Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network

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Original research article

Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network Bih-Chyun Yeh Department of Electrical Engineering, School of Electrical and Computer Engineering, College of Engineering, Chang-Gung University, Tao-Yuan, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 5 August 2015 Received in revised form 28 October 2016 Accepted 28 October 2016 Keywords: One-dimensional multi method codes (1-D MM codes) Optical connected ring set (OCRS) Spectral amplitude coding optical code division multiple access (SAC-OCDMA) system Multi-user interference (MUI) Phase-induced intensity noise (PIIN)

a b s t r a c t We propose the new family of newly constructed codes named the one-dimensional Multi method codes (1-D MM codes) in the spectral amplitude coding optical code division multiple access (SAC-OCDMA) system. The new 1-D MM codes have the auto-cross correlation constraint and cross correlation constraint to be p and zero, respectively. Furthermore, the 1-D MM codes use the easy proposed structure. The proposed structure can use each transmitter, optical connected ring set (OCRS), and each receiver to become the one optical ring network. The proposed system uses the control path to give the user controller, correct optical fiber controller and failure optical fiber controller to achieve the one optical ring network. The numerical results demonstrate that the bit error rate (BER) in the proposed system using the 1-D MM codes outperform that in other systems using the 1-D M Sequence codes, 1-MQC codes, and 1-D RSQC codes. Then, the data transmission rate of the 1-D MM codes can achieve the 2.5 Gbps. © 2016 Elsevier GmbH. All rights reserved.

1. Introduction Optical Code Division Multiple Access (OCDMA) technique has been getting attention recently. Each simultaneous user used the OCDMA method to code the information bits in the transmitter with the code sequences and send the optical signals to the receivers. Thus, the OCDMA technique was considered for the network control to increase the protocol transparency [1] and improve the performance of passive optical networks (PONs) [1–10]. Moreover, the cross correlation constraint [11] used the method to produce the good condition of the system. The potential low cost improved the technological processes of the OCDMA system. However, the spectral amplitude coding OCDMA (SAC-OCDMA) networks adopted the purpose about the reducing multi-user interference (MUI) [11–25]. The MUI [11] produced the interferences of the other simultaneous users and severely reduced the capacity of the OCDMA network [12–23]. The interferences of the other simultaneous users decreased the performance of OCDMA system dramatically. The system adopted the interference cancellation scheme [25] to eliminate the MUI. The OCDMA system utilized the code sequences to produce a cross correlation constraint, which influenced the effect of phase-induced intensity noise (PIIN). Then, the OCDMA was enhanced by the reduction of PIIN [19–25]. However, the scheme had the cardinality reduction problem, which was not able to utilize all code sequences. The conventional codes used the SAC-OCDMA networks as follows: 1-D M Sequence codes [26], 1-D modified quadratic congruence (MQC) codes [27], and 1-D RSQC codes [28], which produced the several limitations. The 1-D M Sequence codes adopted the cross correlation

E-mail address: [email protected] http://dx.doi.org/10.1016/j.ijleo.2016.10.109 0030-4026/© 2016 Elsevier GmbH. All rights reserved.

Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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constraint, but the number of the simultaneous users was too small in the numerical results. The 1-D MQC codes suffered from the PIIN to reduce the system performance. The system performance of the 1-D RSQC codes was limited by the PIIN. In this paper, we propose the new family of newly constructed codes named the one-dimensional Multi Method codes (1-D MM codes) in the SAC-OCDMA system to overcome the MUI. The 1-D MM codes use the novel MUI cancellation scheme to be applied to the proposed system. Moreover, the proposed system performance is analyzed according to the MUI cancellation scheme. The proposed MUI cancellation scheme eliminates the MUI. This code design scheme is simple and can also be easily implemented by the proposed system. The proposed transmitter and receiver are the simple designs to produce a smaller PIIN. In addition, the proposed structure can use each transmitter, optical connected ring set (OCRS), and each receiver to achieve the one optical ring network. The proposed system uses the control path to give the user controller, correct optical fiber controller, and failure optical fiber controller to achieve the one optical ring network. Therefore, we gets the code sequences in the 1-D MM codes to enhance the control path in one optical ring network. The numerical results demonstrate the number of simultaneous users in the proposed system using the 1-D MM codes to be larger users than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. The data transmission rate in the proposed system using the 1-D MM codes is larger rate than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. Therefore, the bit error rate (BER) in the proposed system using the 1-D MM codes outperforms that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. This paper is organized as follows. The new family of newly constructed named the 1-D MM codes is described in Section 2. The corresponding system description is presented in Section 3. The performance analysis is derived in Section 4. The numerical results are shown in Section 5. Finally, we have the conclusion in Section 6. 2. 1-D multi method codes We propose the new family of newly constructed codes named the 1-D MM codes in the SAC-OCDMA system. The 1-D MM codes are characterized by the following parameters (Mp, p, a , c ), where Mp is the code length, p is the code weight, a is the auto-cross correlation constraint, and c is the cross correlation constraint. The code design scheme adopts the auto-cross correlation constraint a and cross correlation constraint c to develop the 1-D MM codes. The 1-D MM codes must satisfy the auto-cross correlation constraint a = p and cross correlation constraint c = 0. In other words, the code sequences of the 1-D MM codes have the auto-cross correlation constraint = p and cross correlation constraint = 0 to produce the recovered bits. The code design scheme is as follows. The 1-D MM codes adopt the code weight p and code length Mp to become the code sequences of the 1-D MM codes. The 1-D MM codes use the code weight p to be the positive integer numbers. The M and p are the most important items to create the 1-D MM codes. The 1-D MM codes can adopt a p to produce a new family of p-set. The code sequences of the 1-D MM codes have the (M-1)p numbers of “0” and p numbers of “1”. The p numbers of “1” adopts the p-set to use the code weight p, which produces the non-zero positions. The S(i) defines the {si,1 , si,2 , . . .,si,p }. The si,j is written as follows: si,j = (Mj⊕i1) + 1,

