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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 9, SEPTEMBER 2006

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DS-OCDMA Receivers Based on Parallel Interference Cancellation and Hard Limiters Claire Goursaud, Student Member, IEEE, Anne Julien-Vergonjanne, Member, IEEE, Christelle Aupetit-Berthelemot, Member, IEEE, Jean-Pierre Cances, Associate Member, IEEE, and Jean-Michel Dumas

Abstract—In an incoherent direct-sequence optical code-division multiple-access (DS-OCDMA) system, multiple-access interference (MAI) is one of the principal limitations. To mitigate MAI, the parallel interference cancellation (PIC) technique can be used to remove nondesired users’ contribution. In this paper, we study four DS-OCDMA receivers based on the PIC technique with hard limiters placed before the nondesired users or before the desired user receiver, or both. We develop, for the ideal synchronous case, the theoretical upper bound of the error probability for the four receivers. Significant performance improvement is obtained by comparison with conventional receivers in the case of optical orthogonal codes. The paper highlights that the number of active users with null error probability is doubled, compared with conventional receivers. Finally, we show that, thanks to their good performances, the PIC structures permit considerably reducing the minimal code length required to have 30 users with bit-error rate < 1009 . So, the hardware constraints are relaxed for realistic application. Index Terms—Hard limiter (HL), multiple-access interference (MAI), optical code-division multiple access (OCDMA), optical orthogonal codes (OOCs), parallel interference cancellation (PIC).

I. INTRODUCTION HE code-division multiple-access (CDMA) method, adapted from the cellular phone network, has appeared for several years as a multiple-access solution for flexible high-speed optical networks. This technique, called optical CDMA (OCDMA), works by assigning each user a specific code, and could provide an asynchronous and simultaneous access to several users [1], [2]. Much research has been reported on incoherent OCDMA systems, which require lower complexity than the coherent ones. In such systems, the incoherent optical signal processing uses unipolar quasi-orthogonal codes that must have good correlation properties in order to reduce the undesired interference due to the other users. The system performance can also suffer from different noises: the beat noise linked to the coherence time of the light source and the receiver noise (thermal noise, shot noise…). However, for an OCDMA incoherent system employing light (with as the light pulse duration [3]), sources as and conventional correlation receivers (CCRs) [1], it has been

T

Paper approved by W. C. Kwong, the Editor for Optical Communications of the IEEE Communications Society. Manuscript received August 31, 2005; revised January 15, 2006. This paper was presented in part at GLOBECOM, St. Louis, MO, 2005. The authors are with the University of Limoges/ENSIL–GESTE–CNRS FRE2701, BP 6804, 87068 Limoges, France (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TCOMM.2006.881252

shown that the multiple-access interference (MAI) is the dominant limitation to the performance [3]. With a conventional receiver, in order to support many simultaneous users with low MAI, very long optical code sequences have to be used. This means that, for high data rates, a very large bandwidth is necessary, not yet provided by the encoding and correlating hardware. To reduce code length and maintain good performance, a solution exists in the MAI mitigation. Several studies have shown that MAI can be well-mitigated in synchronous systems [4]–[6], or in coherent ones [7], [8]. Because of the complexity and the cost of such systems, we focus on an incoherent asynchronous OCDMA system. As regards asynchronous incoherent temporal coding systems, several interference-cancellation techniques have appeared in the literature, aiming at improving the system performance by cancelling MAI [9]–[24]. The simplest techniques are based on the use of a hard limiter (HL). Salehi and Brackett [9] showed that the optical HL (OHL) placed before the optical correlator at the receiver side is able to remove some of the interference patterns. To improve the performance, a solution with double HL (DHL) has been proposed by Ohtsuki et al. [10], [11]. Lin and Wu [12] have proposed a synchronous OCDMA system with an adaptive OHL placed after the correlator receiver. They show that the performance can be improved, compared with the system with DHL. The other studies on interference-cancellation techniques are inspired by radio frequency (RF) communications, such as multiuser detection [13]–[16], parallel interference cancellation (PIC) [17]–[22], serial interference cancellation [23], or turbo codes [24]. These techniques are more complex than the HL techniques, but they are more efficient. For example, in [21] and [22] Shalaby et al. have presented several interference-cancellation techniques which significantly improve the performance for a modified prime sequence. In the case of optical orthogonal codes (OOCs), we have previously demonstrated that the PIC technique is a performing method for MAI reduction [19]. To improve the PIC receiver efficiency by the simplest way, we design new interference-cancellation schemes for direct-sequence (DS)-OCDMA systems, based on the use of an HL device and the PIC technique. We describe four receivers: named PIC (no HL), PIC+HL (HL in front of the desired user receiver), HL+PIC (HL in front of the nondesired users receivers), and HL+PIC+HL (HL in front of both). These receivers have been studied for the OOCs family [1]. Our contribution is five-fold: we first demonstrate theoretically that in opposition to the conventional receivers, these receivers could lead to an error only if the desired user sent a data

