performance analysis of equal-energy two-level ocdma

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 10, MAY 15, 2013 1573

Performance Analysis of Equal-Energy Two-LevelOCDMA System Using Generalized Optical

Orthogonal CodesHamzeh Beyranvand, S. Alireza Nezamalhosseini, Jawad A. Salehi, Fellow, IEEE, and

Farokh Marvasti, Senior Member, IEEE

Abstract—In this paper, we analyze and obtain perfor-mance of a multilevel Optical Code Division Multiple Access(OCDMA) system with Variable-Weight Optical OrthogonalCodes (VW-OOCs) under the same-bit-energy assumption. Theexact error-probability of this system is derived for the General-ized VW-OOCs (codes with arbitrary cross-correlation) which isnecessary for the optimum design of multilevel OCDMA systems.We show that the bit power has an important role on determiningthe performance of codes with different weights. Furthermore, theresults reveal that the performance of low-weight codes dependson the weight of the low-weight codes and the code-weight ratio oftwo classes. Moreover, our exact analytical model has resulted inmore accurate performance analysis than the upper bound in [12].We have found that the accuracy of the upper bound decreaseswhen the number of simultaneously transmitting high-weightcodes increases.

Index Terms—Equal-energy, optical code division multiple ac-cess, quality of service (QoS), variable weight.

I. INTRODUCTION

T HE recent developments of internet and communicationnetworks have caused in a dramatic increase in data

traffic. As a result, the user demand for high speed-high qualityservices with lower costs has also increased. The optical net-works have become efficient alternatives in order to resolvethe need for high data-rates and cost effective transport system.Meanwhile, the use of Optical Code-Division Multiple Access(OCDMA) has been introduced in order to support the growingdemand of data traffic in optical access networks [1]–[3] andalso as the optical label in optical packet and burst switchingnetworks [4]–[6]. However, new applications such as High-Def-inition Television (HDTV), e-learning, video conferencing,interactive gaming, have created diversified data traffic. Con-sequently, the support of multirate and differentiated-Qualityof Service (QoS) transmission is becoming one of the es-sential challenges for future optical networks. Multi-LengthOOC (ML-OOC), Variable-Weight OOC (VW-OOC), andMulti-Length Variable-Weight OOC (MLVW-OOC) have been

Manuscript received September 07, 2012; revised November 26, 2012; ac-cepted February 01, 2013. Date of publication March 07, 2013; date of currentversion April 10, 2013. This work was supported in parts by Iran National Sci-ence Foundation (INSF).The authors are with the Optical Networks Research Laboratory (ONRL),

Advanced Communications Research Institute (ACRI) and the Department ofElectrical Engineering, Sharif University of Technology, Tehran, Iran (e-mail:[email protected]; [email protected]; [email protected]; [email protected]).Digital Object Identifier 10.1109/JLT.2013.2250914

introduced to provide multirate and differentiated-QoS trans-mission in the OOC-based OCDMA systems [7]–[12]. Thebasic principles of these variable-weight codes are: 1) identicalpower in every optical pulse and 2) variation of the weights ofoptical codes without deteriorating their cross-correlation func-tions [11], [12]. Therefore, low-weight codes always carry lesspower per bit duration, and have lower autocorrelation peak.Hence, the performance of low-weight codes (in terms of errorprobability) is lower than high-weight codes. Moreover, lasersources have a power limitation in the sense that the amount ofoptical power generated per bit is limited. However, this limi-tation is not considered in the same-chip-power assumption inVW-OOC. In [12], a modified version of variable-weight codeshas been proposed in which the powers of transmitted bits areequal for various codes. Under such bit-power limitation, thechip power of each variable-weight code depends on the codeweight in use. In this system, which is referred to as multilevelOCDMA, in addition to the code parameters (code length, codeweight, cross-correlation), the chip-power ratio of lower- andhigher- weight codes affects the system performance.Generally, the design of OCDMA systems is an optimization