(1)

where si,j is created by the i code location and j code location,  and ⊕ are the modulo-M subtraction and addition, i code location denotes the integers as 1,2,. . .,M, and j code location denotes the integers as 1,2,. . .,p. When the code design scheme develops the S(i) sequence to produce the 1-D MM codes, the proposed system adopts the S(i) to become the code sequence C(i) = {ci,1 , ci,2 ,. . ., ci,Mp }. There is a one-to-one mapping because we transfer a S(i) to into the positions of the code sequence C(i). The S(i) produces the code sequence C(i) as follows:



ci,n =

1, n = si,j + (j − 1)M, 0,

(2)

otherwise,

where ci,n is the element of the C(i). The total code sequences are as follows:

⎡ ⎢

Ctotal = ⎣

C(1)

⎤ ⎥ ⎦

.. .

(3)

C(M) We operate the code sequence C(i) and code sequence C(ii) of the 1-D MM codes to produce the cross correlation constraint. The cross correlation constraint uses the summation and multiplication to execute the code sequence C(i) and code sequence C(ii). The cross correlation constraint between C(i) and C(ii) are as follows: C(i)  C(ii) =

nM

ci.m cii.m ,

(4)

m=1

Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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Table 1 Example of the code sequence in the proposed 1-D MM codes with p = 3 and M = 3. Number

S

i,j 1 2 3

1 3 1 2

2 2 3 1

3 1 2 3

...

Number

C

i,n 1 2 3

123 001 100 010

456 010 001 100

789 100 010 001

b1 bi

Transmitter(i)

Transmitter(1)

Extra transmitter input optical fiber

bM Transmitter(M) Transmitters region

...

Optical Ring Extra transmitter Connected Set output optical (ORCS) fiber Receiver(1)

Receiver(i) Receiver(M)

Extra receiver input optical fiber Extra receiver output optical fiber

Receivers region Fig. 1. System architecture with the conceptual schematic block diagram using the 1-D MM codes in the SAC-OCDMA system.

where  is the dot-product of two vectors. The dot-product of two vectors is the summation of the multiplication between ci,n using the element of the C(i) and cii,n using the element of the C(ii). C(i)  C(ii) =

p, i = ii, 0,

i= / ii,

(5)

where p is the code weight. When the C(i) and C(ii) have i = ii, the auto cross correlation constraint is the p. When the C(i) / ii, the cross correlation constraint is the zero. The code design scheme uses auto cross correlation and and C(ii) have i = cross correlation to eliminate the MUI. In addition, when the proposed system uses the MUI cancellation property using the auto cross correlation = p and cross correlation = 0, the code design scheme using the 1-D MM codes cancels the MUI. We get Table 1 to show the example of the code sequence in the proposed 1-D MM codes with p = 3 and M = 3. 3. System description The Transmitters get the information bits to encode the code sequences of the 1-D MM codes in the OCDMA system. The Receivers get the code sequences of the 1-D MM codes in the OCDMA system to produce the cross correlation, which become the recovered bits. The system description comprises the architecture and the control path. 3.1. Architecture Fig. 1 shows the system architecture with the conceptual schematic block diagram using the 1-D MM codes in the SACOCDMA system. The system architecture with the conceptual schematic block diagram using the 1-D MM codes in the SAC-OCDMA system comprises the OCRS, Transmitters region (M numbers of the transmitters), and Receivers region (M numbers of the receivers). The OCRS emits the optical light to connect to the Transmitters region. The Transmitters region connects to the OCRS. The OCRS connects to the Receivers region. The Receivers region connects to the OCRS. The ORCS sends the optical light into the Transmitters region and the Receivers region. The system operation is as follows. The transmitter(i) Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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OCRS Transmitter ring OCRS Transmitter output

