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Optik 125 (2014) 6801–6804

Contents lists available at ScienceDirect

Optik

jo ur nal homepage: www.elsev ier .de / i j leo

inimizing performance loss of MMSE algorithm for CDMA-based-MIMO-OFDM

ohammad Ghanbarisabaghaculty of Engineering, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia

r t i c l e i n f o

rticle history:

a b s t r a c t

This paper presents an algorithm to minimize the performance loss (PL) of minimum mean square error

eceived 9 December 2013ccepted 10 July 2014

eywords:DMAptical OFDMSMF

(MMSE) in code division multiple access (CDMA) based optical multiple input multiple output orthogonalfrequency division multiplexing (O-MIMO-OFDM) systems over 1200 km of standard single mode fiber(SSMF). The performance of the system using proposed algorithm scheme is compared to MMSE schemeby simulation results. It shows the superior performance of proposed algorithm.

© 2014 Elsevier GmbH. All rights reserved.

. Introduction

Spectral efficiency (SE) of any communication systems will bemproved by applying multiple input multiple output (MIMO) tech-ique [1]. A lot of study has been done by integrating MIMO systems

nto orthogonal frequency division multiplexing (OFDM). OpticalIMO-OFDM [2,7–14] is a multi-carrier modulation technology

hat has been proposed for fiber optic communication because its an effective solution to inter symbol interference (ISI), whenymbol period of each subcarrier is longer than the delay spreadaused by group velocity dispersion (GVD) [3,4,7–13]. It has severaldvantages including efficient bandwidth usage, transformation of

frequency selective fading channel into a flat fading channel andimplified channel equalization.

On the other hand, CDMA technique is a promising method forIMO-OFDM systems since it can conflict strong fading, eliminate

he effect of narrowband interference and provide high capacity.MMSE algorithm can recover the transmitted data considering

he trade-off between system performance and complexity. Unfor-unately, the performance loss is considerable. To minimize theerformance loss of MMSE in CDMA based O-MIMO-OFDM systems

ver 1200 km of SSMF, an efficient algorithm is proposed withoutncreasing considerably the computational complexity.

E-mail address: m.ghanbarisabagh@gmail.com

ttp://dx.doi.org/10.1016/j.ijleo.2014.07.103030-4026/© 2014 Elsevier GmbH. All rights reserved.

2. System model

By assuming the instance assigning spreading chips over thesubcarriers, the relationship between input and output for the syn-chronous CDMA-based O-MIMO-OFDM systems is given as:

y = ABx + n (1)

where x, y and n are transmitted signal vector of all users, receivedsignal vector of all antennas at the receiver and noise vector of allantennas at the receiver, respectively. x, y and n can be representedas:

x = [ xT1 xT

2 xT3 . . . xT

U ]T (2)

y = [ yT1 yT

2 yT3 . . . yT

N ]T (3)

n = [ nT1 nT

2 nT3 . . . nT

N ]T (4)

where xu is the transmitted signal vector for user number u, u =

1, 2, 3, ..., U and U is the number of active users; yj is the receivedsignal vector for subcarrier number j, j = 1, 2, 3, ...N and N is thenumber of subcarriers; nj is the noise vector for subcarrier numberj, j = 1, 2, 3, ...N, respectively.

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802 M. Ghanbarisabagh / O

By the way, A and B in Eq. (1) are defined as:

=

⎡⎢⎢⎢⎢⎣

H1,1s1,1Iz 0 . . . 0

0 H2,2s2,2Iz . . . 0

......

. . ....

0 0 . . . HN,NsN,NIz

⎤⎥⎥⎥⎥⎦ (5)

= diag{

diag( B1,1 . . . Bz,1 ) . . . diag( B1,U . . . Bz,U )}

(6)

here Hj,u, sj,u, Bi,u, i and Iz are the channel coefficient matrix of theth subcarrier of uth user, the jth chip of the spreading code (SC)f uth user, symbol amplitude for corresponding transmit antenna,

= 1, 2, 3, . . ., z and z × z identity matrix, respectively.To have an accurate tradeoff between system performance and

omputational complexity, a MMSE algorithm is advised. xu is esti-ated as below using MMSE algorithm [5]:

˜u = zHu y (7)

here zu satisfies equation below:

u = arg(

min(E||xu − zHu y||2)

)(8)

By solving Eq. (8), zu will be obtained as [5]:

u = (E[yyH])−1

E[yxHu ] (9)

By replacing zu from Eqs. (7)–(9), x̃u will be obtained as:

˜u = E[xuyH](E[yyH])−1

y (10)

By substituting y from Eq. (3), E[xuyH

]and E

[yyH]

can bebtained as:

[xuyH] = E[xu(ABx + n)H] = E[xu(xHBHAH + nH)]

= E[xuxHBHAH] + E[xunH] = BHu AH + 0

= BHu AH = BH

u sHu HH (11)

here Bu is symbol amplitude for corresponding antenna. H and Slso are given as:

=

⎡⎢⎢⎢⎢⎣

H1,1 0 . . . 0

0 H2,2 . . . 0

......