problem among the code parameters and the characteristics ofthe desired class of service. In [13], a framework was proposedto optimally design an ordinary OOC based OCDMA. In thisframework, code parameters such as code-weight, code-lengthand maximum cross-correlation are computed optimallyto minimize the error-probability subject to a fixed transmis-sion rate and number of users, or alternatively, to maximize thenumber of users subject to a fixed error-probability and trans-mission rate. The reported results revealed that the optimumvalue of is 2 and 3 [13]. This optimum designing frameworkcan be generalized to the design of both ordinary and multilevelVW-OCC based OCDMA.In [12], the code parameters and the power levels of equal-en-

ergyOCDMAwere designed for only the same-chip-power con-straint. Nonetheless, an optimal multilevel OCDMA can be de-signed if the code parameters, the number of transmitting powerlevels, and the values of power levels are computed by solvingan optimization problem. To this aim, the exact error-probabilityof multilevel OCDMA with generalized OOCs is necessary. Itis worth mentioning that the generalized OOC, i.e., codes with

, in comparison with ordinary OOC are preferable dueto its better performance and greater number of available code-words [13].The performance of equal-energyOCDMAwas first analyzed

in [12] by obtaining an approximate upper bound for the error-

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1574 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 31, NO. 10, MAY 15, 2013

probability of 1-D MLVW-OOCs. Chen, et al. [14] improvedthis error-probability upper bound with an approximationmodelfor both 1-D and 2-D codes. Furthermore, the exact performanceanalytical model for 1-D and 2-D codes has been derived in[15]. However, this exact performance analytical model wasproposed for codes with cross-correlation functions of at mostone (i.e., ).In this paper, we shall develop a new analytical model for the

performance of 1-D and 2-D codes with cross-correlation func-tions of at most three (i.e., ). This exact model is bene-ficial to solve the optimization problem of designing multilevelOCDMA systems under the same-bit-energy assumption. In ad-dition, the model is also essential for power-sensitive applica-tions, such as service monitoring and fiber-fault surveillance inoptical networks and sensor identification in fiber-sensor sys-tems [16], [17].The remainder of this paper is organized as follows: Section II

presents the multilevel signaling and the equal-energy multi-level OCDMA systems. In Section III, the exact performanceanalysis for multilevel OCDMA system is derived. Section IVis devoted to numerical discussion and comparisons between theexact and upper bound performance analysis. Finally, the paperis concluded in Section V.

II. AN OVERVIEW ON MULTILEVEL SIGNALING ANDEQUAL-ENERGY MULTILEVEL OCDMA SYSTEM

Multilevel signaling has been proposed to improve the per-formance of 1-D OOC based OCDMA systems and to sup-port multiclass transmission [11]. In a typical M-level OCDMAsystem, users are divided into M classes and users of each classtransmit at a different power level. Two structures were pro-posed to be employed for the receiver of multilevel OCDMAsystem, namely, asymmetric and symmetric [11]. The asym-metric receiver of each class is an ordinary AND logic receiverin which the input hard-limiter is designed based on the powerlevel of the class. On the other hand, in symmetric structures,instead of the input-hard limiter, an interference cancellationblock is employed which is designed based on optical logicgates such as optical AND, OR and XNOR elements.In asymmetric multilevel OCDMA system, optical energy

is unfairly divided among high and low power users, andclearly high-power users have a better performance. In orderto improve the performance of low-power users without usingcomplex symmetric receiver structures, in [12] the equal-en-ergy multilevel system was introduced.In equal-energy multilevel OCDMA, the code weight of low-

power users is greater than that of high-power users, hence,variable-weight optical orthogonal codes are required. Variable-weight optical orthogonal codes in both 1-D and 2-D OCDMAsystems have been introduced to support different QoS [7]–[10].In an ordinary variable-weight OCDMA system, high-weightcodes have a better performance (lower probability of error, ).However, in equal-energy multilevel systems, the performanceof low-weight codes can be improved by choosing appropriatevalues for power levels and code weights. Let ,where denotes the ceiling function, and are the powerlevel of class 1 and class 2 users, respectively . Then,at the receiver of high-power users (class 2 users), there mustbe at least low-power interfering pulses to generate one hit.

