MC-CDMA vs DS-CDMA M. des Noes and D. Ktenas (presented by Sylvie Mayrargue)

COST 289 30-31 Oct 2003 (Kosice)

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MATRICE project

MC-CDMA vs DS-CDMA

M. des Noes and D. Ktenas

(presented by Sylvie Mayrargue)



MATRICE project

Outline

• Context of the comparison : Simulation assumptions

Asymptotic analysis

• DS and MC-CDMA system models.

• For each detector : Linear filter description

Simulation results

• Interpretation

• Conclusion and future work



MATRICE project

Context of the comparison

• Downlink : Base station to mobile.

• No channel coding.

• No inter-cell interferences

• Perfect channel estimation and synchronization

• Linear detectors : MRC, SU-MMSE and MU-MMSE

Comparison of BER based on simulations (Monte Carlo) and asymptotic analysis (theory).



MATRICE project

Asymptotic analysis 1/3

• Symbol estimated at the output of a linear detector for DS or MC-CDMA system :

kkkk τ(n)dη(n)d̂

• k and k depend on the channel, spreading codes and

code power matrices.

• k results from the filtering of the MAI plus the

background noise.



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The main results of the asymptotic analysis are the followings:

• As N,K and =K/N is fixed, k converges to a limit .

• As N,K and =K/N is fixed, k becomes gaussian and

its variance converges to a limit V2

• An analytical expression of the asymptotic SINR is obtained. It is independent of the spreading codes.These demonstrations are based on the so-called ‘free probability theory’.

Zhang, Chong, Tse « Output MAI distribution of linear MMSE multi-user receivers in CDMA systems » Information Theory March 2001



MATRICE project


kkk τ(n)ηd(n)d̂

Fixed Gaussian noiseAWGN transmission !

2

2

V

Signal to Interference plus Noise Ratio (SINR) :

2

12

311211:

)( BER :QPSK-BPSK

MQ

MSERQAMM

Q



MATRICE project

References

MC CDMA

M.Debbah, W.Hachem, P.Loubaton, M.de Courville « MMSE Analysis of Certain Large Isometric Random Precoded Systems »– IEEE Trans on Information Theory Vol 49, n°5, May 2003

DS CDMA

– J.M. Chaufray, W.Hachem, Ph.Loubaton « Asymptotical Analysis of Optimum and Sub optimum CDMA Downlink MMSE Receivers »

– Can be downloaded at http://syscom.univmlv.fr/~loubaton/index.html



MATRICE project

DS-CDMA system model 1/2

•Channel :

• C=(c1 c2 … cK), d(n) = (d1(n), …, dK(n))T, P = diag(P1, …, PK)

• Y(n) = (Y1(n) , …, YN(n))T

• N : spreading factor , K : number of codes

• W : delay spread of the channel (W< N)

1

0

][)(W

l

lzlhzh

cK(z)

c1(z)

h(z)

v[n]

Y[n]

d1(n)

dK(n)

X[n]

0P

1KP

N

N



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DS-CDMA system model 2/2

V1)-d(n P C H d(n) P C H Y(n) 10

00

]1[

..

]1[.]1[00

]0[]1[0

]1[

]0[]1[

]0[

0]0[

1

0

Wh

hWh

H

hWh

Wh

hWh

h

h

H

ISI+MAINoise N(0,2I)

Useful + MAI

Received signal :



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MC CDMA System model 1/2

S/ P

1: N

IFFTN: N

s1

sN

P/S

GI Insertion

x1(n)

xN(n)z[i]

N:1Spr

eadi

ng

dK(n)

d1(n)

cK-1(z)

c0(z)d0(n)

dK-1(n)

X[n]

N

N

0P

1KPcK-1(z)

c0(z)d0(n)

dK-1(n)

X[n]

N

N

0P

1KP



MATRICE project

MC CDMA System model 2/2

S/P

1: N

FFTN: N

Remove GI

SU

/MU

D

etec

tor

h(z)z[i]

y0(n)

yN-1(n)

v[i] d0(n)

dK-1(n)

S/P

1: N

FFTN: N

FFTN: N

Remove GI

SU

/MU

D

etec

tor

h(z)z[i]

y0(n)

yN-1(n)

v[i] d0(n)

dK-1(n)

)(v )(.)( nnXHnY Received signal :

Tap delay channel :

where is the channel impulse response. )(e)(h /Nj2i

ihn

1

0

][)(W

l

lzlhzh



MATRICE project

MRC: Maximum Ratio Combining

1)Y(n C H Y(n) C H (n)d̂ H1

H0 )( n)(d̂ k nYHc HH

k

DS-CDMA MC-CDMA

1

0

22

2

21

0

22

1

0

42

)(1

)(

)(

dfehdfeh

dfehp

p

fifi

fi

k



MATRICE project

MRC: Simulation vs. Asymptotic DS-CDMA

DS-CDMA, Rake, BRAN A

1,00E-02

1,00E-01

1,00E+00

2 4 6 8 10 12 14

Eb/N0 (dB)