. . ....

0 0 . . . HN,N

⎤⎥⎥⎥⎥⎦ . (12)

=

⎡⎢⎢⎢⎢⎣

s1,1 0 . . . 0

0 s2,2 . . . 0

......

. . ....

0 0 . . . sN,N

⎤⎥⎥⎥⎥⎦ . (13)

[yyH] = E[(ABx + n)(ABx + n)H] = E[(ABx + n)(xHBHAH + nH)]

= E[ABxxHBHAH + ABxnH + nxHBHAH + nnH]

= E[ABxxHBHAH + 0 + 0 + nnH] = E[ABxxHBHAH]

+ E[nnH] = E[HSBxxHBHSHHH] + E[nnH]

2 H H 2

= ||B|| HE[SS ]H + � IN2 (14)

here �2 is the variance of the noise and ||B||2 is defined as:

|B||2 = BBH (15)

25 (2014) 6801–6804

If the SCs for all active users are known by any user, then Eq.(10) will be obtained as:

x̃u = BHu sH

u HH(||B||2HSSHHH + �2IN2 )−1

y (16)

As each user must know the SCs for all active users, thereforesome information about signal needs to be sent time by time to theusers. Consequently, the SE will be reduced.

If the SCs for all active users are not known by other users butthey know the number of active users, then Eq. (10) will be obtainedas:

x̃u = BHu sH

u HH(||B||2HHH + �2IN2 )−1

y (17)

Using Eq. (17) to estimate xu compared to using Eq. (16), haslarger PL when the number of active users is less than number ofusers which be supported in a spreading block.

To overcome the problems mentioned above, a new algorithmis proposed to minimize the PL for the MMSE in CDMA based O-MIMO-OFDM systems. In this method, there is no need for the usersto know the SCs. Users must know the channel. However, to imple-ment the new algorithm, SSH in Eq. (16) must be estimated. Thecomputational complexity will not significantly increased by usingnew algorithm because SSH can be repeatedly used for multiplespreading block.

By multiplying both sides of Eq. (3) to H−1, Eq. (3) will be mod-ified as:

H−1y = H−1ABx + H−1n = H−1HSBx + H−1n = SBx + H−1n (18)

Now, the autocorrelation function of H−1y will be obtained as:

rH−1yH−1y = E[(H−1y)(H−1y)H

] = E[(SBx + H−1n)(SBx + H−1n)H

]

= E[SBxxHBHSH] + E[SBxnHH−1H] + E[H−1nxHBHSH]

+ E[H−1nnHH−1H] = ||B||2SSH + 0 + 0 + �2E[H−1H−1H]

= ||B||2SSH + �2rH−1H−1 (19)

rH−1H−1 can be broken down as:

rH−1H−1 = diag(rH−1

1H−1

1. . .r

H−1N

H−1N

) (20)

By assuming identical distribution for OFDM subchannels, we have:

rH−1

1H−1

1= r

H−12

H−12

= . . . = rH−1

NH−1

N(21)

Then, only rH−1

1H−1

1must be computed and Eq. (20) will be rewrit-

ten as:

rH−1H−1 = IN ⊗ rH−1

1H−1

1(22)

Then, by combining Eqs. (18) and (22), SSH will be obtained as:

SSH = 1||B||2 rH−1yH−1y − �2

||B||2 (IN ⊗ rH−1

1H−1

1)

= 1N||B||2

N∑i=1

H(i)−1y(i)y(i)HH(i)−1H

− �2

N||B||2N∑

i=1

H(i)−1H(i)−1H (23)

where H(i) and y(i) are channel matrix and received vector of the

ith spreading block, respectively.

SSH is a non-negative matrix so that second term of Eq. (23)must be smaller than the first term of Eq. (23). For the higher signalto noise ratio the second term is much smaller of the first term.

M. Ghanbarisabagh / Optik 125 (2014) 6801–6804 6803

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FS

Fig. 3. BER versus OSNR for a CDMA based O-MIMO-OFDM system over 1200 km ofSSMF using MMSE, MPL 1, MPL 2 and MPL 3 for 20 active users.