The probability of error of class 1 in both one-level andmultilevel system are the same which can be computed by usingthe equations given in [11] and [16] for 1-D and 2-D OCDMAsystems, respectively. On the other hand, due to the suppressionof low-power interfering pulses at the receiver of class 2, theevaluation of the probability of error in class 2 is differentthan .There are three approaches in the literature to obtain [12],

[14] and [15]. In [12], an upper bound for in equal-energy1-D OCDMA system was derived. The upper bound was eval-uated for optical codes with arbitrary cross-correlation .Chen, et al. [14] obtained a lower bound for of both 1-Dand 2-D OCDMA systems; and recently Yang et al. [15] accu-rately evaluated . The accurate performance analyses waspresented for 1-D and 2-D OCDMA systems based on opticalcodes with , [15]. In the present paper, we analyze accu-rately the performance of equal-energy 1-D and 2-D OCDMAsystems based on the generalized OOC, ., optical codes with

and . It is worth mentioning that the accurateperformance analyses of OCDMA with and isnecessary to optimally design equal-energy OCDMA systems.As shown in [13], the optimal design of OCDMA system is anoptimization problem among OCDMA parameters such as codeweight , code length , cross-correlation , the toler-able probability of error , and the number of simultaneouslytransmitting users . It was shown that the optimum valueof is between 1 and 3 (i.e., [13].

III. PERFORMANCE ANALYSIS

In the previous studies, the performance of multilevelOCDMA system has been evaluated considering only the effectof Multiple Access Interference (MAI). In this paper as wellwe only investigate MAI effect as our paper is focused onthe derivation of accurate for OCDMA with and. Furthermore, our MAI analyses can be generalized to theeffects of other types of noise, such as laser beat noise, shotnoise, and thermal noise by utilizing the results of [19], [20].The error probability of low-power user in multilevel

VW-OOC based OCDMA, , was analyzed for on-offkeying (OOK) modulation, and was obtained as follows[12],

(1)

where indicates the number of class t interfering users anddenotes the probability that the class i desired user gets

interference hits from a class t user such that:

(2)

where denotes the code length and indicates the number ofwavelengths in 2-D OCDMA system. In 1-D OCDMA system,is set to 1. The evaluation of is not straightforward, and

BEYRANVAND et al.: PERFORMANCE ANALYSIS OF EQUAL-ENERGY TWO-LEVEL OCDMA SYSTEM 1575

this is mainly due to the multilevel interference pattern gener-ated by low-power interfering users.Generally, the error probability of high-power users, can

be evaluated as

(3)

where represents the probability that marked chips arehit by low-power interfering pulses generated by class 1interfering users, and denotes the probability thatmarked chips are interfered by high-power interfering pulsesreceived due to the presence of class 2 interfering users.Furthermore, and in (3) are defined as

(4.a)

(4.b)

where denotes the number of hits occurred in the th markedchip of the desired class 2 user. Generally, can be com-puted by using the same approach employed to obtain , whilethe evaluation of due to the multilevel property of the in-terference pattern is complex. In [12], was approximatelycomputed using the following upper bound,

(5)

Furthermore, Chen, et al. [14] employed a Markov chainmethod and derived another approximation for whichrecently Yang, et al. [15] showed that the Chen’s relation [14]is a lower-bound for . Yang, et al. [14] presented a recursivemethod to accurately derive for 1-D and 2-D OCDMAsystem with . This relation is given by [15],

(6)

where is a recursive function denoting the number ofall interference patterns generated by low-power interferingusers in which each marked chip is hit by at least low-powerpulses, and has the same definition as . However,these parameters are slightly different; , unlike ,does not satisfy (2) but obeys the relation

. Hence, by comparing this relation and (2), we

have . These notational differences are

due to [13] and [18]. In the rest of the paper, in order to avoidconfusion, we use as the hit probability.It is worth mentioning that was first introduced

by Azizoglu, et al. [21] to analyze the performance of 1-DOCDMA systems for . The number of patterns in which

all marked chips of the desired user are hit at least by oneinterfering pulse is computed by as shown below [21]:

