Orthogonal Frequency Division Multiplexing and Multi-Carrier CDMA · 2012-04-01 · 1 Wireless...

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W i r e l e s s C o m m u n i c a t i o n

Orthogonal Frequency Division Multiplexing and Multi-Carrier

CDMA

Jean-Paul Linnartz1,2 & Nathan Yee11D e p t. of Electr ical Engineering and Com p u ter Science

U n iversity of California, Berke ley CA 94720-1770 USA

2N a tuurkundig Laborator ium , Philips Research,

5656 AA Eindhoven, The Netherlands

22

Multi-Carrier Modulation Signal Spectra

• MCM Transmit Signal Spectrum

• MCM Received Signal Spectrum

• Subcarrier orthogonality is not eroded by dispersive multi-path propagation if and

Tb Trms»

fD 1 Tb⁄«

Frequency

Frequency

33


What is MC-CDMA?

• A digital modulation / multiple access technique

• A combination of OFDM and DS-SS• A CDMA method using the FFT of DS-SS

signals• A spread spectrum modulation technique in

which each bit is modulated on multiple subcarriers with relative phase polarity according to a spreading code

44


channel

frequency

signal

Comparison of Modulation Technique Spectrums

• Narrowband (BPSK)

• SS-CDMA

• MC-CDM

55


Motivation

• Narrowband susceptible to flat fading in frequency selective channels

• CDMA-SS spreads signal energy over large bandwidth for frequency diversity

• However, wideband signals more sensitive to delay spreads because of inter-chip interference

• Use multi-carrier modulation with narrowband subcarriers

• Lower spreading factor required

66


MC-CDMA signal

Frequency

OFDM signal

Frequency

77


Time - Frequency Diagram

Narrowband Wideband OFDM

Time

Frequency

a[0]

a[1]

a[0]

a[1]

1/Tb

TbTb/N

N/Tb

a[0]

a[4]

1/Tb

a[1]

a[5]

a[2]

a[6]

a[3]

a[7]

Tb

88


Time - Frequency (cont.)

DS-CDMA MC-CDMA

Time

Frequency

Tb/NN/Tb

a[0] c2Tb

1/Tb

a[0]

c0

a[0]

c1

a[0]

c2

a[0]

c3

a[1]

c3

a[1]

c2

a[1]

c1

a[1]

c0

a[1] c0

a[0] c1

a[0] c0

a[1] c3

a[1] c2

a[1] c1

a[0] c3

Tb

1/Tb

a[0]

a[2]

a[1]

FH-SS

99


X

cos{2π(fc + (N-1)F/Tb)t}

X

cos{2π(fc + F/Tb)t}

X

cos{2πfct}

X

ci, N-1

X

ci, 1

X

ci, 0

ai[k]

Σ

Transmitter Model

......

si(t)

1010


Implementation Aspects

• MC-CDMA requires no chip synchronization. It requires only carrier and bit synchronization.

• MC-CDMA may use FFT devices• Charged-capacitor domain detector circuit?• MC-CDMA receiver might be simpler than

DS-SS receiver with full MRC for all resolvable paths. MC-CDMA does not require multiple despreaders

• Subcarrier amplitude estimation can be simple for the downlink

1111

Synchronization & Estimation in Downlink

• “Interfering” signals to other users help• Rapid acquisition of synchronization and channel

estimation• Improvement: Use PN sequence in Frequency

Domain

NNNN

NN

NNNN

NN

-N-N-N-N

-N-N

-N-N-N-N

-N-N

amcm N,∑

amcm 2,∑amcm 1,∑

Freq

uenc

y

Timesyncword

identical for all usersMC-CDMA

1212

Joint Signal in Downlink

• Interference helps during acquisition

φ2 I

Q

Subcarrier 2

φ1 I

Q

Subcarrier 1

1313


Simplified Channel Model

• Frequency selective channel with

• Narrowband behavior of subcarrier

•

• Rayleigh / Rician amplitude and uniform phase• IID fading at the subcarriers

1Tb------ B« Wc

FTb------«

Hm fci

Tb----F+

ρm i, ejθm i,=

ChannelSignal

1414


frequency

1515


Uplink vs. Downlink

ρm i, θm i,,{ }m 0=

M 1– ρm i, ρ0 i,=

θm i, θ0 i,= m∀

USER 0

USER 1

USER 2

BASESTATION

USER 0

USER 1

USER 2

BASESTATION

1616


X

cos{2πfct + φi,0}

X

cos{2π(fc + F/Tb)t + φi,1}

X

cos{2π(fc + (N-1)F/Tb)t + φi,N-1}

d0,0

d0,1

d0,N-1

Receiver Model

......

Σr(t) ν0

X

c0,0

X

ci,1

X

ci,N-1

...