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“one.” Then, considering only MAI, we develop the theoretical error-probabilities expressions for the synchronous case, which provides an upper bound of the error probability for the asynchronous case. Moreover, with the choice of a particular set of parameters, we will prove that the error probability is null. This result permits determining the maximum number of active users for an error-free system. In addition to that, with the theoretical expressions, we compare the performance evolution as a function of the OOC parameters. Finally, we show that such receivers permit decreasing the code length required to have a bit-error . This is a more realistic approach for rate (BER) inferior to application of OCDMA to a high-speed multiple-access system than conventional ones. II. DS-OCDMA SYSTEM A. The DS-OCDMA Structure We consider an incoherent, DS-OCDMA system. Each user employs an on–off keying (OOK) modulation to transmit independent and equiprobable binary data upon an optical channel. A sequence code is impressed upon the binary data by the encoder. The sequence code is specific to each user, in order to be able to extract the data at the end receiver: the received signal would be compared with the sequence code for the data recovery.

We consider that the desired user is . With a CCR described is multiplied by the code sequence in [1], the received signal , then the result is intecorresponding to the desired user grated. We get the decision variable value

(3) where denotes the bit duration. The second term in (3) is the interference due to all the nondesired users. It is the MAI term. is compared with the deciThe decision variable value sion threshold level of a decision device, then an estimation is given. Because of the CCR strucof the transmitted bit ture, and because of the decision variable which is bigger than or equal to what it should be, an error can occur only when is a zero datum and the MAI term is greater than the threshold level value . In this case, the desired user’s code chips are overlapped by at least nondesired user chips from users who sent a “1.” It has been shown [1] that the analytical upper-bound expresfor the ideal chip-synchronous sion of the error probability case is

B. Optical Orthogonal Codes We consider OOCs [1] in this paper. A class of codes is defined by , where is the sequence length and the weight. and are the auto- and cross-correlation constraints. The maximum number of users in the OOC class is defined as with

(4) D. CCR With HL (HL+CCR) The HL+CCR receiver is made of an HL device in front of a CCR receiver. The HL is an optical device that reduces the as received optical power. Its function can be defined by

(1) if if

C. Conventional Correlation Receiver In realistic systems, the performance can be limited by the MAI, by the noises due to the optical and electronic components, and by impairments of the optical link. In order to study the MAI cancellation, we consider that all the optical and electronic components are ideal, i.e., errors are only due to MAI. Moreover, all the users are supposed to have the same transmitting energy, so there is no strongest interfering signal. is the sum of In this case, at the receiver end, the signal the users’ signal

(5)

where the optical power of one chip is normalized to “1.” Therefore, a received optical power bigger than or equal to one will be set to one, whereas a received optical power smaller than one will be set to zero. Consequently, for , all the code chips must be overlapped to create an error, and all the other interference patterns are cancelled. It has been shown [1] that the theoretical expression of the HL+CCR’s error-probability upper bound for the ideal chipsynchronous case is (6)

(2) III. PARALLEL INTERFERENCE CANCELLATION where

is the sequence code of the th user, and is the th datum bit of the th user. We consider an ideal . It has been shown [1] that the synchronous case, i.e., synchronous case is the worst case. Thus, the synchronous results upper bound the asynchronous ones.

A. Principle In a PIC structure (Fig. 1), the interference due to all the nondesired users is estimated in order to be removed from the renondeceived signal [19], [20]. The first stage detects the

GOURSAUD et al.: DS-OCDMA RECEIVERS BASED ON PARALLEL INTERFERENCE CANCELLATION AND HARD LIMITERS

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Fig. 1. PIC structure. Fig. 2. HL+PIC structure. TABLE I RECEIVER’S NAME CORRESPONDING TO THE DESIRED AND NONDESIRED USERS’ RECEIVER STRUCTURE

The decision-making concerning is related to user #1’s decision variable, which is expressed as

(8)