(7)

In [15], was recursively related to using theproperty of union of events as follows:

(8)

In what follows, we generalize to compute forboth 1-D and 2-D OCDMA systems with and 3. First,we show that can be generalized to obtain of ordinaryone-level OCDMA system with and .In Appendix, the generalized is derived as,

(9.a)

(9.b)

where denotes the number of interfering users that generatehits. Note that in the above equations, for the sake of simplicity,

we assumed that if , then . In Appendix, we will

show that by using the generalized , the of an OCDMAsystem, for an ordinary OOCs with is obtained as,

(10)


Surprisingly, (10) is the same as the relation obtained in [18] byusing a Markov chain method. In the next subsections, we willtry to evaluate the generalized . First, we drive ofOCDMA system with and then the results are extendedto obtain of the system with .

A. Derivation of in an OCDMA System With

In order to evaluate the probability of error for class 2 users inboth 1-D and 2-D OCDMA systems with , it is sufficientto compute the corresponding function as follows:

(11)

where is computed recursively based onfrom the property of union of events. First,and are obtained, then the results are

extended to derive . Similar to (8), we have

(12)

where is the number of interference patterns in which thefirst chips have exactly one hit and the other chips have at leastone hit. Hence, is defined as,

It should be noted that (8) can be interpreted the same as (12).By generalizing the approach used in (8), is evaluated as,

(13)

where is the number of permutations andinterfering users have to occupy positions and all positionshave exactly hits. It should be noted that all interfering pulsesmust be equal to the number of available positions which is

. Moreover, denotes the number of interfering userswhich have one interfering pulse, and indicates the numberof interfering users which interfere with two pulses. Hence, thenumber of all interfering pulses are which must be equalto (i.e., . For the sake of simplicity,in the rest of the paper, the users with one and two interferingpulses are referred as group 1 and group 2 users, respectively. InFig. 1(a), the relation between and have beenillustrated schematically.

It is worthy to note that the right-hand side of (13) representsthe number of states that the first chip has exactly one hit and theother chips have at least one hit. Furthermore, in this equation,the first term counts all states in which the first chip is interferedby one pulse of the group 1 users, while the second term showsall states that the first chip is hit by one pulse of the group 2users. Note that in the states shown by the second term, whenone of the pulses of a group 2 user hits the first chip, the re-maining pulse is considered as a group 1 user. Thus, as it canbe seen in the second term, the number of group 1 users wasincreased to . Similarly, can be obtained as,

(14)

where counts all the states in which the first and secondchips have exactly one interference and the other chips have atleast one hit. In the right-hand side of (14); the first term repre-sents all the states that the two chips are hit by two individualpulses of group 1 users. The second term shows all the statesin which one chip is hit by a group 1 user, and the other oneis hit by one pulse of a group 2 user. The third term shows allthe states that one chip is hit by one pulse of a group 2 user andthe other one is hit by one pulse of another group 2 user. Fi-nally, the forth term shows all the states that both chips are hitby two pulses of an individual group 2 user. Pursuing the aboveapproach, is given in (15),

(15)

In (15), denotes the number of permutations ofgroup 1 and group 2 users to occupy chips in which all chipshave exactly one hit.The number of permutations can be obtained recursively as

follows:

(16)


Fig. 1. Relation of (a) and , and (b) and .

The recursive relation of and is de-rived by using (12) as follow:

(17)

where represents the number of interference patterns inwhich thefirst chipshaveexactly two interferencesand theotherchipshaveat least two interferences.Therefore, isdefinedas:

Considering the same approach employed in (13), can beobtained as follows:

(18)

where thefirst term shows the patterns inwhich thefirst chip is hitby two group 1 interferences; the second term represents the pat-terns that thefirstchip ishitbyagroup1interferenceandonepulse

of a group 2 interference, and the last term counts the number ofpatterns in which the first chip is hit by two pulses of two group2 interferences. In Fig. 1(b), we demonstrate a simple pattern foreach term in (18) in order to understand the derivation of .Continuing the above procedure, can be derived as follows,

