4.1.2 Second and (N�1)th cancelation stage

The decision variable for the desired user #1 is:

$$Z\_i^{(1)} = \mathsf{W}b\_i^{(1)} + I\_2 + A\_1 + A\_2$$

$$\begin{aligned} \text{where } I\_2 &= \sum\_{k=2}^{N-2} \int \,\_0^{T\_b} b\_i^{(k)} c\_k(t) c\_1(t) dt, \, A\_1 = \left( b\_i^{(N)} - \dot{b}\_i^{(N)} \right) \int \,\_0^{T\_b} c\_N(t) c\_1(t) dt, \text{ and} \\\ A\_2 &= \left( b\_i^{(N-1)} - \dot{b}\_i^{(N-1)} \right) \int \,\_0^{T\_b} c\_{N-1}(t) c\_1(t) dt. \end{aligned}$$

In this case, the term A<sup>2</sup> can take three values (�1.0 and +1):

$$A\_1 = \begin{cases} -1 \text{ if } an \text{ error is made on the data } b\_i^{(N-1)} = \mathbf{0} \left( \hat{b}\_i^{(N-1)} = \mathbf{1} \right) \\\\ \mathbf{0} \text{ if } \left( b\_i^{(N-1)} = \hat{b}\_i^{(N-1)} \text{ no error in detection} \right) \\\\ + \mathbf{1} \text{ if } an \text{ error is made on the data } b\_i^{(N-1)} = \mathbf{1} \left( \hat{b}\_i^{(N-1)} = \mathbf{0} \right) \end{cases},\tag{21}$$

hence, Pe<sup>2</sup> <sup>¼</sup> <sup>1</sup> <sup>2</sup> Pe<sup>21</sup> <sup>þ</sup> <sup>1</sup> <sup>2</sup> Pe<sup>20</sup> , where Pe<sup>21</sup> <sup>¼</sup> prob ^ b ð Þ1 <sup>i</sup> <sup>¼</sup> <sup>0</sup>=bð Þ<sup>1</sup> <sup>i</sup> ¼ 1 � � and Pe<sup>20</sup> <sup>¼</sup> prob ^ b ð Þ1 <sup>i</sup> ¼ 1=b ð Þ1 <sup>i</sup> ¼ 0 � �

$$\begin{split} P\_{c\mathbf{1}} &= \operatorname{prob} \left( Z\_i^{(1)} < \mathcal{S}\_1 / b\_i^{(1)} = \mathbf{1} \right) \\ &= \operatorname{prob} \left( W + I\_2 + A\_1 + A\_2 < \mathcal{S}\_1 / b\_i^{(1)} = \mathbf{1} \right) \\ &= \operatorname{prob} \left( A\_1 = \mathbf{0} / b\_i^{(1)} = \mathbf{1} \right) \cdot \operatorname{prob} \left( W + I\_2 + A\_2 < \mathcal{S}\_1 / b\_i^{(1)} = \mathbf{1} \right) \\ &\quad + \operatorname{prob} \left( A\_1 = -\mathbf{1} / b\_i^{(1)} = \mathbf{1} \right) \cdot \operatorname{prob} \left( W + I\_2 + A\_2 < \mathcal{S}\_1 + \mathbf{1} / b\_i^{(1)} = \mathbf{1} \right) \end{split} \tag{22}$$

and

$$\begin{aligned} P\_{\epsilon\_{\mathfrak{B}}} &= \operatorname{prob} \left( Z\_i^{(1)} \succeq \mathbb{S}\_1 / b\_i^{(1)} = \mathbf{0} \right) \\ &= \operatorname{prob} \left( I\_2 + A\_1 + A\_2 \succeq \mathbb{S}\_1 / b\_i^{(1)} = \mathbf{0} \right) \end{aligned}$$

First, in order to evaluate the number of cancelation stages (Cs), we have studied the SIC performances with modifying the code weight. We can remark, in Figure 7, that when the number of cancelation stages increases, the BER first decreases slowly, and after a high decrease, it reaches a floor. Thus, it is not necessary to eliminate all

The BER of the Opt-SIC system versus the cancelation stage for different code lengths and for threshold value

Bit error rate (BER) versus the threshold values for a code length, F = 73 and for the conventional and the first

Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures…

DOI: http://dx.doi.org/10.5772/intechopen.85860

Moreover, in order to illustrate the benefit of the SIC in regard to conventional receivers, we have plotted on Figure 8 the evolution of the BER as a function of the code weight W. We can observe that we obtain better performances with the SIC than with the CCR and the HL + CCR. Moreover, we can point out that the SIC is all

In this section, an optical successive interference cancelation was examined, a

technique based on the conventional O-CDMA receiver, in which the MAI is

). We can also

<sup>N</sup>1 stages in the SIC method to obtain a correct optical BER rate (10<sup>9</sup>

just change the code length to obtain this achievement.

