1340 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 6, JUNE 2005

Impact of Fiber Chromatic Dispersion onthe BER Performance of an OpticalCDMA IM/DD Transmission System

S. P. Majumder, Member, IEEE, Afreen Azhari, and F. M. Abbou

Abstract—A theoretical analysis is presented to evaluate the im-pact of fiber chromatic dispersion on the bit-error-rate (BER) per-formance of a direct sequence optical code-division multiple-access(OCDMA) system with intensity modulation direct detection trans-mission link using sequence inverse keying optical correlator oper-ating at 10 Gchip/s. The numerical results show that the systemsuffers a power penalty of 3.48 dB corresponding to chromatic dis-persion index, = 0 3 for seven-chip m-sequence, at a BER of10

9. It is further noticed that the number of simultaneous usersare limited to 14 for = 0 1 and 10 for = 0 3, for 31-chip goldsequence, at 6-dB power penalty.

Index Terms—Fiber chromatic dispersion, gold sequence, in-tensity modulation direct detection (IM/DD), m-sequence, opticalcode-division multiple-access (OCDMA), sequence inverse keying(SIK).

I. INTRODUCTION

I N RECENT years, optical code-division multiple-access(OCDMA) systems are attractive as they offer several

attractive features such as asynchronous access, privacy andsecurity in transmission, ability to support variable bit rateand busy traffic, and scalability of the network. Until now,research on OCDMA focused on direct time spread OCDMA[1], spectral encoding–decoding, pulse position modulationOCDMA, asynchronous phase-encoding OCDMA [2], andfrequency hopping OCDMA [3], [4]. Most of the researchworks on OCDMA system, performance analyses are carriedout without considering the effect of fiber chromatic dispersion,which causes spreading and overlapping of chips and degradessystem performance due to increased interchip interference andreduced received optical power. Recently, the performance ofan asynchronous phase-encoded OCDMA system consideringfiber chromatic dispersion has been reported in [5] in the caseof standard single-mode and dispersion-shifted optical fiber. Inthis letter, analysis is carried out for direct-sequence OCDMAsystem with intensity modulation and direct detection (IM/DD)sequence inversion keyed (SIK) receiver [6], in the presenceof fiber chromatic dispersion and multiple access interference

Manuscript received February 15, 2005.S. P. Majumder is with Bangladesh University of Engineering and Technology

(BUET), Dhaka 1000, Bangladesh (e-mail: spmajumder@eee.buet.ac.bd;spmajumder2002@yahoo.com).

A. Azhari is with Military Institute of Science and Technology (MIST),Dhaka 1216, Bangladesh (e-mail: afreen_74@hotmail.com; afreen_74@yahoo.com).

F. M. Abbou is with the Faculty of Engineering, Multimedia University,Cyberjaya 63100, Selangor, Malaysia (e-mail: fouad@mmu.edu.my).

Digital Object Identifier 10.1109/LPT.2005.846924

Fig. 1. Schematic block diagram of an asynchronous OCDMA transmissionsystem with SIK.

(MAI) to evaluate the bit-error-rate (BER) performance degra-dation due to dispersion and to determine the power penaltysuffered by the system at a specific BER. Seven-chip m-se-quence, 127-, 31-, and 7-chip gold sequences are consideredto investigate the performance for different values of fiberchromatic dispersion index at a given chip rate of 10 Gchip/s.

II. SYSTEM DESCRIPTION

The schematic block diagram of an OCDMA transmissionsystem with asynchronous SIK correlator receiver is shown inFig. 1. In the transmitter, a user’s binary data is modulated ei-ther by a unipolar signature sequence or by its complement, de-pending on whether it is a “1” or “0,” respectively. In the re-ceiver, a bipolar reference sequence is correlated directly withthe channel unipolar signature sequence in order to recover theoriginal data by an all-optical correlator. The bipolar referencesequence is separated into two complementary unipolar refer-ence sequences by means of unipolar switching functions, todespread the incoming optical channel signal. This is subtractedin a balanced p-i-n diode receiver and then integrated over a databit period prior to detection.