(19)

where the right-hand side of (19) counts all interference patternsin which the first two chips have exactly two interferences andthe other chips have at least two interferences. The first term


shows the patterns in which the first two chips are hit by fourgroup 1 interferences; the second term represents the patternsthat the first two chips are hit by three group 1 interferences anda pulse of a group 2 interference, and so on. Obtaining the other

is derived as follows,

(20)

where as shown in Fig. 2(a) is obtained recursivelyas follows,

(21)

where is the number of permutations of group1 and group 2 interferences to occupy positions and to gen-erate two-level interference patterns (i.e., patterns in which allpositions have exactly two hits). Furthermore, out of posi-tions have one hit before interfered by group1 and group2interferences. As shown in Fig. 2(b), is evaluatedas (22), shownat the bottomof the page. In general,we canobtain

recursively by continuing the above procedure as (23),

(23)

In (23), denotes the number of permutations thatgroup 1 and group 2 interferences have to occupy posi-

tions with exact hits. Generalizing (21), we have (24),shown at the bottom of the page, where is thegeneral form of . Also,where denotes the number of positions with hits. By gen-eralizing (22), is obtained as (25), shown atthe bottom of the page, where is the modified computedas (26), shown at the bottom of the page. By utilizing the above

(22)

(24)

(25)

(26)


Fig. 2. Evaluation of (a) and (b) .

formulations, the exact value of is computed, and by em-ploying (4a), the exact can be obtained. In the next subsec-tion, we will extend the above formulations to obtain ofOCDMA with .

B. Derivation of in an OCDMA System With

As described in the previous subsection, to obtain the prob-ability of error for class 2 users in both 1-D and 2-D OCDMAsystems, the corresponding function should be derived. Forthe case of OCDMA systems with is evaluated asfollows:

(27)


where denotes the number of interfering users hitting threemarked chips of the desired user, and canbe derived following the same procedure applied to obtain

. For the case 2, is obtainedas follows:

(28)

where is given in (9b) and is obtained asfollows:

(29)

Continuing the above approach, we have:

(30)

where is obtained by generalizing(24) as (31), shown at the bottom of the page. In (31),

is obtained by generalizing (25) as (32),shown at the bottom of the page. In (32), is computed usingthe generalized (26). It should be noted that in (31) for the case

and , the extended version of (22) can beused. At this point, we can use the above relations to computethe probability of error of multilevel OCDMA with .

IV. NUMERICAL SIMULATIONS AND COMPARISONS

In order to validate the derived formulas on the probabilityof error, we should compare the error probabilities obtained inthis paper with the error probabilities upper bound derived in[12]. The use of 1-D double-weight codesis considered here. It should be noted that the error probabilityof the high-weight codes, , in both the approximation modelin [12] and the exact model in this paper are identical. Therefore,

(31)

(32)


Fig. 3. Same-bit-energy, hard-limiting error probabilities, , of thelow-weight codes versus the number of simultaneously transmittinghigh-weight codes for and .

Fig. 4. Same-bit-energy, hard-limiting error probabilities, , of thelow-weight codes versus the number of simultaneously transmitting low-weightcodes for and .

we only compare the error probabilities of the low-weight codes,, in the approximation and exact models.Fig. 3 shows the hard-limiting probability of error, , of

the low-weight codes in the 1-D double-weight codes versus the number of simultaneously transmittinghigh-weight codes under the same-bit-energy assumption,where . The dotted curve is based oncalculation derived from [12] and the solid curve is based on theexact formulation derived in this paper. As depicted in Fig. 3, as

or increases, there are more interfering codes, andtherefore the probability of errors begin to degrade. Hence, toacquire a satisfactory performance the number of active usersshould be limited. As an example for the numberof active class 1 and class 2 users should be limited by 10 and 5,respectively, otherwise, the desired of will be deteri-orated. Furthermore, the solid and dotted curves agree initiallywhen is small but as increases, the solid curves be-come worse. Therefore, the performance upper bound is moreaccurate when the number of users decreases.Fig. 4 illustrates the hard-limiting probability of error, , of

the low-weight codes in the 1-D double-

Fig. 5. Same-bit-energy, hard-limiting error probabilities, , of thelow-weight codes versus code weight , where .