BLS OCRS Transmitter input

OCRS Receiver input PD

OCRS Receiver output OCRS Receiver ring

Fig. 2. The structure of the optical ring connected set.

Transmitter(i)

Transmitter input i

hi=0

FBGti_1 tcpi

+ bi gi=0 Transmitter output i

ji=x Intra optical fiber

ki=x

Transmitter connected ring Fig. 3. The structure of the transmitter(i).

and receiver(i) design the specific code sequence C(i) in the 1-D MM codes. The proposed system uses the OCRS to output the optical light. The optical light goes through all transmitters to produce the code sequences of the optical light signals. The code sequences of the optical light signals go through all receivers to produce the recovered bits. Therefore, the transmitter(i) encodes the information bit into the specific code sequence C(i) and then broadcasts to the receiver(i). The receiver(i) gets the specific code sequence C(i) to produce the recovered bits. Fig. 2 shows the structure of the OCRS. The OCRS comprises the unpolarized BLS, OCRS Transmitter output, OCRS Transmitter input, OCRS Receiver output, OCRS Receiver input, OCRS Transmitter ring, OCRS Receiver ring, and OCRS photodiode. The OCRS Transmitter output, OCRS Transmitter input, OCRS Receiver output, OCRS Receiver input, OCRS Transmitter ring, and OCRS Receiver ring are the optical fibers. The unpolarized BLS emits the optical light to pass through the OCRS Transmitter output, which connect to the transmitter(i), i = 1,2,. . ., M. The transmitter(M) connects to the OCRS Transmitter input. The OCRS Transmitter input connects to the OCRS Receiver output, which connects to the receiver(i), i = 1,2,. . ., M. The receiver(M) connects to the OCRS Receiver input. The OCRS Receiver input connects to the OCRS photodiode. Therefore, the connections are the one optical ring network. Moreover, the users of the all transmitters and the all receivers control the control path. The detail discussion is on the 3.2 control path. Fig. 3 shows the structure of the transmitter(i), which is composed of the Transmitter input i, one fiber Bragg gratings (FBGs), (i.e., FBGti 1.), optical circulator, logical bitwise OR ⊕, three numbers of the 2 × 1 optical switches, three numbers of the 1 × 2 optical switches, and Transmitter output i. The intra optical fiber and transmitter connected ring are the optical fibers. If the user i uses the control path, the transmitter connected path tcpi is set to 1. The detail discussion is on the 3.2 control path. If the user i does not use the control path, the transmitter connected path tcpi is set to 0. The transmitter operation is as follows. If the transmitter(i) is set to the transmitter connected path tcpi = 0, we set hi = 0, gi = 0, ji = x for the unknown bit, and ki = x for the unknown bit as the line path in Fig. 3. The optical light signals go through the Transmitter input i to connect to the 2 × 1 optical switch turned on the voltage hi = 0. The transmitter connected path tcpi is the 0 to get the 1 × 2 optical switch and 2 × 1 optical switch turned on the voltage tcpi ⊕bi = bi . If the tcpi = 0, bi = 0, and tcpi ⊕bi = 0, the optical light signals connect to the one optical circulator. The one optical circulator connects to the FBGti 1. FBGti 1 has the number of gratings to design the spectral code sequence C(i). The FBGti 1 with the spectral code sequence C(i) filters out the spectral code sequence C(i) in the 1-D MM codes. The bi = 0 adopts the FBGti 1 to cancel the spectral code sequence C(i) in the transmitter(i). The 2 × 1 optical switch turned on the voltage tcpi ⊕bi = 0 connects to the 1 × 2 optical switch turned on the voltage gi = 0 to go through the Transmitter output i. If tcpi = 0, bi = 1, and tcpi ⊕bi = 1, the proposed system chooses the intra optical fiber to pass through the optical light signals. The optical light signals have the spectral code sequence C(i) of the transmitter(i). The intra optical fiber connects to the 2 × 1 optical switch turned on the voltage tcpi ⊕bi = 1. The 2 × 1 optical switch turned on the voltage tcpi ⊕bi = 1 connects to the 1 × 2 optical switch turned on the voltage gi = 0 to go through the Transmitter output i. Therefore, the transmitter operation adopts the transmitter(i) to output the code sequences of the 1-D MM codes, which broadcasts to the receiver(i). Fig. 4 shows the structure of the receiver(i), which consists of Receiver input i, two FBGs, (i.e., FBGri 1 and FBGri 2.), two optical circulators, three numbers of the 2 × 1 optical switches, three numbers of the 1 × 2 optical switches, one photodiode PDi , and Receiver output i. The intra optical fiber and receiver connected ring are the optical fibers. If the user i uses the Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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Receiver connected ring