In this section, the expressions of the error probability for the four receivers based on PIC will be demonstrated in a synchronous case, for OOCs and for simultaneous users. We consider the same threshold level ( ) nondesired users’ receivers. The threshold level for the ( ). for user #1 is The methodology used to establish the mathematical expression of the error probability is the theoretical counting of errors: we define the cases when an error occurs. In a general way, the error probability can be written as

is called The term the interfering term. Errors on user #1’s data are due to this term. Indeed, let user # be a nondesired user. is the interference term due to user # on user #1. is either null when there is no error, or non-null when there is an error. With conventional receivers (CCR and HL+CCR), an error can occur only when the sent data . In the synchronous case, is a “0.” In this case, as is either equal to 1 (overlapping) or 0 (no overlapping), is either null or equal to . When is equal to , the user # is called the interfering user. The interfering users are the ones that sent a 0 detected as a 1, and have a common chip with user #1. is either null or equal to , is alAs ways negative or null. As one interfering user generates an in, interfering users generate an interference of terference of ; thus, is an integer number and corresponds to the number of interfering users. Because of the negative interference term , the decision variable is less than (or equal to) what it should be. So, there can be errors only for . Indeed: , we have , so • for is always well detected; • for , we have , thus, there can be i.e., error on user #1 if

(7)

(9)

sired users data. Then the estimation of the nondesired user # ’s data is spread by the corresponding code sequence. The estimated interference is removed from the received signal. In the next stage, the bit sent by the desired user (whom we consider to be user #1) is evaluated. The desired and nondesired users’ receivers can be either CCR or HL+CCR. We name the corresponding receivers as shown in Table I. For example, the HL+PIC structure is represented in Fig. 2. B. Theoretical Analysis

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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 9, SEPTEMBER 2006

Thus, with PIC, there can be errors only if the desired user , contrary to the CCR. Therefore, has sent a data the expression of the error probability is

(10) . In this case, From now on, we consider the case can be expressed as a function of the probabilities of two dependant events: for a nondesired user # who sent a “0” • the probability to be an interfering user, when ; , the error probability for • for all possible values of user #1, i.e., the probability that when , interfering users. assuming that there are For the determination of and , we consider that , nondesired users sent a “1.” and that C. Expression of is the probability for a nondesired user to be an interfering user, thus is linked to the nondesired user’s receiver struc. So, ture, and the nondesired user’s receiver threshold level according to the we have to calculate two expressions for and ). nondesired user receiver ( For the two receiver structures, is the probability for a nondesired user # who sent a “0” to have an overlapping with user #1’s code, and to have its datum detected as a “1” instead of a “0.” So

1) Case A: If the nondesired user’s receiver is a CCR, in nondesired order to create an error, there must be at least users who sent a “1.” users interfering among the A nondesired user # who sent a “1” is interfering with user , with probability . So, # if users among are interfering with user # with the probability

There are at least with the probability

interfering nondesired users among

(13) 2) Case B: If the nondesired user’s receiver is an HL+CCR, the interfering signal must contain contributions from at least nondesired users who sent a “1,” at the same time, and the overlaps must be on different chips and must not be on the same chip as user #1’s. So, there must be overlaps on at least different chips among the remaining ones of user # . There are

possibilities of choosing chips from among . The probability for a chip to be overlapped by at least one user is the complementary of the probability for a chip among users. As the overlapping to be overlapped by none of the , a chip is overlapped by at least one user probability is among with the probability

(11) The probability that there is an overlap between two codes is , thus

(14) In addition to that, for the first chip studied among the reones of user # , there are users that can maining overlap. Thus, the probability for this chip to be overlapped is , and is expressed as deduced from (14) with

When , there is an overlapping between user #1’s and user # ’s codes. Consequently, the user #1 (who sent a datum “1”) generates an interference of value on user . Thus, the contribution of the others users (i.e., the nondesired users who sent a “1”) must be greater than . Thus

(15) For the second chip, at most users can overlap the second chip when the first chip is overlapped. Indeed, we use ; thus two users can not have two chips codes with in common. Therefore, the probability for the second chip, for , and we the worst case, is deduced from (14) with obtain

(12) (16) At this step, we have to consider separately two cases, to calculate and .

And so on …

GOURSAUD et al.: DS-OCDMA RECEIVERS BASED ON PARALLEL INTERFERENCE CANCELLATION AND HARD LIMITERS

To conclude, the probability that at least , of user # are overlapped is among

different chips

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1) Case C: If the desired user’s receiver is a CCR, we have

(22) Thus, there is an error if i.e., . interfering users So, there must be at least users who sent a 0. So, from (21) we get among the

We finally get the probability upper bound

(17) D. Expression of is the error probability for user #1, thus is linked to the desired user’s receiver structure, and the desired user’s receiver . threshold level As for , we have to distinguish two different values for , and . according to the desired user structure: can be written For the two receivers,

(18) interfering users. The probaWe assume that there are bility to select nondesired users who sent a “1” and interfering users, from among the nondesired users, is

As

for

, we obtain

(23) 2) Case D: On the contrary, if the desired user’s receiver is an HL+CCR, the interfering users must overlap on different chips, and not on the same as user #1. There are

possibilities of choosing chips to be overlapped among . The number of possibilities that the interfering given chips is users are interfering on (19) Moreover, the probability

to have

interfering users is (20)

So

(21) for So, we have to express and given, for a CCR and an HL+CCR. At this step, we have to consider separately the two cases to calculate and .

