2

nΓ, Γ = FL×PFHL×P


.. Mathmatical Model - Receiver

• Oversampling MMSE Receiver

wH = E[dyH] · E

[yyH]†

=(

HΩ)H

HΩΩHHH +σ2

nσ2

sΓ†

Based on Bayesian Gauss-Markov theorem• Estimation

Ψ = wHy

• De-mappingXi = MiΨ

• N-point IDFT operationdi = FH

N×NXi




wH = E[dyH] · E

[yyH]†

=(

HΩ)H

HΩΩHHH +σ2

nσ2

sΓ†


Ψ = wHy



N×NXi




wH = E[dyH] · E

[yyH]†

=(

HΩ)H

HΩΩHHH +σ2

nσ2

sΓ†


Ψ = wHy



N×NXi


.. Outline

• Backgroud



• Conclusions

• Future Work


.. Simulation outline

• Simulation Setup

• Reconsctrction of OFDM Oversampling Equalizer based on [1]

• BER Performance Comparison between SC-FDMA and OFDM without CFO

• BER Performance Comparison between SC-FDMA and OFDM with CFO

• BER Performance of SC-FDMA under different CFO

• Effect of Oversampling Factor

• Oversampling Gain Discussion

• One Path Rayleigh Channel with Different CFO


.. Simulation Setup

• Simulation System Parameters

Total Subcarriers 64

Pre-DFT subcarriers number 16

Modulation QPSK

Equalization Conventional and Oversampling

MMSE

Mapping Scheme Interleaved

CP number 16

Iteration Number 1000000

Channel 16path Rayleigh channel

Carrier Frequency Offset(CFO) [0,0.02,0.05,0.1]

Attention: Here CFO is normalized by subcarrier spacing


..Reconsctruction of OFDM Oversampling Equalizer basedon [1]

0 2 4 6 8 10 12 14 16 18 2010

−4

10−3

10−2

10−1

100

Eb/N0(dB)

Ave

rage

BE

R

Performance Comparison of OFDM

Conv. MMSE with εg = 0

Conv. MMSE with εg = 0.02

Conv. MMSE with εg = 0.05Oversamping MMSE with εg = 0

Oversamping MMSE with εg = 0.02

Oversamping MMSE with εg = 0.05

• 1. Shi, Q., Liu, L., Member, S., and Guan, Y. L. (2010). Fractionally SpacedFrequency-Domain MMSE Receiver for OFDM Systems, 59(9), 4400-4407.


..BER Performance Comparison between SC-FDMA andOFDM without CFO

0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

EbN0

BE

R

Performance Comparison of OFDM and SC−FDMA

OFDM Conventional MMSEOFDM OverSampling MMSESC−FDMA Conventional MMSESC−FDMA Oversampling MMSE


..BER Performance Comparison between SC-FDMA andOFDM with CFO

0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

EbN0

BE

R

Performance Comparison of OFDM and SC−FDMA with CFO = 0.02




0 5 10 15 20 2510

−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

EbN0

BE

R





0 2 4 6 8 10 12 14 16 18 2010

−4

10−3

10−2

10−1

100

EbN0

BE

R




.. BER Performance of SC-FDMA under different CFO

0 2 4 6 8 10 12 14 16 18 2010

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

EbN0

BE

R

BER Performance of SC−FDMA

SC−FDMA Conventional MMSE with CFO = 0SC−FDMA Oversampling MMSE with CFO = 0SC−FDMA Conventional MMSE with CFO = 0.05SC−FDMA Oversampling MMSE with CFO = 0.05SC−FDMA Conventional MMSE with CFO = 0SC−FDMA Oversampling MMSE with CFO = 0.1