Figure 6.

Figure 7.

equal to 2.

81

cancelation stage.

the more performing when the BER decreases for the CCR.

The calculation of the probability of error requires the determination of more and more terms. We have calculated the error probabilities by using the iterative method [8].

Figure 6 shows the theoretical and simulation bit error rate (BER) versus the threshold values of an OOC(73,4,1) for the conventional and the first cancelation stage of the Opt-SIC. We could see that the theoretical lines correlate with the simulation ones, and the Opt-SIC outperforms the traditional correlation receiver. From here on, we could validate the theoretical figures in order to show the performance of such receiver.

Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures… DOI: http://dx.doi.org/10.5772/intechopen.85860

### Figure 6.

hence

Multiplexing

Pe<sup>10</sup> <sup>¼</sup> <sup>1</sup> 2 W<sup>2</sup>

> <sup>þ</sup> <sup>1</sup> � <sup>1</sup> 2 W<sup>2</sup>

The decision variable for the desired user #1 is:

Zð Þ<sup>1</sup>

<sup>i</sup> <sup>¼</sup> Wbð Þ<sup>1</sup>

<sup>0</sup> cN�<sup>1</sup>ð Þt c1ð Þt dt: In this case, the term A<sup>2</sup> can take three values (�1.0 and +1):

�<sup>1</sup> if an error is made on the data bð Þ <sup>N</sup>�<sup>1</sup>

<sup>þ</sup><sup>1</sup> if an error is made on the data bð Þ <sup>N</sup>�<sup>1</sup>

� �

� �

ð Þ1 <sup>i</sup> ¼ 1

Pe<sup>20</sup> <sup>¼</sup> prob Zð Þ<sup>1</sup>

<sup>i</sup> ¼ 1

<sup>i</sup> ckð Þ<sup>t</sup> <sup>c</sup>1ð Þ<sup>t</sup> dt, <sup>A</sup><sup>1</sup> <sup>¼</sup> <sup>b</sup>ð Þ <sup>N</sup>

<sup>i</sup> no error in detection

ð Þ1 <sup>i</sup> ¼ 1

<sup>i</sup> ≥S1=b

¼ prob I<sup>2</sup> þ A<sup>1</sup> þ A<sup>2</sup> ≥S1=b

� �

The calculation of the probability of error requires the determination of more and more terms. We have calculated the error probabilities by using the iterative

Figure 6 shows the theoretical and simulation bit error rate (BER) versus the threshold values of an OOC(73,4,1) for the conventional and the first cancelation stage of the Opt-SIC. We could see that the theoretical lines correlate with the simulation ones, and the Opt-SIC outperforms the traditional correlation receiver. From here on, we could validate the theoretical figures in order to show the perfor-

� prob W þ I<sup>2</sup> þ A<sup>2</sup> <S1=b

ð Þ1 <sup>i</sup> ¼ 0

� � :

� �

4.1.2 Second and (N�1)th cancelation stage

k¼2

0 if bð Þ <sup>N</sup>�<sup>1</sup>

<sup>2</sup> Pe<sup>21</sup> <sup>þ</sup> <sup>1</sup>

b ð Þ1 <sup>i</sup> <sup>¼</sup> <sup>0</sup>=bð Þ<sup>1</sup>

<sup>i</sup> < S1=b

� �

¼ prob W þ I<sup>2</sup> þ A<sup>1</sup> þ A<sup>2</sup> < S1=b

ð Þ1 <sup>i</sup> ¼ 1 � �

� �

<sup>i</sup> <sup>¼</sup> ^ b ð Þ N�1

<sup>2</sup> Pe<sup>20</sup> ,

ð Þ1 <sup>i</sup> ¼ 1

Ð Tb <sup>0</sup> <sup>b</sup>ð Þ<sup>k</sup>

where <sup>I</sup><sup>2</sup> <sup>¼</sup> <sup>∑</sup><sup>N</sup>�<sup>2</sup>