(24) Moreover, the probability that an interfering user overlaps one particular chip is . So, the probability that the inchips of terfering users are interfering on at least user #1 is

(25) Thus, from (21) we get (26), shown at the bottom of the page.

(26)

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Fig. 3. Equation (HL+PIC+HL) validation with (64,4,1,1) OOC,

N = 5.

E. Expressions Analysis expressions and , we On observing the , and that the can note that is . minimum value for So, if , there will be no term in (23) and (26)’s summation. In this case, there is no error if

(27) and , we get . Consequently, for If we analyze the CCR error-probability expression (4), we for can remark that there is no error with the CCR if . Hence, the PIC receivers allow double the users without error than the CCR with the same code weight. F. Receivers’ Error-Probability Expression From theoretical analysis, we can deduce the error probability for the four receivers, according to their nondesired users and desired user’s receivers structure (Table I). For example, the theoretical expression of the PIC+HL’s error probability (whose nondesired users’ receiver is a CCR, and whose desired user’s receiver is an HL+CCR) is obtained from with .

Fig. 4. Receiver performance for OOC (F,4,1,1) with

N = 30.

of the threshold values for and , respectively, of the desired and nondesired users’ CCR, for a OOC with users. We can first point out that the theoretical expression correctly describes the receiver’s performance, as we obtain the same results as by simulation. In addition, we can notice missing points on the curves. All , , the missing points , , , correspond to a null error probability in the theoretical case, and are defined by the inequality (27). In order to verify this inequality, we choose a border point. is set to one, and is set to two. In this case, the inequality (27) is points without any error. well-verified. We have simulated So, we can conclude that the error probability is less than . Compared with the value of the probability for the non-null results (at least , Fig. 3), we consider that the simulation calculation confirms the theoretical result of inequality (27). Moreover, we can deduce from the curves evolution that the optimal threshold levels are and . Indeed, for the conventional receiver, the lowest error probability is obtained for . In this case, there is less negative interference on the nondesired users. As the interference on user #1 is always negative, the optimal threshold for user #1 is the smallest positive number, that is, . B. Performance Analysis

IV. PERFORMANCE ANALYSIS A. Validation of Theoretical Analysis We have checked that the theoretical expressions of the four receivers fit with a simulation exercise, but we only show in this paper the verification of the most complex receiver, the HL+PIC+HL. Fig. 3 shows the comparison between theoretical results and those obtained by numerical simulation for the HL+PIC+HL receiver in the synchronous case. The BER is plotted as a function

We present some theoretical results as a function of the OOC parameters: the length , the code weight , and the number of users . Our parameters set is . In Figs. 4–6, respectively, we plot the theoretical performance of the CCR, the HL+CCR, the PIC, the HL+PIC, the PIC+HL, and the HL+PIC+HL as a function of , respectively, in the synchronous case. We consider the optimal threshold levels for these receivers, i.e., for the CCR and the HL+CCR, , and for the PIC, the HL+PIC, the PIC+HL, and the HL+PIC+HL, and .

GOURSAUD et al.: DS-OCDMA RECEIVERS BASED ON PARALLEL INTERFERENCE CANCELLATION AND HARD LIMITERS

Fig. 5. Receiver performance for OOC (361,W,1,1) with

Fig. 6. Receiver performance for OOC (361,4,1,1) with

N = 30.

N users.

First, we can verify that for all the receivers the BER decreases when either the length or the weight increases, or the number of users decreases. In addition to that, we can verify that even for high MAI, these receivers significantly improve the performance. For example, for with , the error probability is with a CCR and with HL+PIC+HL. Moreover, the HL+PIC+HL receiver outperforms the other receivers. However, we get almost equivalent performance with HL+PIC and HL+PIC+HL. So, we can reduce the complexity of the receiver by using only one HL in front of the nondesired users’ receivers. Furthermore, in order to evaluate the code-length reduction thanks to these receivers, we have plotted in Fig. 7 the minimal code length required to get the optical specifications (BER ), for as a function of the code weight .

Fig. 7. Minimal code length required to obtain BER users.

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