∫

1717


ASSUMPTIONS

• LARGE NUMBER OF SUBCARRIERS

• FREQUENCY NON-SELECTIVE FADING FOR SUBCARRIER BANDWIDTH (F/Tb)

• IID RAYLEIGH FADING AT SUBCARRIERS OR RANDOM CODE SEQUENCES

• PERFECT PHASE CORRECTION AT RECEIVER FOR WANTED SIGNAL

1818

Analysis of Performance

• Transmitted Signal of the mth user

• Received Signal

• Decision Variable

sm t( ) cm i, am k[ ] 2πfct 2πiFTb-----t+

cosi 0=

N 1–

∑= pTbt kTb–( )

cm i, 1 1,–{ } cl i, cm i,i 0=

N 1–

∑ Nδl m,=

r t( ) ρm i,i 0=

N 1–

∑ cm i, am

k[ ]m 0=

M 1–

∑= 2πfct 2πiFTb-----+ t θm i,+

n t( )+cos

ν0 a0 k[ ] ρ0 i, d0 i, am k[ ]m 1=

M 1–

∑+i 0=

N 1–

∑=

ρm i, d0 i, θ0 i, θm i,–( ) cm i, c0 i, η+cosi 0=

N 1–

∑×

1919


Receiver Equalization Techniques

• Contribution to decision variable by mth interferer in downlink is proportional to

ρm i,i 0=

N 1–

∑ dm i, c0 i, cm i,

..... EGC ....

MRC

.....

CE X

amplitude

ith subcarrier0 1 2 3

2020


Receiver Equalization Techniques

• Equal Gain Combining (simplicity)

• Maximum Ratio Combining (combats noise)

• Controlled Equalization (restores orthogonality)

d0 i, 1=

d0 i, ρ0 i,=

d0 i,1

ρ0 i,---------u ρ0 i, ρTHRESH–( )=

2121


• Optimum Filtering

d0 i,

ρ0 i,

ρ0 i,2 c+

------------------=

2222

EGC and MRC in Uplink

• Decision Variable for Uplink:

• Conditional BER for EGC:

• Distribution of amplitudes

ν0 a0 k[ ] ρ0 i, d0 i, am k[ ]m 1=

M 1–

∑+i 0=

N 1–

∑=

ρm i, d0 i, θ0 i, θm i,–( ) cm i, c0 i, η+cosi 0=

N 1–

∑×

Pr error ρ0 i,{ }i 0=

N 1–M 1–( ) pm,

=

12---erfc

12--- ρ0 i,

i 0=

N 1–

∑ 2

Tb

M 1–( ) pmTb NN0+---------------------------------------------------

=

ρ0 i,i 0=

N 1–

∑

NEρ0 i,

N µ σ2,( )small argument

∼

2323

EGC and MRC in Uplink (cont.)

• Average BER for EGC (LLN)

• Average BER for MRC (LLN)

BER12---erfc γ

p0TbM 1–( )

N--------------------pmTb N0+-----------------------------------------------

≅

γπ4---

e K–

K 1+-------------

1 K+( ) I0K2----

K I1

K2----

×+

2=

BER12---erfc

p0TbM 1–( )

N--------------------pmTb N0+-----------------------------------------------

≅

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Uplink BER for EGC & MRC vs. # of Interferers

BER vs. the # of interferers for EGC using small argument approx. (1), CLT (2), and

# of interferers

BER

1e-05

1e-04

1e-03

1e-02

1e-01

0 50 100

(1,2,3)

(4,5)

LLN (3) and MRC exact (4) and LLN (5). N = 128.

(Rayleigh, SNR=10dB)

2525

EGC and MRC in Downlink

• Decision Variable:

• Average BER for EGC (LLN)

• Average BER for MRC (LLN)

ν0 a0 k[ ] ρidi am k[ ] ρidicm i, c0 i, η+i 0=

N 1–

∑m 1=

M 1–

∑+i 0=

N 1–

∑=

a0 k[ ] ρidi am k[ ] ρajdaj

ρbjdbj

– η+

j 0=

N 2⁄

∑m 1=

M 1–

∑+i 0=

N 1–

∑=

BER12---erfc

γpTb

2M 1–

N--------------

1 γ–[ ] pTb N0+-----------------------------------------------------------------

≅

γπ4---

e K–

K 1+-------------

1 K+( ) I0K2----

K I1

K2----

×+

2=

BER12---erfc

pTbM 1–

N-------------- 4K 2+

K 1+( ) 2---------------------- pTb N0+--------------------------------------------------------------------------

≅

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Downlink BER for EGC & MRC vs. # of Interferers

BER vs. the # of interferers for EGC using small argument approx. (1), CLT (2), and

BER

LLN (3) and MRC exact (4) and LLN (5). N = 128.


1e-05

1e-04

1e-03

1e-02

1e-01

0 50 100

(1,2,3)

(4,5)

# of interferers

27

Downlink BER for EGC vs. # of Interferers

BER vs. the # of interferers for EGC with Rician Fading using CLT and LLN

BER

approximations for (1) K=0, (2) K=5, (3) K=10, (4) K=15, (5) K=20, (6) K=25. N = 128.