III. SYSTEM ANALYSIS

At the transmitter, a sequence of unit amplitude rectangulardata bits each of duration s, , is used to SIK with ,

1041-1135/$20.00 © 2005 IEEE

MAJUMDER et al.: IMPACT OF FIBER CHROMATIC DISPERSION ON THE BER PERFORMANCE OF AN OCDMA IM/DD 1341

where is a periodic sequence of unit amplitude, rectan-gular chips each of duration and . The SIK mod-ulated signal then drives a laser diode, which gives the output,for the th user, as follows:

(1)

where is chip optical power for the th user at the transmitteroutput, corresponds to the th chip, and is the operator thatdenotes SIK modulation such that either the sequence orits complement is transmitted for a 1 or 0 data bit, respec-tively. is transmitted through the single-mode fiber, under-going dispersion; it gives the output at the end of the fiber.For the th user, it is given as

(2)

where is the received optical power which is the differencebetween transmitted power and fiber loss, stands for theoutput pulse shape due to fiber chromatic dispersion, given by[7]

(3)

where is the fiber chromatic dispersion index, is the optical carrier wavelength, is

the fiber chromatic dispersion coefficient, is the chip rate,is the length of the fiber. The OCDMA signal as well asall other users’ OCDMA signals are despread by the all-opticalcorrelator receiver with balanced photodetectors and thenpassed through an integrator. The correlator output matched tothe th user is given by

(4)

where is responsivity of each p-i-n photodiode, is thenumber of simultaneous users, is the complement of

, and is the total channel noise at the correlatoroutput. Since and

and , where

and are bipolar forms of ,and respectively, then (4) reduces to

(5)

The first term in (5) is the offset effect, removed by using bal-anced signature sequence. The third and fourth term in (5) arethe in-phase autocorrelation peak and MAI, respectively. Themean of and the variance of interference due to MAI

are given as [6]

(6)

(7)

where is the variance of the noise, represents receiverthermal noise, photodetector shot noise power, as

. The signal-to-noise ratio (SNR) and theBER at the correlator output can be obtained as

(8)

(9)

IV. RESULTS AND CONCLUSION

Following the analytical formulation, the BER performanceof an OCDMA system with fiber chromatic dispersion, is eval-uated at a chip rate of 10 Gchip/s. Fig. 2 shows the plot ofBER versus received optical power for different values offiber chromatic dispersion index ranging from .05 to 1 for anm-sequence 1 110 010. It can be observed that higher transmitterpower is needed with the increase of in order to maintain a

1342 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 6, JUNE 2005

Fig. 2. BER performance of an OCDMA transmission system with seven-chipm-sequence and DD-SIK receiver for different values of , when the chipsequence is 1 110 010.

Fig. 3. Plots of power penalty in signal power versus different values of fiberchromatic dispersion index for different types of seven-chip m-sequencepseudorandom code when the reference sequence is 1 110 010.

Fig. 4. Eye diagram of an OCDMA transmission system with seven-chipm-sequence and DD SIK receiver when the value of = 0:05 and the chipsequence is 1 110 010.

BER of . The system suffers a power penalty of 3.48 dBcorresponding to at a BER of for a seven-chipm-sequence. Fig. 3 depicts various plots of power penalty versus

at a BER of for seven different types of seven-chipm-sequences. It is found that the power penalty depends on thechange in position of 1 and 0 though the number of chips andnumber of “1s” and “0s” in all seven sequences are the same.Fig. 4 shows the simulated eye diagram for , while Fig. 5depicts the power penalty curves derived from the eye diagramswith different and from the average of the plots of Fig. 3, ob-tained from the BER performance. It is observed that the differ-ence between the two curves is less than 0.5 dB which validatesthe approximation made in carrying out the theoretical analysisfor BER. Fig. 6 depicts the plots of power penalty versus the

Fig. 5. Plots of the power penalty versus obtained from BER performanceand from eye diagram, for seven-chip m-sequence, 1 110 010.

Fig. 6. Plots of power penalty versus various numbers of users for differentvalues of , in case of 7-, 31-, and 127-chip gold sequence.

number of simultaneous users for the 7-, 31-, and 127-chip goldsequence with the values of as 0.1 0.3, 0.5, and 1. The receiversensitivity corresponding to 127-chip gold sequence is taken asthe reference to determine the power penalty at .The power penalty increases exponentially with the increasednumber of simultaneous users in each case. It is observed thatfor a specific chip sequence and power penalty, the number ofusers decreases with the increase in . For example, for an al-lowable power penalty of 6 dB, the maximum allowable numberof users is 14 for and for , for 31 chip gold se-quence. It is also evident that the increase in the sequence lengthresults in reduced power penalty.

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