li=x Receiver output i

ri=0

q =x Intra optical fiber i FBGri_2

FBGri_1

PD,i

Receiver input i

si=0

Circulator ri_2 Circulator ri_1 rcpi=0 Receiver(i) Fig. 4. The structure of the receiver(i).

control path, the receiver connected path rcpi is set to 1. The detail discussion is in the 3.2 control path. If the user i does not use the control path, the receiver connected path rcpi is set to = 0. The receiver operation is as follows. If the reviewer(i) sets the receiver connected path rcpi = 0, we set ri = 0, si = 0, li = x for the unknown value, and qi = x for the unknown value as the line path in Fig. 4. The optical light signals go through the Receiver input i to connect to the 2 × 1 optical switch turned on the voltage si = 0. The receiver connected path rcpi is set to the 0 to get the 1 × 2 optical switch and 2 × 1 optical switch turned on the voltage rcpi = 0. The 1 × 2 optical switch turned on the voltage rcpi = 0 connects to the Circulator ri 1. The passed path of the Circulator ri 1 connects to the FBGri 1. The FBGri 1 connects to the 2 × 1 optical switch turned on the voltage rcpi = 0. The he 2 × 1 optical switch turned on the voltage rcpi = 0 connects to the 1 × 2 optical switch turned on the voltage ri = 0 to output the Receiver output i. The optical light signals go through the FBGri 1, which is reflected back the code sequence C(i). The reversed path of the Circulator ri 1 connects to the optical circulator Circulator ri 2. The passed path of the Circulator ri 2 connects to the FBGri 2. In other words, the arrangements of the gratings in FBGri 1 are the same but contrary to that in FBGri 2. The reversed path of the Circulator ri 2 connects to the photodiode PDi . Since the receiver(i) can use the optical light signals to produce the cross correlation to output the photodiode PDi , the cross correlation is proportional to the photocurrent of the photodiode PDi . We adopt the photocurrent of the photodiode PDi to produce the system performance, which gets the photocurrent of the photodiode PDi and noises. Therefore, the receiver operation adopts the receiver(i) to decode the code sequences of the 1-D MM codes, which operate the cross correlation. The cross correlation of the receiver(i) eliminates the MUI property to recover the recovered bits. 3.2. Control path We derive the control path about the three terms. The three terms are the user controller, correct optical fiber controller and failure optical fiber controller. First, we derive the control path about the user controller. When the user controller is happening on the transmitter(i) in Fig. 3 and receiver(i) in Fig. 4, the user adopts the conditions of the out off in the 1-D MM codes or error (such as the error photodiode PDi ) to produce the transmitter connected path tcpi = 1 of the transmitter(i) and receiver connected path rcpi = 1 of the receiver(i). Then, the user controller uses the transmitter(i) and receiver(i) to produce the intra optical fiber of the transmitter(i) and intra optical fiber of the receiver(i) to do not communicate the i’th code sequence of the 1-D MM codes. Therefore, the user controller adopts the transmitter(i) and receiver(i) to control the transmitter connected path tcpi = 1 of the transmitter(i) and receiver connected path rcpi = 1 of the receiver(i), which do not communicate the i’th code sequence of the 1-D MM codes. Second, we derive the control path about the correct optical fiber controller. We operate the correct optical fiber controller to connect to the transmitter(m) and receiver(m) (∀m) without the Transmitter connected rings and Receiver connected rings. If the correct optical fiber controller connects to the transmitter(m) and receiver(m) using the gm = 0 (∀m), hm = 0 (∀m), km = x (∀m), jm = x (∀m), we use the transmitter(m) in Fig. 3 and receiver(m) in Fig. 4 to have the connections without the Transmitter connected rings and Receiver connected rings. The control path comprises the OCRS, transmitter(1), . . ., transmitter(m), . . ., and transmitter(M), OCRS Transmitter input of the OCRS, OCRS Receiver output of the OCRS, receiver(1), . . ., receiver(m), . . ., receiver(M), and OCRS Receiver input of the OCRS, which send to the PD of the OCRS in Fig. 2 to be the connections without the Transmitter connected rings and Receiver connected rings to become one optical ring network. Then, the correct optical fiber controller connects to the transmitter(m) and receiver(m) using the connections without the Transmitter connected rings and Receiver connected rings to communicate the m’th code sequence of the 1-D MM codes. Therefore, the correct optical fiber controller connects to the transmitter(m) and receiver(m) to control the connections without the Transmitter connected rings and Receiver connected rings to become the one optical ring network. Third, we derive the control path about the failure optical fiber controller. We operate the failure optical fiber controller to connect to the transmitter(m) and receiver(m) (∀m) with the Transmitter connected rings and Receiver connected rings. Fig. 5 shows the failure optical fiber between the transmitter(i) and transmitter(i + 1) and failure optical fiber between the / i), hi+1 = 1, hm = 0 receiver(i) and receiver(i + 1). If the failure optical fiber controller is happening using the gi = 1, gm = 0 (∀m = (∀m = / i + 1), ki = 0, km = 1 (∀m = / i), jj+1 = 0, jm = 1 (∀m = / i + 1), the control path in Fig. 5 comprises the OCRS, transmitter(1), Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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tcpi-1 + bi-1 gi--1=0