<sup>i</sup> � ^ b ð Þ N�1 i � � <sup>Ð</sup> Tb

> 8 >>>>>>><

> >>>>>>>:

where Pe<sup>21</sup> <sup>¼</sup> prob ^

Pe<sup>21</sup> <sup>¼</sup> prob Zð Þ<sup>1</sup>

¼ prob A<sup>1</sup> ¼ 0=b

þ prob A<sup>1</sup> ¼ �1=b

<sup>A</sup><sup>2</sup> <sup>¼</sup> <sup>b</sup>ð Þ <sup>N</sup>�<sup>1</sup>

A<sup>1</sup> ¼

hence, Pe<sup>2</sup> <sup>¼</sup> <sup>1</sup>

and

method [8].

80

mance of such receiver.

<sup>L</sup> f S<sup>ð</sup> <sup>N</sup>; <sup>N</sup> � <sup>2</sup>; <sup>N</sup> � <sup>2</sup>Þ � f Sð Þ <sup>1</sup> <sup>þ</sup> <sup>1</sup>; <sup>N</sup> � <sup>2</sup>; <sup>N</sup> � <sup>2</sup>

<sup>i</sup> þ I<sup>2</sup> þ A<sup>1</sup> þ A<sup>2</sup>

<sup>i</sup> � ^ b ð Þ N i � � <sup>Ð</sup> Tb

<sup>i</sup> <sup>¼</sup> <sup>0</sup> ^

<sup>i</sup> <sup>¼</sup> <sup>1</sup> ^

and Pe<sup>20</sup> <sup>¼</sup> prob ^

� �

� prob W þ I<sup>2</sup> þ A<sup>2</sup> < S<sup>1</sup> þ 1=b

b ð Þ N�1 <sup>i</sup> ¼ 1 � �

b ð Þ N�1 <sup>i</sup> ¼ 0 � �

> b ð Þ1 <sup>i</sup> ¼ 1=b

ð Þ1 <sup>i</sup> ¼ 1

� �

ð Þ1 <sup>i</sup> ¼ 0

� f Sð Þ <sup>1</sup>; N � 2; N � 2

: (20)

<sup>0</sup> cNð Þt c1ð Þt dt, and

,

ð Þ1 <sup>i</sup> ¼ 0

� �

ð Þ1 <sup>i</sup> ¼ 1 (21)

(22)

<sup>L</sup> f Sð Þ <sup>N</sup>; <sup>N</sup> � <sup>2</sup>; <sup>N</sup> � <sup>2</sup> � �

Bit error rate (BER) versus the threshold values for a code length, F = 73 and for the conventional and the first cancelation stage.

### Figure 7.

The BER of the Opt-SIC system versus the cancelation stage for different code lengths and for threshold value equal to 2.

First, in order to evaluate the number of cancelation stages (Cs), we have studied the SIC performances with modifying the code weight. We can remark, in Figure 7, that when the number of cancelation stages increases, the BER first decreases slowly, and after a high decrease, it reaches a floor. Thus, it is not necessary to eliminate all <sup>N</sup>1 stages in the SIC method to obtain a correct optical BER rate (10<sup>9</sup> ). We can also just change the code length to obtain this achievement.

Moreover, in order to illustrate the benefit of the SIC in regard to conventional receivers, we have plotted on Figure 8 the evolution of the BER as a function of the code weight W. We can observe that we obtain better performances with the SIC than with the CCR and the HL + CCR. Moreover, we can point out that the SIC is all the more performing when the BER decreases for the CCR.

In this section, an optical successive interference cancelation was examined, a technique based on the conventional O-CDMA receiver, in which the MAI is

eliminated successively by a multistage cancelation system for the purpose of achieving a better performance. We have showed that the optical-SIC receiver manages to upgrade the performance of the conventional receiver by choosing the best threshold value, the cancelation stage, and the code length. It is important to note that, we could also improve the performance by using other parameters such as the code weight and the correlation values.