0.07-ps/sqrt(km) resulting a mean differential group delay (DGD)value of ∼2.5 ps. The Walsh-Hadamard code has been used as SC

Fig. 1. Block diagram of simulation setup.

herefore, to simplify Eq. (23) the second term of Eq. (23) can begnored. Then Eq. (23) will be obtained as:

SH = 1N||B||2

N∑i=1

H(i)−1y(i)y(i)HH(i)−1H (24)

Now, SSH given by Eq. (24) is substituted to Eq. (16) and the newlgorithm will be obtained to minimize the PL for the MMSE usingn CDMA based O-MIMO-OFDM systems over 1200 km of SSMF as:

˜u = BHu sH

u HH

(||B||2H

N||B||2

(N∑

i=1

H(i)−1y(i)y(i)HH(i)−1H

)× HH + �2IN2

)−1

y = BHu sH

u HH

(H

N

(N∑

i=1

H(i)−1y(i)y(i)HH(i)−1H

)× HH + �2IN2

)−1

y (25)

. Result and discussion

Two transmit and receive antennas are used in a direct-etection optical OFDM. What do antennas mean here is the outputf modulator going to SMF channel and the output of SMF channeloing to demodulator as shown in Fig. 1.

A 4-QAM constellation modulates 512 sub-carriers with theub-carrier spacing of 40 MHz. The duration of OFDM symbol is

= 25 ns and for transmission line, 15 spans of 80 km SSMF are used.he channel model with dispersion coefficient of 17 ps/(km-nm),avelength of 1.55 �m, fiber length of 1200 km and attenuation

oefficient of 0.2 dB/km is characterized by GVD. The contributions

f shot noise and thermal noise create the photodiode noise. Theyre independent random processes with approximately Gaussiantatistics [6]. Amplifiers with a flat gain of 20 dB and a noise fig-re (NF) of 5 dB employ after each span. Moreover, polarization

ig. 2. BER versus OSNR for a CDMA based O-MIMO-OFDM system over 1200 km ofSMF using MMSE, MPL 1, MPL 2 and MPL 3 for 10 active users.

Fig. 4. BER versus OSNR for a CDMA based O-MIMO-OFDM system over 1200 km ofSSMF using MMSE, MPL 1, MPL 2 and MPL 3 for 30 active users.

mode dispersion (PMD) coefficient of the lab fibers is considered

with the code length of 32. The data rate for optical OFDM itselfis 40.96 Gb/s (512 subcarrier × 40 MHz × 2 bit/symbol) but using

Fig. 5. BER versus OSNR and number of active users for the CDMA based O-MIMO-OFDM system over 1200 km of SSMF using MMSE, MPL 1, MPL 2 and MPL 3.

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804 M. Ghanbarisabagh / O

DMA technique reduce the data rate to 1.28 Gb/s (40.96/32 as SCode length). To evaluate the performance of new algorithm, MPL1,PL2 and MPL4 are defined to estimate SSH by selecting half of the

C from 1, 2 and 4 frames, respectively. The reason for choosing halff the SC from 1, 2 and 4 frames is just a choice. By using MATLAB,he bit error rate (BER) versus optical signal to noise ratio (OSNR) islotted to evaluate the system performance. The BER is measuredver a 12.5 GHz noise bandwidth, which is equivalent to 0.1 nm at550 nm.

Figs. 2–4 present the BER in terms of OSNR for the CDMA based-MIMO-OFDM system over 1200 km of SSMF using MMSE fromq. (17), MPL1, MPL2 and MPL4 for 10, 20 and 30 number of activesers, respectively. However, Fig. 4 shows the BER versus OSNR andumber of active users. According to Fig. 5, it is clear that by increas-

ng the number of active users, the BERs also have been increased.sing BER of 10−3 as a reference in Fig. 4, the maximum systemerformances that have been saved are 5.4 dB, 7.7 dB and 9.2 dB ifPL1, MPL2 and MPL4 are used instead of MMSE, respectively.

. Conclusion

An efficient algorithm is proposed to minimize the PL of MMSEn CDMA based O-MIMO-OFDM system over 1200 km of SSMF. Theerformance of the system using proposed algorithm scheme isompared to MMSE scheme by simulation results. The results showhe improvement of 5.4 dB, 7.7 dB and 9.2 dB since MPL 1, MPL 2 and

PL 3 are used, respectively.

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[

25 (2014) 6801–6804

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