Transmitter(i)

hi=0

Transmitter(i+1)

hi+1=1 FBGt(i+1)_1 tcpi +1 + bi+1 gi+1=0

FBGti_1 tcpi + bi gi=1

hi+2=0 .

.

ki-1=1

. .

.

.

.

Intra optical fiber

ji=1 Intra optical fiber ki=0

ji+1=0

Transmitter connected ring

Transmitter connected ring

ki+1=1

.

. . .

. OCRS Transmitter ring OCRS Transmitter output BLS

optical connected ring set OCRS Transmitter input

OCRS Receiver input

PD

OCRS Receiver output

OCRS Receiver ring .

li=0

.

q =1 Intra optical fiber i

li-1=1

.

.

.

.

.

.

li+1=1 Intra optical fiber qi+1=0

.

.

qi+2=1

.

.

Receiver connected ring

Receiver connected ring

FBGr(i+1)2

si+2=0

ri+1=0 PD,i+1

FBGr(i+1)1

FBGri2

si+1=1

Correlator r(i+1)_2 Correlator r(i+1)_1 Receiver(i+1)

rcpi+1 =1

ri=1

FBGri1

PD,i

si=0

ri-1=0

Correlator ri_2 Correlator ri_1 Receiver(i) rcpi =1

Fig. 5. The failure optical fibers between the transmitter(i) and transmitter(i + 1) and failure optical fibers between the receiver(i) and receiver(i + 1).

. . ., transmitter(i), transmitter connected ring of the transmitter(i), . . ., transmitter connected ring of the transmitter(1), OCSR Transmitter ring of the OCRS, transmitter connected ring of the transmitter(M), . . ., transmitter connected ring of the transmitter(i + 1), transmitter(i + 1), . . ., transmitter(M), OCRS Transmitter input of the OCRS, OCRS Receiver output of the OCRS, receiver(1), . . ., receiver(i), receiver connected ring of the receiver(i), . . ., receiver connected ring of the receiver(1), OCRS Receiver ring of the OCRS, receiver connected ring of the receiver(M), . . ., receiver connected ring of the receiver(i + 1), receiver(i + 1), . . ., receiver(M), and OCRS Receiver input, which send to the PD of the OCRS to be the connections to become one optical ring network. Then, the failure optical fiber controller connects to the transmitter(m) and receiver(m) using the connections with the Transmitter connected rings and Receiver connected rings to communicate the m’th code sequence of the 1-D MM codes. Therefore, we develop the control path about the failure optical fiber controller using the connections with the Transmitter connected rings and Receiver connected rings to achieve the one optical ring network.