weight codes versus the number of simultaneously transmittinglow-weight codes under the same-bit-energy assumption,where , and . Therefore,the probability of errors are shown for different values of

.As shown in the figure, for a fixed , the probability of

error get worse as increases, because there are more in-terfering code. In addition, by decreasing , the probability oferror gets worse. This is due to the fact that the interfering high-weight codes must contribute at least c hits onto the markedchips of the low-weight code in order to constitute one com-plete hit after the hard-limiter. As a result, by increasing c, thenumber of interfering high-weight codes required to contributea hit is increased.Fig. 5 shows the hard-limiting error probabilities, , of the

low-weight codes in the 1-D double-weight codes. In this figure, we consider the weight of class1 users, i.e., , as a constant parameter. Then is plottedas a function of , and is chosen as a variable less than. We have chosen in the range of 3 to 14, and

. Furthermore, the total number of users in bothclasses is 40, and . The dotted curve isbased on calculation derived from the performance upperbound of the 1-D low-weight codes. The solid curve is basedon the exact formulation derived in this paper. As depicted inthis figure, by increasing , the performance of class 2 users isimproved.

V. CONCLUSION

In this paper, we have analyzed the effect of the same-bit-en-ergy double weight codes in OCDMA systems with differ-entiated-QoS. We derived the exact performance analysis forVW-OOCs with cross-correlation greater than 1 by modelingthe multilevel interference patterns. We showed that the bitpower has an important effect on determining the performanceof codes with different weights. From our analysis, we havefound that the performance of low-weight codes depends onthe weight of the low-weight codes and the code-weight ratioof two classes. We have shown that the performance of thelow-weight codes is always improved when the code-weightratio increases. In addition, our exact analytical model hasresulted in more accurate performance analysis than the upper


bound in [12]. We have found that the accuracy of the upperbound decreases when the number of simultaneously transmit-ting high-weight codes increases.

APPENDIX

In this Appendix, we show that the procedure introduced byAzizoglu et al., [21] can be generalized to OCDMA systemswith . As mentioned, Azizoglu et al. [21] derived theprobability of error of the OCDMA system with asfollows:

(A.1)

Substituting in (A.1), we have:

(A.2)

We can generalize the above approach to obtain of theOCDMA with and . First, the corresponding func-tion, i.e., , is derived as,

(A.3)

Similarly, the probability of error can be evaluated as,

(A.4)

By substituting (A.3) into (A.4), we get,

(A.5)

Using the same procedure for , we have,

(A.6)


and

(A.7)

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Hamzeh Beyranvand was born in Khorramabad, Iran, on June 27, 1984. Hereceived the B.S. degree (with honors, first rank) in electrical engineering fromShahed University, Tehran, Iran, in 2006 and the M.S. degree from SharifUniversity of Technology (SUT), Tehran, Iran, in 2008, where he is currentlyworking toward the Ph.D. degree in the Department of Electrical Engineering.Since summer of 2007, he has been working as a member of the Optical

Networks Research Laboratory (ONRL), SUT. His research interests includeoptical CDMA systems, wireless indoor optical CDMA, optical OFDMA, freespace optical communication, GMPLS network, QoS provisioning in opticalnetworks, queuing theory, wireless networks, and RFID systems.

S. Alireza Nezamalhosseini was born in Iran in 1984. He received the B.S. de-gree from Amirkabir University of Technology (AUT), Tehran, Iran, in 2006,and the M.S. degree in electrical engineering from Sharif University of Tech-nology (SUT), Tehran, Iran, in 2008, where currently he is working toward thePh.D. degree in the Department of Electrical Engineering.He is also a member of Advanced Communications Research Institute

(ACRI).