### 4.2 Parallel interference cancelation receiver (PIC)

### 4.2.1 Principles

The principle of a PIC receiver is based on the estimation of the interference due to all the nondesired users. Once the IAM is determined, it is discarded from the received signal before detecting the desired user. We start by detecting all the (N�1) nondesired users by a CCR receiver with a threshold level ST (0 < ST ≤ W). Each receiver generates the estimation ^ bð Þj <sup>i</sup> of the nondesired user # j data. This last one is spread by the corresponding code sequence. Then, the reconstructed interference is removed from the received signal. Finally, the data of the desired user are detected with a CCR with a threshold level SF (0 < SF ≤ W) (Figure 9) [9].

### 4.2.2 PIC receiver

The first stage of parallel interference cancelation receiver is a parallel structure whose receivers are all CCR. The signal applied to the second stage is expressed as:

$$\begin{split} s(t) &= r(t) - \sum\_{j=2}^{N} \hat{b}\_i^{(j)} c\_j(t) \\ &= \hat{b}\_i^{(1)} c\_1(t) + \sum\_{j=2}^{N} \left( b\_i^{(j)} - \hat{b}\_i^{(j)} \right) c\_j(t) \end{split} \tag{23}$$

where b

Figure 10.

Figure 9.

contrary to CCR.

probability is:

PePIC <sup>¼</sup> <sup>1</sup>ð Þ <sup>=</sup><sup>2</sup> <sup>N</sup>: <sup>∑</sup>

83

ð Þj <sup>i</sup> � ^ b ð Þj i

Parallel interference cancelation structure.

DOI: http://dx.doi.org/10.5772/intechopen.85860

N�1 N1¼ST�1

with PIPIC <sup>¼</sup> <sup>W</sup><sup>2</sup>

∑ N�1�N<sup>1</sup> N2¼Wþ1�SF

> <sup>F</sup> <sup>∑</sup> N<sup>1</sup> n1¼ST�1

N � 1 N<sup>1</sup>

BER as a function of the number of simultaneous users N:F = 121 and W = 3.

N<sup>1</sup> n1 ! <sup>W</sup><sup>2</sup>

� � can take two values: "0" or "�1". So, the second term in Eq.

ð Þ PIPIC ð Þ 1 � PIPIC

:

W<sup>2</sup> F � �<sup>n</sup><sup>1</sup>

<sup>1</sup> � <sup>W</sup><sup>2</sup> F � �<sup>N</sup>1�n<sup>1</sup>

(24)

(23) generates negative interference on user #1. Thus, one of the structure originalities is that errors can occur only when the desired user's sent datum is 1,

Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures…

We have established in [8] that the theoretical expression of the PIC error

N<sup>2</sup> !

A theoretical comparison of the performances of a CCR, a CCR with an optical hard limiter and a PIC receiver was made according to the number of simultaneous

<sup>1</sup> � <sup>W</sup><sup>2</sup> F � �<sup>N</sup>1�n<sup>1</sup>

! <sup>N</sup> � <sup>1</sup> � <sup>N</sup><sup>1</sup>

F � �<sup>n</sup><sup>1</sup> Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures… DOI: http://dx.doi.org/10.5772/intechopen.85860

Figure 9. Parallel interference cancelation structure.

### Figure 10.

eliminated successively by a multistage cancelation system for the purpose of achieving a better performance. We have showed that the optical-SIC receiver manages to upgrade the performance of the conventional receiver by choosing the best threshold value, the cancelation stage, and the code length. It is important to note that, we could also improve the performance by using other parameters such as

BER as a function of the code weight W for F = 361 and N = 10, Cs = N�W + 1, SN = 4, and S1 = 3.

The principle of a PIC receiver is based on the estimation of the interference due to all the nondesired users. Once the IAM is determined, it is discarded from the received signal before detecting the desired user. We start by detecting all the (N�1) nondesired users by a CCR receiver with a threshold level ST (0 < ST ≤ W).

<sup>i</sup> of the nondesired user # j data. This last

cjð Þt

(23)

bð Þj

one is spread by the corresponding code sequence. Then, the reconstructed interference is removed from the received signal. Finally, the data of the desired user are

The first stage of parallel interference cancelation receiver is a parallel structure whose receivers are all CCR. The signal applied to the second stage is expressed as:

> N j¼2 b ð Þj <sup>i</sup> � ^ b ð Þj i

detected with a CCR with a threshold level SF (0 < SF ≤ W) (Figure 9) [9].