4. Performance analysis The performance analysis defines the bit error rate (BER). The cross correlation is proportional to the photocurrent of the photodiode and the noises are proportional to the photocurrent noises variances. The signal-to-noise ratio (SNR) divides the square of the photocurrent of the photodiode by the photocurrent noises variances. The BER calculates the SNR. In order to simplify the analysis, we make some assumptions as follows. Each of the spectral components has the identical spectral width. The broadband light source is ideally unpolarized and has the flat spectrum over [fo -f/2,fo + f/2], where fo and f are the central frequency and the bandwidth of the source. Each simultaneous user has equal power at the receivers. The power spectral density (PSD) of the received optical light signals can be written as:

L(f ) =

Psr f

W ω=1

Mp

d(ω)

ci,n (ω)F(f, n),

(6)

n=1

where Psr is the effective source power at the receiver, f is the bandwidth of the source, d(ω) is the information bit of the ω-th user, which can be information bit “1” or information bit “0”, W is the number of simultaneous users, p is the code Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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weight, ci,n (ω) represents an element of the ω-th user’s code sequence, and F(f, n) is the function. For the convenience of analysis, F(f, n) defines as follows: F(f, n) = { (f − f 0 − f (−Mp + 2n)/2/M/p) −  (f − f 0 − f (−Mp + 2n + 2)/2/M/p)},

(7)

where  (f) is the unit step function defined as:



1, f ≥ 0,

 (f ) =

(8)

f < 0.

0,

Therefore, the PSD of the received optical light signals operates the cross correlation to become the PSD of the received photodiode in the receiver(i). The cross correlation is proportional to the PSD of the received photodiode in the receiver(i). The cross correlation between code sequences C(1) and C(i) is proportional to the PSD of the received photodiode in the receiver(i) using the codeword during one bit period, which can be written as follows: W

Psr f

G(f ) =

Mp

d(ω)

(c1,n ci,n (ω))F(f, n),

(9)

n=1

ω=1

where the c1,n is an element of the first user’s code sequence and ci,n (ω) is an element of the i user’s code sequence. We adopt the d(ω) as 1, ω = 1, 2, . . ., W. The photodiodes are the photodiode PD1 , photodiode PD2 , . . ., and photodiode PDM . Therefore, the photocurrents of the photodiodes IPDi , i ∈ [1,2, . . ., M] is derived as follows:



∞

IPD,i = R RPsr Mp

=

G(f )df



0 ∞ W



0

Mp

d(ω)

ω=1

= RPsr /M,

(10)

(c1,n ci,n (ω))F(f, n)df

n=1

where R is the responsivity of the photodiode given by R = eo/hc,  is the quantum efficiency of the photodiode, e is the electron’s charge, h is the Planck’s constant, c is the light speed, and Psr is the effective source power of each receiver. The MUI has the interferences of the other simultaneous users because the proposed system is set to d(ω) = 1 and ω= 1,2,. . .,W to produce the worst case. The photocurrent of the photodiode in the receiver(i) can be written as Ir = IPDi . We derive the photocurrent noises variances. The photocurrent noises variances of the photodiode are the PIIN, shot noise, and thermal noise. In the following, we first consider the photocurrent noises variances as follows: = + < ishot 2 > + < ithemal 2 > = I r 2 Br ␶r + 2eI total Br + 4 K b Tn Br /R L ,

(11)

where PIIN, shot noise, and thermal noise are considered in the photocurrent analysis, the effect of the dark photocurrent is neglected, Ir is the photocurrent, Itotal is the total photocurrents, Br is the electrical bandwidth,  r is the coherence time of the light incident to the photodiode, e is the electron’s charge, Kb is Boltzmann’s constant, Tn is the absolute noise temperature, and RL is the load resistance. Therein,  r can be as follows [27]:





∞

0

2

∞

U 2 (f )df/

r =

U(f )df

,

(12)

0

where U(f) is the PSD of the received photodiode in the receiver(i). The photocurrent PIIN variance is given by Eq. (13), shown as the reference [27]. Based on the statistically independent noise characteristics, the PIIN are independent to the shot noise, and thermal noise. The photocurrent PIIN variance develops as follows:



2

2

< iPIIN >= Br Ir r , = Br R

2

∞

G2 (f )df,

(13)

0

where Br is the electrical bandwidth and  r is the coherence time of the light incident to the photodiode. We have the following results:



∞

G2 (f )df 0



= 0

∞

 Psr f

W

Mp

d(ω)

ω=1

2 (c1,n ci,n (ω))F(f, n)

2 = Psr /(fM),

(14)

df

n=1

where f is the bandwidth of the source. When we use the above equation with all number of simultaneous users, we can express the as follows: < iPIIN 2 > =

2 Br R2 Psr . fM

(15)

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8 Table 2 Parameters Used In The Numerical Calculation. Parameter

Number

PD quantum efficiency Wavelength location Spectral width of broadband light source Receiver noise temperature Receiver load resistor

 = 0.6 1.55 um ␭ = 60 nm Tn = 300 K RL = 1030 ˝

Since the information bit “1” and information bit “0” are sent with the equal probability for every simultaneous user, we have consequently Eq. (15) to be further revised as: < iPIIN 2 > =

2 Br R2 Psr . 2fM

(16)

Since the shot noise is independent of the PIIN and thermal noise, the photocurrent shot noise variance can be expressed as: = 2eBr (I total ) = 2eBr RPsr /M,

(17)

where Itotal = Ir . Since the information bit “1” and information bit “0” are sent with the equal probability for every user, we have = eBr RPsr /M.

