Optimal Code Design for Multi-Wavelength OOC Optical CDMA system

Optimal Code Design for Multi-Wavelength OOC Optical CDMA system C. Goursaud, M. Morelle, A. Julien-Vergonjanne, C. Aupetit-Berthelemot, J.P. Cances and J.M. Dumas University of Limoges / XLIM Dpt -C2S2 UMR CNRS 6172 ENSIL Parc ESTER, BP 6804, 87068 Limoges Cedex, France Phone number: +33 5 55 42 36 70 Fax number: +33 5 55 42 36 80 [email protected] , [email protected] Abstract-The objective of this work is to design optimal codes for a 2 Dimensional Optical Code Division Multiple Access system (2D-OCDMA), and to test their robustness to noise perturbation. 2D coding is performed by Multi-Wavelength Optical Orthogonal Codes (MWOOC). They are obtained with our new construction method which permits to choose the code parameters with high flexibility. Different receiver structures are studied: a Conventional Correlation Receiver (CCR), and a Parallel Interference Cancellation receiver (PIC). For each structure, the optimal code parameters are evaluated, in order to obtain a Bit Error Rate (BER) ≤10-9, for 30 active users, with a minimal temporal code length, and a minimal number of wavelengths. Finally, we show that, compared to the CCR, the PIC receiver permits to reduce the temporal code length and the number of wavelength, and that it also permits to reduce the required SNR for noisy signal.

I. INTRODUCTION For several years, the Optical Code Division Multiple Access (OCDMA) is studied for application in optical networks [1,2]. This spread spectrum technique consists in allocating to each user a specific and distinct code. Coherent optical systems are costly and difficult to implement. So, most of the studies concern the incoherent optical systems. In incoherent systems, codes are unipolar and can not be strictly orthogonal. Thus, the main limitation is linked to Multiple Access Interference (MAI). Other limitations, especially thermal noise and beat noise [3] can also severely degrade the performances. It has been shown that 1D spreading codes [4,5] are not very efficient to provide high data rates to at least 30 users with required performances (Bit Error Rate BER ≤ 10 −9 ). An alternative approach is based on both 1D coding methods (temporal and spectral) simultaneously. This approach is called two dimensions (2D) coding method. Most of the 2D code constructions are issued from the 1D code families such as: prime/prime [6], OOC/prime [7], prime/EQC [8], OOC/OOC [9,10]. In this paper, we focus on Multi-Wavelength Optical Orthogonal Code (MWOOC) based on the OOC/OOC spreading [9,10], and we modify the construction method to be able to choose the code parameters with high flexibility. We particularly investigate the 2D-OCDMA for a high-speed optical link which provides at least 155Mbit/s to 30 active users. The main objective of this work is to determinate the optimal 2D code parameters, i.e. minimal temporal code length and minimal number of wavelengths, for a given

BER (set to 10-9 in this paper). The performances are compared for different receiver structures [11] and the robustness to noise perturbation is evaluated. In the first part, the 2D-OCDMA system and the 2D coding method are described. In the second part, we present two receivers structures: the CCR (Conventional Correlation Receiver) [4] and the PIC (Parallel Interference Cancellation) receivers [11]. Then, the 2D code parameters allowing 30 active users, with a BER ≤ 10 −9 (BER required in optical links), with the minimal temporal code length F and the minimal number of wavelengths L , are obtained in the noiseless case and for each receiver. We show that the PIC receiver permits to reduce the 2D code parameter values F and L . Finally, we evaluate the robustness of the obtained 2D codes with noise contribution, to conclude on the feasibility of 2D OCDMA systems.

II. SYSTEM DESCRIPTION A. The 2D-OCDMA system We consider an incoherent system using 2D codes. Each user employs an On/Off Keying (OOK) modulation to transmit independent and equiprobable binary data upon an optical channel (figure 1.a). Before transmission, data are coded by multiplication with a code matrix of dimension (L×F). 2D codes are defined by: (L×F,W,ha,hc) where L is the wavelength number, F is the temporal code length (the bit period is subdivided in F intervals called chips), W is the weight corresponding to the number of chips set to one, ha and hc are the auto and cross-correlation values. The jth user’s 2D code C Lj, F , is a matrix composed of L row vectors d kj, F related to the temporal spreading: d j

1,F

dj Cj

L,F

with d kj, F = [ckj,1 , ckj,2 ,..., ckj, F ]

2,F

= d j

L − 1,F

and

c kj,i

∈ {0,1}

d j

L,F

k is related to the emitted wavelength: k ∈{1, …, L} with j ∈ [1, N u ] where N u is the active user number.