N j¼2 ^ bð Þ<sup>j</sup> <sup>i</sup> cjð Þt

<sup>i</sup> c1ðÞþt ∑

s tðÞ¼ r tðÞ� ∑

¼ ^ bð Þ<sup>1</sup>

the code weight and the correlation values.

Each receiver generates the estimation ^

4.2.1 Principles

Figure 8.

Multiplexing

4.2.2 PIC receiver

82

4.2 Parallel interference cancelation receiver (PIC)

BER as a function of the number of simultaneous users N:F = 121 and W = 3.

where b ð Þj <sup>i</sup> � ^ b ð Þj i � � can take two values: "0" or "�1". So, the second term in Eq.

(23) generates negative interference on user #1. Thus, one of the structure originalities is that errors can occur only when the desired user's sent datum is 1, contrary to CCR.

We have established in [8] that the theoretical expression of the PIC error probability is:

$$P\_{\rm PIC} = \langle \mathbf{1}\_{2} \rangle^{N} \cdot \sum\_{N\_{1} = S\_{T} - 1}^{N - 1} \sum\_{N\_{2} = W + 1 - S\_{T}}^{N - 1 - N\_{1}} \binom{N - 1}{N\_{1}} \binom{N - 1 - N\_{1}}{N\_{2}} (P\_{\rm IPC}) (1 - P\_{\rm IPC}) \left(\frac{W^{2}}{F}\right)^{n\_{1}} \left(1 - \frac{W^{2}}{F}\right)^{N\_{1} - n\_{1}}.\tag{24}$$
 
$$\text{with } P\_{\rm IPC} = \frac{W^{2}}{F} \sum\_{n\_{1} = S\_{T} - 1}^{N\_{1}} \binom{N\_{1}}{n\_{1}} \left(\frac{W^{2}}{F}\right)^{n\_{1}} \left(1 - \frac{W^{2}}{F}\right)^{N\_{1} - n\_{1}}.\tag{25}$$

A theoretical comparison of the performances of a CCR, a CCR with an optical hard limiter and a PIC receiver was made according to the number of simultaneous

restriction in the OCDMA optical link networks. In reality, in an optical transmission system, several physical phenomena can degrade the performances of the system [10–12]. The main limitation is due to the chromatic dispersion of the fiber. Indeed, chromatic dispersion leads to optical pulse broadening. This broadening results in overlapping between the pulses, which create the interference inter different chip transmitted over optical fiber, which can affect the system performances. At the output of the optical fiber, it is possible to express the electric field of the jth chip (code) of the lth bit (data) as a function of the in-phase

Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures…

<sup>T</sup>�Tc <sup>2</sup>Tc ½ �

0 @

where (ypi, yqi) are the components, respectively, in phase and quadrature of the electric field of the user ith and (yDp, yDq) those due to the chromatic dispersion. The first term corresponds to the data of the desired user, the second is the corresponding term to the MAI, and the last is due to the chromatic dispersion. Indeed, the superposition of the MAI term and the term due to the dispersion

The propagation distance is usually short in the access networks. For such networks, we deploy the G652 single-mode fiber optics. Therefore, intramodal dispersion can be neglected. Asymmetries and stress distribution in fiber core, which leads to birefringence, cause the polarization mode dispersion (PMD). It affects only long-haul communication systems. Nonlinear effects (Kerr and Raman effects) in optical fiber can degrade the performances of the system, but mainly for long-distance communication. Such nonlinearities are dependent on the signal intensity, which are not significant at the low power. Therefore, for a short access optical link, chromatic dispersion effect is an important factor, which needs to be addressed. For high data rates, the OCDMA technique requires the generation of ultrashort pulses. Indeed, for a given data rate D, the chip rate Dc is expressed as:

To study the impact of chromatic dispersion on the performances of the system, several simulations have been made in the case when there is no dispersion compensation component deployed. The study has been done according to different

At first, we analyze the performances as a function of the fiber length for a fixed pulse duration Tc = 1/(F \* D) = 2.51 10�<sup>11</sup> s and the number of active users N = 5.