.. Effect of Oversampling Factor

1 1.5 2 2.5 3 3.5 4 4.5 510

−7

10−6

10−5

10−4

10−3

10−2

10−1

100

EbN0

BE

R

Effect of oversampling factor

S = 77/64S = 78/64S = 79/64


.. Oversampling Gain

0 2 4 6 8 10 12 14 16 18 2010

−6

10−5

10−4

10−3

10−2

10−1

100

EbN0

BE

R

BER Performance of Different Paths

Conv. OFDM − 1 PathConv. SC−FDMA − 1 PathOverSampling SC−FDMA − 1 PathConv. SC−FDMA − 4 PathOverSampling SC−FDMA − 4 PathConv. SC−FDMA − 6 PathOverSampling SC−FDMA − 6 PathConv. SC−FDMA − 8 PathOverSampling SC−FDMA − 8 Path


.. One Path Channel with Different CFO

0 2 4 6 8 10 12 14 16 18 2010

−3

10−2

10−1

100

EbN0

BE

R

BER Performance of One Paths with different CFO

Conv. SC−FDMA − 1 PathConv SC−FDMA − 1 Path with CFO = 0.05Oversampling SC−FDMA 1 path with CFO = 0.05Conv. SC−FDMA − 1 Path with CFO = 0.1OverSampling SC−FDMA − 1 Path with CFO = 0.1Conv. SC−FDMA − 1 Path with CFO = 0,2OverSampling SC−FDMA − 1 Path with CFO = 0.2


.. Outline

• Background



• Conclusions

• Future Work


.. Conclusion

• Uncoded SC-FDMA is always better than uncoded OFDM

• SC-FDMA has a remarkable improvement with Oversampling MMSEEqualizer, which extract more frequency diversity than conventionalSC-FDMA

• Oversampling MMSE Equalizer improves the performance with CFO

• Oversampling factor S = 1+(Q-1)/N could get the optimal performance

• Oversampling Gain gets from frequency diversity, which could compensatedeep fading.


.. Conclusion







.. Conclusion







.. Conclusion







.. Conclusion







.. Outline

• Background



• Conclusions

• Future Work


.. Future Work

• USRP Implementation

−10 −5 0 5 10

−10

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0

2

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6

8

10

Qua

drat

ure

In−Phase

Scatter plot

−8 −6 −4 −2 0 2 4 6 8

−8

−6

−4

−2

0

2

4

6

8

Qua

drat

ure

In−Phase

Scatter plot


.. Future Work


−10 −5 0 5 10

−10

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Qua

drat

ure

In−Phase

Scatter plot

−8 −6 −4 −2 0 2 4 6 8

−8

−6

−4

−2

0

2

4

6

8

Qua

drat

ure

In−Phase

Scatter plot


.. Future Work


−10 −5 0 5 10

−10

−8

−6

−4

−2

0

2

4

6

8

10

Qua

drat

ure

In−Phase

Scatter plot

−8 −6 −4 −2 0 2 4 6 8

−8

−6

−4

−2

0

2

4

6

8

Qua

drat

ure

In−Phase

Scatter plot


.. Future Work

• Effect of Oversampling Factor

• Theorem Analysis of Oversampling MMSE Equalizer• Python Programming for Numerical Analysis


.. Future Work

• Effect of Oversampling Factor• Theorem Analysis of Oversampling MMSE Equalizer

• Python Programming for Numerical Analysis


.. Future Work

• Effect of Oversampling Factor• Theorem Analysis of Oversampling MMSE Equalizer• Python Programming for Numerical Analysis


.. Future Work

• Effect of Oversampling Factor• Theorem Analysis of Oversampling MMSE Equalizer• Python Programming for Numerical Analysis


.. Reference

• 1. Shi, Q., Liu, L., Member, S., and Guan, Y. L. (2010). Fractionally SpacedFrequency-Domain MMSE Receiver for OFDM Systems, 59(9), 4400-4407.


Thanks

YunXiang LIU


Documents

SC-FDMA Oversampling MMSE Equalizer - …leoliuyunxiang.net/talks/SC_FDMA_oversampling_MMSE_equalizersli… · SC-FDMA Oversampling MMSE Equalizer YunXiang LIU, Leo INFINITUS, Nanyang