Jawad A. Salehi (M’84–SM’07–FM’10) was born in Kazemain, Iraq, on De-cember 22, 1956. He received the B.S. degree from the University of California,Irvine, CA, USA, in 1979, and the M.S. and Ph.D. degrees from the Universityof Southern California (USC), Los Angeles, CA, USA, in 1980 and 1984, re-spectively, all in electrical engineering.He is currently a Full Professor at the Optical Networks Research Labora-

tory (ONRL), Department of Electrical Engineering, Sharif University of Tech-nology (SUT), Tehran, Iran, where he is also the Co-Founder of the AdvancedCommunications Research Institute (ACRI). From 1981 to 1984, he was a Full-Time Research Assistant at the Communication Science Institute, USC. From1984 to 1993, he was a Member of Technical Staff of the Applied ResearchArea, Bell Communications Research (Bellcore), Morristown, NJ. During 1990,he was with the Laboratory of Information and Decision Systems, Massachu-setts Institute of Technology (MIT), Cambridge, as a Visiting Research Scien-tist. From 1999 to 2001, he was the Head of the Mobile Communications Sys-tems Group and the Co-Director of the Advanced andWideband Code-DivisionMultiple Access (CDMA) Laboratory, Iran Telecom Research Center (ITRC),Tehran. From 2003 to 2006, he was the Director of the National Center of Excel-lence in Communications Science, Department of Electrical Engineering, SUT.He is the holder of 12 U.S. patents on optical CDMA. His current research in-terests include optical multi-access networks, optical orthogonal codes (OOC),fiber-optic CDMA, femtosecond or ultrashort light pulse CDMA, spread-timeCDMA, holographic CDMA, wireless indoor optical CDMA, all-optical syn-chronization, and applications of erbium-doped fiber amplifiers (EDFAs) in op-tical systems.Prof. Salehi is an Associate Editor for Optical CDMA of the IEEE

TRANSACTIONS ON COMMUNICATIONS since May 2001. In September 2005,he was elected as the Interim Chair of the IEEE Iran Section. He was therecipient of several awards including the Bellcore’s Award of Excellence,the Nationwide Outstanding Research Award from the Ministry of Science,Research, and Technology in 2003, and the Nation’s Highly Cited ResearcherAward in 2004. In 2007 he received Khwarazmi International prize, firstrank, in fundamental research and also the outstanding Inventor Award (Goldmedal) from World Intellectual Property Organization (WIPO), Geneva,Switzerland. He is among the 250 preeminent and most infiuential researchersworldwide in the Institute for Scientific Information (ISI) Highly Cited in theComputer-Science Category. He is the corecipient of the IEEE’s Best PaperAward in 2004 from the International Symposium on Communications andInformation Technology, Sapporo, Japan.


Farokh Marvasti received the B.S., M.S., and Ph.D. degrees all from Rensse-laer Polytechnic Institute, Troy, NY, USA, in 1970, 1971 and 1973, respectively.He has worked, consulted and taught in various industries and academic insti-

tutions since 1972. Among which are Bell Labs, University of California Davis,Illinois Institute of Technology, University of London, King’s College. He iscurrently a professor at Sharif University of Technology and the director Ad-vanced Communications Research Institute (ACRI) and a former head of Centerfor Multi-Access Communications Systems. He is presently spending his sab-batical leave at the Communications and Information Systems Group of Uni-versity College London.

Dr. Marvasti was one of the Editors and Associate Editors of IEEETRANSACTIONS ON COMMUNICATIONS AND SIGNAL PROCESSING from1990-1997. He has about 100 Journal publications and has written severalreference books; he has also several international patents. His last book ison Nonuniform Sampling: Theory and Practice (Kluwer, 2001). He was alsoa Guest Editor on Special Issue on Nonuniform Sampling for the SamplingTheory and Signal and Image Processing Journal, May 2008. Besides beingthe co-founders of two international conferences (ICT’s and SampTA’s), hehas been the organizer and special session chairs of many IEEE conferencesincluding ICASSP conferences.

performance analysis of equal-energy two-level ocdma

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