(18)

Afterward, the photocurrent thermal noise variance is as follows: = 4 K b Tn Br /R L ,

(19)

where Kb is the Boltzmann’s constant, Tn is the absolute temperature, and RL is the load resistance. Therefore, the PIIN, shot noise, and thermal noise are the independent noises to achieve the photocurrent noise variances = photocurrent PIIN variance + photocurrent shot noise variance + photocurrent thermal noise variance. Therefore, we obtain the SNR as SNR = I r 2 / .

(20)

The Gaussian approximation is employed to estimate the BER. As a result, the proposed system calculates the SNR to produce the BER. The BER [27] is obtained as follows: √ √ BER = Pr(0)Pe(1|0) + Pr(1)Pe(0|1) 1 1 SNR ∗ 1/2 SNR √ = ) = erfc( erfc( √ √ ) 1 SNR ∗ (b1 − (b0 + b1 )/2) 2 2 ) = erfc( 8 2 √ 2 2

(21)

where Pr(0) and Pr(1) are the probabilities “0” and “1”, respectively, Pe(1|0) and Pe(0|1) are conditional error probabilities “0” and “1”, respectively, b0 is the “0”, b1 is the “1”, and erfc(•) is the complementary error function as [8]: 2 erfc(x) = √



∞

exp(−z 2 )dz.

(22)

x

Therefore, the BER produces the number of the simultaneous users, data transmitter rate, and effective source power to use the system performance. 5. Numerical results Table 2 shows the parameters used in the numerical calculation, which calculate the numerical results. Fig. 6 shows the number of simultaneous users versus the BER in the systems using the 1-D MM codes, 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes when the effective source power is set to 0 dBm and data transmission rate is set to 2.5Gbps. Fig. 6 compares the number of simultaneous users in the proposed system using the 1-D MM codes with that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. In Fig. 6 the proposed system observes the BER to be set to the BER = 10−9 . According to the BER = 10−9 , the number of simultaneous users in the proposed system using the 1-D MM codes reaches 25, that in the other system using the 1-D M Sequence codes reaches 2, that in the other system using the 1-D MQC codes reaches 19, and that in the other system using the 1-D RSQC codes reaches 14. The number of the simultaneous users in proposed system using the 1-D MM codes can accommodate more users than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. According to the number of the simultaneous users = 25, the BER in the proposed system using the 1-D MM codes reaches the 10−9 , that in the other system using the 1-D M Sequence codes reaches the 10−0.4 , that in the other system using the 1-D MQC codes reaches the 10−5.6 , and that in the Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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Fig. 6. The number of simultaneous users versus the BER in the systems.

Fig. 7. The data transmission rate versus BER in the systems.

other system using the 1-D RSQC codes reaches the 10−4 . The BER in the proposed system using the 1-D MM codes is lower rate than that in the other system using 1-D M Sequence codes, 1-D MQC, and 1-D RSQC codes. Fig. 7 shows the data transmission rate versus BER in the systems using the 1-D MM codes, 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes when the number of simultaneous users is 25 and the effective source power is 0dBm. Since the BER in the systems is set to the 10−9 , the data transmission rate in the proposed system using the 1-D MM codes is the 2.5Gbps, that in the other system using the 1-D M Sequence codes is the 0.01Gbps, that in the other system using the 1-D MQC codes is the 1.4Gbps, and that in the other system using the 1-D RSQC codes is the 0.9Gbps. Furthermore, Fig. 7 shows that the data transmission rate in the proposed system using the 1-D MM codes is larger rate than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. According to the data transmission rate = 2.5Gbps, the BER in the proposed system using the 1-D MM codes reaches the 10−9 , that in the other system using the 1-D M Sequence codes reaches the 10−0.5 that in the other system using the 1-D MQC codes reaches the 10−5.4 , and that in the other system using the 1-D RSQC codes reaches the 10−3.8 . The BER in the proposed system using the 1-D MM codes is lower rate than that in the other system using 1-D M Sequence codes, 1-D MQC, and 1-D RSQC codes. Fig. 8 shows the effective source power versus the BER in the systems using the 1-D MM codes, 1-D M Sequence codes, 1-MQC codes, and 1-D RSQC codes. The number of simultaneous users is 25 and data transmission rate is 2.5Gbps. Since the effective source power is 0dBm, the BER in the proposed system using the 1-D MM codes is the 10−9 , that in the other system using the 1-D M Sequence codes is the 10−0.4 , that in the other system using the 1-D MQC codes is the 10−5.6 , and that in the other system using the 1-D RSQC codes is the 10−4 . The BER in the proposed system using the 1-D MM codes is lower rate than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. According to the BER = 10−9 , the effective source power in the proposed system using the 1-D MM codes reaches the 0dBm, that in the other system using the 1-D M Sequence codes, 1-D MQC codes, 1-D RSQC codes reach the no point in Fig. 8. The effective Please cite this article in press as: B.-C. Yeh, Noncoherent spectral optical CDMA system using 1-D multi method codes in one optical ring network, Optik - Int. J. Light Electron Opt. (2016), http://dx.doi.org/10.1016/j.ijleo.2016.10.109