<sup>h</sup>¼� <sup>T</sup>�Tc <sup>2</sup>Tc ½ �

yDpj�<sup>h</sup>

þ j ∑ <sup>T</sup>�Tc <sup>2</sup>Tc ½ �

<sup>h</sup>¼� <sup>T</sup>�Tc <sup>2</sup>Tc ½ �

yDqj�<sup>h</sup>

1 A (25)

component and quadrature as follows:

DOI: http://dx.doi.org/10.5772/intechopen.85860

N i¼2 y l,j pi þ j ∑ N i¼2 y l,j qi � � <sup>þ</sup> <sup>∑</sup>

produce a sufficient power to degrade the system performances.

Dc = 1/Tc = F.D. These pulses are sensitive to chromatic dispersion.

Variation of BER as a function of fiber length, where Tc (F,D) = 2.51 10�<sup>1</sup> s and N = 5.

network parameters and those of the code.

E1 l,j ¼ y l,j <sup>p</sup><sup>1</sup> <sup>þ</sup> jyl,j q1 � � <sup>þ</sup> <sup>∑</sup>

Figure 12.

85

Figure 11.

Bit error probability versus the weight of OOCs W:F = 121 and N = 10.

users for an OOC (F = 121, W = 4) code. The bit error rate versus the number of simultaneous users is presented in Figure 10. We can observe that the PIC receiver has better BER than the conventional receiver. So, the PIC receiver can support more users than the conventional ones. For example, for BER equal to 10<sup>5</sup> , the PIC can support N = 16 users, while the conventional receiver with hard limiter can support only N = 4 users.

The BER versus the weight W for DS-CDMA systems for a CCR with and without a hard limiter, and a PIC receiver is plotted on Figure 11. F = 121 and N = 10 have been considered as the OOC's code parameters. According to the simulation results, we note that the PIC receiver has a better BER than the traditional ones. Furthermore, at a bit error probability of 10<sup>4</sup> , for example, the PIC needs a weight of W = 2, while the conventional receiver with hard limiter needs W = 4. This configuration of receiver shows so many advantages. First of all, the required power is reduced. In a second time, as the weight is reduced, the number of potential users increases. On the one hand, with W = 4, we have 10 available code sequences, so with N = 10 users, all the sequences are used. On the other hand, W = 2 corresponds to 60 available code sequences; thus, there are 50 unused sequences. Consequently, we can build a system where the sequence codes are definitively assigned to the users, but only 10 of them are allowed to simultaneously communicate.

In order to reduce the effect of the only limitation of an ideal DS-OCDMA system (without taking into account the impact of optoelectronic components), which is multiple access interference (MAI), we have studied the performance of an optical parallel interference cancelation receiver.

This study is based on the analytic expression of the error probability and the system simulation, a comparison with the conventional receiver has been made in each case. The results found prove that the interference cancelation receiver outperforms the ones of conventional receiver.

The PIC receiver could be a suitable receiver in the case of highly loaded networks.

### 5. Fiber chromatic dispersion effects on OCDMA

In the previous paragraphs, we have showed that the performances of a DS-OCDMA system are degraded by the MAI. However, the MAI is not the only

Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures… DOI: http://dx.doi.org/10.5772/intechopen.85860

restriction in the OCDMA optical link networks. In reality, in an optical transmission system, several physical phenomena can degrade the performances of the system [10–12]. The main limitation is due to the chromatic dispersion of the fiber. Indeed, chromatic dispersion leads to optical pulse broadening. This broadening results in overlapping between the pulses, which create the interference inter different chip transmitted over optical fiber, which can affect the system performances. At the output of the optical fiber, it is possible to express the electric field of the jth chip (code) of the lth bit (data) as a function of the in-phase component and quadrature as follows:

$$E\_{l,j}^1 = \left(\boldsymbol{\mathcal{y}}\_{p1}^{l,j} + j\boldsymbol{\mathcal{y}}\_{q1}^{l,j}\right) + \left(\sum\_{i=2}^{N} \boldsymbol{\mathcal{y}}\_{pi}^{l,j} + j\sum\_{i=2}^{N} \boldsymbol{\mathcal{y}}\_{qi}^{l,j}\right) + \left(\sum\_{h=-\left[\frac{T\_c-T\_c}{2T\_c}\right]}^{\left[\frac{T-T\_c}{2T\_c}\right]} \boldsymbol{\mathcal{y}}\_{Dq\_{j-k}} + j\sum\_{h=-\left[\frac{T\_c-T\_c}{2T\_c}\right]}^{\left[\frac{T-T\_c}{2T\_c}\right]} \boldsymbol{\mathcal{y}}\_{Dq\_{j-k}}\right) \tag{25}$$