BE

R

simul, a=1

asymp, a=1

simul, a=1/2

asymp, a=1/2

simul, a=1/4

asymp, a=1/4



MATRICE project

MRC: Simulation vs. Asymptotic MC-CDMA

MC-CDMA, MRC, BRAN A

1,00E-02

1,00E-01

1,00E+00

2 4 6 8 10 12 14

Eb/N0 (dB)

BE

R

simul, a=1

asymp, a=1

simul, a=1/2

asymp, a=1/2

simul, a=1/4

asymp, a=1/4



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MRC: Comparison MC-CDMA DS-CDMA

MC-CDMA vs DS-CDMA, MRC, BRAN A

1,00E-02

1,00E-01

1,00E+00

2 4 6 8 10 12 14

Eb/N0 (dB)

BE

R

MC-CDMA, a=1

DS-CDMA, a=1

MC-CDMA, a=1/2

DS-CDMA, a=1/2

MC-CDMA, a=1/4

DS-CDMA, a=1/4



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SU-MMSE

DS-CDMA MC-CDMA

1

0

12

11000

1

)(. (n) ˆ

K

kk

HHHH

pK

p

nYp

HHHHHCd

)(. (n) ˆ12

nYp

HHHcd HHHkk

1

0 222

22

)(

)(

1

df

peh

eh

p

p

fi

fi



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SU-MMSE : simulation vs asymptotic – MC CDMA

MC-CDMA, SU MMSE, BRAN A

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

2 4 6 8 10 12 14

Eb/N0 (dB)

BE

R

simul, a=1

asymp, a=1

simul, a=1/2

asymp, a=1/2

simul, a=1/4

asymp, a=1/4



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SU-MMSE : Comparison DS-CDMA – MC CDMA

Comparison MC-CDMA DS-CDMA. SU MMSE - BRAN A

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

2 4 6 8 10 12 14

Eb/N0 (dB)

BE

R

DS-CDMA, a=1

MC-CDMA, a=1

DS-CDMA, a=0.5

MC-CDMA, a=0.5



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MU-MMSE Multiple User MMSE (for DS-CDMA)

MU-MMSE : equalize the global channel : h(z) c(z)

Asymptotic SINR :

)(. (n) ˆ12

11000 nYIHCPCHHCPCHHCPd HHHHHH

duβ.up

(u)μβ),g(p

β),(p .gp1 β),p ,B(

β),(p α.β.gp

βα)(1 β),p ,A(

df

β),p ,α.B( β),p ,A(h(e

σ

11

k

powerk

kkk

kk

k

1

0

kk2f)j2

2

1K

0ipower

c

)( (u)μ ii pp

Distribution of powers : Kc classes of powers



MATRICE project

MU-MMSE Multiple User MMSE (for MC-CDMA)

Asymptotic SINR

Y(n) (n)d̂12

k

IσHH.CP CHcp HHHHkk

duβ.up

(u)μβ),g(p

β),(p .gp1 β),p ,B(

β),(p α.β.gp

βα)(1 β),p ,A(

k

powerk

kkk

kk

k

df

β),p ,α.B( β),p ,A(h(e

σ

11

1

0

kk2f)j2

2



MATRICE project

MU-MMSE : simulation vs asymptotic – DS CDMA

DS-CDMA, MU MMSE, BRAN A

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

0 2 4 6 8 10 12 14

Eb/N0 (dB)

BE

R

simul, a=1

asymp, a=1

simul, a=1/2

asymp, a=1/2

simul, a=1/4

asymp, a=1/4



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MU-MMSE : DS-CDMA – MC CDMA

MC-CDMA vs.DS-CDMA MU MMSE - BRAN A

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

2 4 6 8 10 12 14

Eb/N0 (dB)

BE

R

DS-CDMA, a=1

MC-CDMA, a=1

DS-CDMA, a=0.5

MC-CDMA, a=0.5

DS-CDMA, a=0.25

MC-CDMA, a=0.25



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Interpretation

V1)-d(n P C H d(n) P C H Y(n) 10 1(N,K)

Vd(n) P C H~

Y(n) 2(N,K)

)0()1()1(00

0)0(

)1(0

0)0()1(

)1(

0)0(

)1()1(00)0(

~10

hhWh

h

Wh

hWh

Wh

h

hWhh

HHH

Both systems have the same asymptotic SINR

2(N,K)- 1(N,K)2

0N,K

DS-CDMA

DS-CDMA with Cyclic Prefix



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Interpretation

•Both matrices have the same eigenvalue distribution.

• When computing the asymptotic SINR, we only use the eigenvalue distribution.

• MC-CDMA and DS-CDMA have the same asymptotic SINR.

matrixFourier :

~

F

FHFH HCDMAMC



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Conclusion

• With our assumptions : MC-CDMA = DS-CDMA in an uncoded scenario.

• MC-CDMA receiver is less complex than a DS-CDMA receiver ? DS-CDMA : possibility to perform frequency domain equalization (with the same performance), but needs one FFT and one IFFT at the receiver side.

MC-CDMA gains one FFT on the complexity for a MS.

Need to take into account the overall complexity (including channel estimation,

synchronization ,…, RF).

Future work: coding impact?

.

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MC-CDMA vs DS-CDMA M. des Noes and D. Ktenas (presented by Sylvie Mayrargue)

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