(1)

d11, F

bi1(t)

C1L,F

d1Nu ,F

biNu(t)

MultiWavelength Laser

1

d 1L ,F

d LNu ,F

Optical to Electrical Converter (OEC) r1,F(t)

r1,F(t) r2,F(t)

2

Wavelength MUX L-1 L

RL,F(t)

Wavelength DEMUX

Optical Channel

rL-1,F(t)

rL-1,F(t)

rL,F(t)

rL,F(t)

Electrical part

O/E

O/E O/E

Tb

d1j, F

0

d 2j, F

0

Tb

Nu j =1

bi (t )d k , F j

j

(2)

where bi j (t ) ∈ {0, 1} is the ith data bit of the jth user. The L signals rk,F(t) are multiplexed and the total signal RL,F(t) is transmitted on the optical channel. B. Construction of 2D codes The construction of a code matrix C Lj,F is based on a 1D code vector. We use vectors from the family called Optical Orthogonal Codes (OOC) [4] with correlation values set to one (ha=hc=1). The cardinality of OOC code is given by the following expression: F −1 W (W − 1)

j bˆ (t ) i

Tb

d Lj −1, F

0

d Lj, F

0

S

Tb

Electrical part Figure 1.b: 2D-OCDMA scheme with a CCR structure .

The signals rk,F(t) are the sum of the temporal spreading data of each user carried on the wavelength k. They are expressed as:

N OOC ≤

O/E

Optical part

Figure 1.a: 2D-OCDMA emission scheme.

rk , F (t ) =

r2,F(t)

CCR

(3)

Existing methods for MWOOC construction [9,10] impose a temporal length F equal to a prime number and, either a number of wavelength too large (L=F), or a fixed weight W=3, for an optimal value of cross-correlation (hc=1). Thus, we have modified the construction method presented in [9] by Yang and Kwong, in order to generate MWOOC codes such as L≤F and for any value of W. We use a sort algorithm on the matrix rows in order to select a wavelength number L≤F. The main advantage is that it permits to obtain 2D code sets with a minimal wavelength number equal to the weight: L=W. The total number of users depends on the number of wavelength sets selected by the algorithm. If this number is α, it can be shown that the code cardinality is Numax=αF+L. In the case L=W, the value of α is minimal and equal to 1. So: (4) Nu ≤ F + W We can observe that, for a given temporal code length

F , a given weight W , and with L = W , the 2D codes

have a bigger cardinality than OOC. From now on, we study 2D codes such as L = W , i.e. MWOOC ( L × F , L)

III. 2D SYSTEM DESIGN In this part, we consider 2D OCDMA system with different receivers schemes: a conventional correlation receiver called CCR [4], and an interference cancellation receiver named PIC [11].

As the objective is to study the application of 2D OCDMA to high-speed optical link, the required performance is a Bit Error Rate of 10 −9 , for a minimal data rate of 155 Mbit/s, for N u = 30 active users. With these constraints, the performance study will lead to design the corresponding code parameters L = W and F . For a cheapest implementation, we search 2D code with a minimal temporal code length F . Moreover, the number of wavelength should be as little as possible, in order to minimize the interferometric noise impact [3]. A. The Conventional Correlation Receiver We have first considered the Conventional Correlation Receiver (CCR) [4]. The CCR (figure 1.b) has the knowledge of the desired user code matrix. At the reception end, each wavelength is separated. The electrical signal corresponding to the optical signal rk, F (t ) at wavelength

k

is multiplied by the sequence d k,j F (t) of the

desired user #j; then, the resulting signal is integrated over the bit duration. The values obtained for each wavelength are summed. We get the decision variable value of the desired user, which is compared to the threshold level S of the decision device to provide an estimation of the transmitted data bˆ j . i