where (ypi, yqi) are the components, respectively, in phase and quadrature of the electric field of the user ith and (yDp, yDq) those due to the chromatic dispersion. The first term corresponds to the data of the desired user, the second is the corresponding term to the MAI, and the last is due to the chromatic dispersion. Indeed, the superposition of the MAI term and the term due to the dispersion produce a sufficient power to degrade the system performances.

The propagation distance is usually short in the access networks. For such networks, we deploy the G652 single-mode fiber optics. Therefore, intramodal dispersion can be neglected. Asymmetries and stress distribution in fiber core, which leads to birefringence, cause the polarization mode dispersion (PMD). It affects only long-haul communication systems. Nonlinear effects (Kerr and Raman effects) in optical fiber can degrade the performances of the system, but mainly for long-distance communication. Such nonlinearities are dependent on the signal intensity, which are not significant at the low power. Therefore, for a short access optical link, chromatic dispersion effect is an important factor, which needs to be addressed. For high data rates, the OCDMA technique requires the generation of ultrashort pulses. Indeed, for a given data rate D, the chip rate Dc is expressed as: Dc = 1/Tc = F.D. These pulses are sensitive to chromatic dispersion.

To study the impact of chromatic dispersion on the performances of the system, several simulations have been made in the case when there is no dispersion compensation component deployed. The study has been done according to different network parameters and those of the code.

At first, we analyze the performances as a function of the fiber length for a fixed pulse duration Tc = 1/(F \* D) = 2.51 10�<sup>11</sup> s and the number of active users N = 5.

Figure 12. Variation of BER as a function of fiber length, where Tc (F,D) = 2.51 10�<sup>1</sup> s and N = 5.

users for an OOC (F = 121, W = 4) code. The bit error rate versus the number of simultaneous users is presented in Figure 10. We can observe that the PIC receiver has better BER than the conventional receiver. So, the PIC receiver can support more users than the conventional ones. For example, for BER equal to 10<sup>5</sup>

can support N = 16 users, while the conventional receiver with hard limiter can

The BER versus the weight W for DS-CDMA systems for a CCR with and without a hard limiter, and a PIC receiver is plotted on Figure 11. F = 121 and N = 10 have been considered as the OOC's code parameters. According to the simulation results, we note that the PIC receiver has a better BER than the traditional ones.

of W = 2, while the conventional receiver with hard limiter needs W = 4. This configuration of receiver shows so many advantages. First of all, the required power is reduced. In a second time, as the weight is reduced, the number of potential users increases. On the one hand, with W = 4, we have 10 available code sequences, so with N = 10 users, all the sequences are used. On the other hand, W = 2 corresponds to 60 available code sequences; thus, there are 50 unused sequences. Consequently, we can build a system where the sequence codes are definitively assigned to the

users, but only 10 of them are allowed to simultaneously communicate.

In order to reduce the effect of the only limitation of an ideal DS-OCDMA system (without taking into account the impact of optoelectronic components), which is multiple access interference (MAI), we have studied the performance of an

This study is based on the analytic expression of the error probability and the system simulation, a comparison with the conventional receiver has been made in each case. The results found prove that the interference cancelation receiver out-

The PIC receiver could be a suitable receiver in the case of highly loaded networks.

In the previous paragraphs, we have showed that the performances of a DS-OCDMA system are degraded by the MAI. However, the MAI is not the only

support only N = 4 users.

Figure 11.

Multiplexing

84

Furthermore, at a bit error probability of 10<sup>4</sup>

Bit error probability versus the weight of OOCs W:F = 121 and N = 10.

optical parallel interference cancelation receiver.

5. Fiber chromatic dispersion effects on OCDMA

performs the ones of conventional receiver.

, the PIC

, for example, the PIC needs a weight

equal to 1. We have verified that SIC improves performance with respect to the conventional correlation receiver (CCR). Due to the dependency of a stage on previous ones, the exact theoretical analysis is very difficult to carry out.

Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures…

Then, the efficiency of the PIC structure for unipolar codes whose intercor-

We have studied theoretically and by simulation the performance of a system using OOC codes, and we have shown that the PIC can significantly improve the

Finally, since IAM is not the only limitation of performance, we have studied the impact of chromatic dispersion. It is demonstrated that chromatic dispersion has a significant negative effect on system performance, which cannot be neglected for systems with a short fiber length and a high data rate. It is reported that system performance can be significantly overestimated if chromatic dispersion is ignored.

relation is '1' has been investigated.

DOI: http://dx.doi.org/10.5772/intechopen.85860

Appendices and nomenclature

FFH-CDMA fast FH-CDMA FTTB fiber to the building FTTC fiber to the curb FTTH fiber to the home HL hard limiter

OCDMA optical CDMA

Younes Zouine and Zhour Madini\*

provided the original work is properly cited.

Author details

Morocco

87

ADSL asymmetric digital subscriber line CCR conventionnal correlation receiver CDMA code-division multiple access DS-CDMA direct sequence-CDMA

FDMA frequency-division multiple access

PIC parallel interference cancelation receiver

SIC successive interference cancelation receiver

Department of Electrical and Telecommunication, ISET Laboratory ENSA, Kenitra,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

MAI multiple access interference

PMD polarization mode dispersion PON passive optical network

TDMA time-division multiple access WDMA wavelength-division multiple access

\*Address all correspondence to: zmadini@gmail.com

OOC optical orthogonal code

performance.

Figure 13. BER versus data rate D for an OCDMA link with OOC (F = 181, W = 4) and N = 5 active users.

Figure 12 illustrates the variation of the BER as a function of the fiber length for three codes with various Fs and Ds. It can be noted that the dispersion effect increases as the fiber length increases. However, for this particular chip duration, the dispersion has no impact on the BER for optical fibers shorter than 5 km. On the other hand, when the fiber's length is greater than 5 km, system performance is deteriorated.

In order to complete our study, the BER versus data rate D, for a code length F = 181, has been simulated (Figure 13). For example, on the one hand, we can observe that the performances of an OOC (F = 181, W = 4) are not affected by the fiber dispersion up to D = 600 Mbits/s for a 1-km-long optical link. On the other hand, for a 20-km-long optical link, the performances are degraded from a data rate D = 100 Mbits/s.

The curves indicate that for making the effect of dispersion negligible, without using in the OCDMA link, a dispersion compensated component, we should have a trade-off between OOC code length F and data rate D.

The parametric study has shown that the OCDMA link performances in the access network context are significantly overestimated when the fiber chromatic dispersion is neglected.

## 6. Conclusion

In this chapter, we studied the DS-OCDMA multiple access technique envisaged for optical communications, in particular in PON access networks. To maintain high rates, the code spreading length should be as low as possible. In this case and for an incoherent system, it has been shown that the IAM multiple access interference, linked to the use of quasi-orthogonal unipolar codes, is very important and does not make it possible to maintain the quality of the link. It is, therefore, necessary to reduce the MAI in order to be closer to the specifications. For this purpose, two structures were studied: the serial interference cancelation (SIC) and the parallel interference cancelation (PIC). We first developed the approximate theoretical expression of the SIC error probability for unipolar codes whose intercorrelation is

Direct Sequence-Optical Code-Division Multiple Access (DS-OCDMA): Receiver Structures… DOI: http://dx.doi.org/10.5772/intechopen.85860

equal to 1. We have verified that SIC improves performance with respect to the conventional correlation receiver (CCR). Due to the dependency of a stage on previous ones, the exact theoretical analysis is very difficult to carry out.

Then, the efficiency of the PIC structure for unipolar codes whose intercorrelation is '1' has been investigated.

We have studied theoretically and by simulation the performance of a system using OOC codes, and we have shown that the PIC can significantly improve the performance.

Finally, since IAM is not the only limitation of performance, we have studied the impact of chromatic dispersion. It is demonstrated that chromatic dispersion has a significant negative effect on system performance, which cannot be neglected for systems with a short fiber length and a high data rate. It is reported that system performance can be significantly overestimated if chromatic dispersion is ignored.