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Fig. 8. The effective source power versus the BER in the systems.

source power in the proposed system using the 1-D MM codes is lower power than that in the other systems using 1-D M Sequence codes, 1-D MQC, and 1-D RSQC codes. 6. Conclusion In this paper, we propose a new family of new constructed codes named 1-D MM codes in the SAC-OCDMA system. The proposed system architecture uses the OCDMA using one optical ring network. The proposed system architecture adopts the transmitters region, OCRS, and receivers region. The proposed system adopts the control path to give the user controller, correct optical fiber controller and failure optical fiber controller. The user controller gives the users to control the transmitter connected path tcpi = 1of the transmitter(i) and receiver connected path rcpi = 1 of the receiver(i), which determine to do not communicate the code sequence of the OCDMA. If the proposed system has the correct optical fiber controller to be happening, the proposed system adopts the connections without the Transmitter connected rings and Receiver connected rings to produce the connections in one optical ring network. If the proposed system has the failure optical fiber controller to be happening, the proposed system adopts the connections with the Transmitter connected rings and Receiver connected rings to produce the connections in one optical ring network. In addition, the proposed system can eliminate the MUI. In fact, the effect of PIIN thereby can be reduced by the proposed system. The numerical results demonstrate that the numbers of simultaneous users in the proposed system using the 1-D MM codes reaches the 25 users. The code size of the 1-D MM codes is equal the 25. The numbers of simultaneous users in the proposed system using the 1-D MM codes are more users than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. The data transmission rate in the proposed system using the 1-D MM codes achieve the 2.5Gbps and is larger rate than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes and 1-D RSQC codes. The effective source power in the proposed system using the 1-D MM codes is the 0 dBm and is less power than that in the other systems using the 1-D M Sequence codes, 1-D MQC codes, and 1-D RSQC codes. Acknowledgment The authors wish to thank the facilities and financial support from High Speed Intelligent Communication (HSIC) Research Center in Chang Gung University Taiwan. References [1] W.C. Kwong, P.A. Perrier, P.R. Prucnal, Performance comparison of asynchronous and synchronous code-division multiple-access techniques for fiber-optic local area networks, IEEE Trans. Commun. 39 (1991) 1625–1634. [2] I.B. Djordjevic, B. Vasic, J. Rorison, Multi-weight unipolar codes for spectral-amplitude-coding optical CDMA systems, IEEE Commun. Lett. 8 (2004) 259–261. [3] R. Prucnal, M.A. Santoro, T.R. Fan, Spread spectrum fiber-optic local area network using optical processing, IEEE J. Lightwave Technol. 4 (1986) 547–554. [4] M. Noshad, K. Jamshidi, Bounds for the BER of codes with fixed cross correlation in SAC-OCDMA systems, IEEE J. Lightwave Technol. 29 (2011) 1944–1950. [5] G.C. Yang, W.C. Kwong, Prime Codes with Applications to CDMA Optical and Wireless Networks, Artech House, Norwood, MA, USA, 2002. [6] R.K.Z. Sahbudin, M. Kamarulzaman, S. Hitam, M. Mokhtar, S.B.A. Anas, Performance of SAC OCDMA-FSO communication systems, Optik 124 (2013) 2868–2870. [7] W.B. Yang, K. Sayrafian-Pour, A low complexity interference cancellation technique for multi-user DS-CDMA communications, IEEE Int. Conf. Commun. (ICC) (2010) 1–5. [8] C.C. Yang, Compact optical CDMA passive optical network with differentiated services, IEEE Trans. Commun. 57 (2009) 2402–2409.

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