It has been shown that in the ideal chip synchronous case [4], this receiver leads to error only when the sent bit is a zero data. Interference occurs when the code matrix of an undesired user who sent a data one, has a common pulse with the code matrix of the desired user. Since there is up to one chip one per row in a 2D code matrix, the probability for two matrices to have a pulse one on the same wavelength is W 2 L . Furthermore, the probability for two pulses, from different code matrices but on the same wavelength, to be on the same time slot is 1/F. As an overlap occurs only when both wavelength and time slots coincide simultaneously, the probability to have an overlap is given by q =

W2 . L× F

The theoretical probability upper bound PECCR, is then given by the following equation [9]: PECCR

1 ≤ 2

N u −1 i= S

Nu −1 i

W

2

2L × F

with Nu: number of active users.

i

1−

W

2

2L × F

N u −1− i

(5)

2 CCR #2 bˆi (t ) ST

RL,F(t)

OEC CCR #Nu ST

N bˆi u (t )

Σ

CL2,F

N

C L,uF

-

+

CCR #1 SF

bˆi1 (t )

Figure 2: Parallel Interference Cancellation receiver structure.

B. The Parallel Interference Cancellation receiver Figure 2 presents the Parallel Interference Cancellation receiver structure when the desired user is user #1. The aim of a Parallel Interference Cancellation receiver (PIC) [11] is to estimate the interference term due to all interfering users and to remove it from the received signal. The PIC receiver first detects the Nu-1 interfering users with the CCR defined in the previous part with a threshold level ST. Each CCR provides the estimation bˆip of the

Figure 3: Theoretical and simulated BER for a MWOOC(5x23,5) code with a CCR and a PIC receiver with S=W-1, SF=3 and ST=W.

undesired user #p data. Next, each estimated data is spread by the corresponding code matrix; the interference is built and removed from the received signal. Then, we detect the transmitted data of the desired user with a CCR and a threshold level SF. We have shown in the case of OOCs [11] that, contrary to CCR, the PIC receiver leads to error only for a sent data bi(1) = 1 . This can be extended to all unipolar codes, and especially for 2D codes. By using the same method presented in [11] for the OOC, we deduce the error probability bound of the PIC receiver PEPIC for MWOOC codes in the ideal chip synchronous case, by considering, as in the previous part, that the probability to have an overlap is given by q=

W2 . We get : L× F

PEPIC ≤

1 2

with

Nu

Nu −1

Nu −1− N1

N1 = ST −1 N2 =W +1−S F

Q=q

N1

Nu − 1 Nu − 1 − N1 (Q) N2 (1 − Q) Nu −1− N1 − N2 N1 N2

(6)

In addition to that, we can verify that the most efficient receiver is the PIC receiver. Moreover, the numerical results fit with the theoretical expression, so this validates the theoretical formulas (5) and (6). Thus, from now on, we use these theoretical expressions to obtain the receivers’ performances.

n1

CNn1 (q) (1 − q)N1 − n1

n1 = ST −1

Figure 4: Theoretical and minimal 2D code parameters values for a CCR and a PIC receiver, to have a BER ≤ 10 − 9 for 30 active users.

1

and Nu : number of active users. C. Receivers Performances III.C.1. Theoretical expressions validation On figure 3, we present the theoretical BER values from equations (5) and (6) and numerical BER values obtained by a C language simulation program of the two receivers for a MWOOC code whose parameters are: (L×F=5×23,W=L=5). First, we can notice that, for the two receivers, the performances are worse when the number of users increases.

III.C.2. Design of 2D codes in the noiseless case First, we have searched for the CCR and PIC receivers, the 2D code, allowing a BER lower than 10-9 for N u = 30 active users, for different values of L = W , and with the lowest temporal code length F . Results are reported on figure 4. First of all, we can observe that the curves first decrease, and then increase. The decrease is linked to the fact that, for the same number of users, as the weight increases, it becomes less probable for a user to be bad detected with an optimal receiver. So, the temporal code length corresponding to a given BER is lower. The curves’ increase is linked to the maximum number of users allowed in an OOC class. Indeed, if W increases, the temporal length F has to be high enough to have at least N OOC = 1 , to permit the code construction.

CCR PIC

OOC 336GHz 56GHz

MWOOC 21GHz 6,5GHz

Table I: Bandwidth required to provide 155Mbit/s to N=30 users, with BER