(Rician Fading, SNR=10dB)

# of interferers

1e-05

1e-04

1e-03

1e-02

0 50 100

(1)

(2) (3,4,5,6)

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Downlink BER for MRC vs. # of Interferers

BER vs. the # of interferers for MRC with Rician Fading using CLT and LLN

BER

approximations for (1) K=0, (2) K=5, (3) K=10, (4) K=15, (5) K=20, (6) K=25. N = 128.

(Rician Fading, SNR=10dB)

# of interferers

1e-05

1e-04

1e-03

1e-02

1e-01

0 50 100

(1)(2,3,4,5,6)

2929


Controlled Equalization (CE)

• Reduce interference by normalizing and restoring orthogonality

• Greatest effect in downlink where phase correction of interferers may be performed

• Reduce amplification of noise by discarding subcarriers below threshold

d0 i,1

ρ0 i,---------u ρ0 i, ρTHRESH–( )=

3030

Analysis of CE in Downlink

• Decision variable given n0 subcarriers are above threshold

• Interference, ni:

• BER

ν0 n0 a0 k[ ] n0 am k[ ] cm j, c0 j, η+j 0=

n0 1–

∑m 0=

M 1–

∑+=

pΣm n0σm n0

N 2⁄n0 σm+( ) 2⁄

N 2⁄n0 σm–( ) 2⁄

Nn0

-------------------------------------------------------------------------------=

pni n0ni n0

pΣm n0σm n0

⊗=

Pb e( )Nn0

pa

n0 1 pa–( )N n0–

pni n0ni n0

ni

∑n0 0=

N

∑=

1 n n–

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Downlink BER for CE vs. # of Interferers

BER

# of interferers

BER vs. the # of interferers for MRC (1), EGC (2), and CE for pmin = 0.006 (3),pmin = 0.008 (4), pmin = 0.012 (5), and pmin = 0.018 . The SNR is 10dB, p0 = 0.1, and

1e-05

1e-04

1e-03

1e-02

1e-01

0 50 100

(1)

(2)

(3,4,5,6)

N = 128.


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BER vs. the # of interferers for MRC (1), EGC (2), and CE for pmin = 0.0008 (3),pmin = 0.0015 (4), pmin = 0.002 (5), and pmin = 0.004 (6). The SNR is 20dB, p0 = 0 .1 , and

N = 1 2 8 .

# of interferers

1e-22

1e-20

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

1e-06

1e-04

1e-02

1e+00

0 50 100

BER

(1)(2)

(3,4,5,6)


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BER vs. the # of interferers for MRC (1), EGC (2), and CE for pmin = 0.002 (3),pmin = 0.008 (4), and pmin = 0.014 (5). The SNR is 10dB, p0 = 0 .1 , and N = 128.

# of interferers

BER

(Rician: K=5, SNR=10dB)

1e-05

1e-04

1e-03

1e-02

0 50 100

(1)

(2)

(3,4,5)

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BER vs. the # of interferers for MRC (1), EGC (2), and CE for pmin = 0.016 (3),pmin = 0.002 (4), and pmin = 0.008 (5). The SNR is 10dB, p0 = 0 .1 , and N = 128.

# of interferers

BER

(Rician: K=10, SNR=10dB)

1e-05

1e-04

1e-03

1e-02

0 50 100

(1)

(2)

(3,4,5)

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Wiener Filtering

• Optimum weighting vector in a mean-squared error sense

• Weighting vector

• Decision variable

D RY1–

Ra0Y=

ν0 D Y•=

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Downlink BER for Wiener vs. # of Interferers

Simulation results for the average BER vs. the # of interferers for (1) MRC, (2) EGC,

(Rayleigh, SNR=10dB, N=8)

Avg. BER

# of interferers

2

5

1e-03

2

5

1e-02

2

5

1e-01

0 5 7

(1)

(2)

(3)

1 632 4

and (3) Wiener filtering.

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Downlink BER for Wiener vs. SNR

Simulation results for the average BER vs. the SNR for (1) Wiener filtering with a,

(Rayleigh, Full Load, N=8)

full load, (2) single subcarrier with noise only, and (3) single subcarrier with noise

Avg. BER

SNR (dB)

3

1e-05

3

1e-04

3

1e-03

3

1e-02

3

1e-01

5 10 152 18

(2)

(3)

(1)

and Rayleigh fading.

3838


Conclusions

• MC-CDMA is a new, promising CDMA method

• Most effective in downlink• Can operate well with large delay spreads• Controlled equalization better than MRC and

EGC for combating interference• If F>>1, exploit frequency diversity without

excessive spreading

Orthogonal Frequency Division Multiplexing and Multi-Carrier CDMA · 2012-04-01 · 1 Wireless...

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