ARTICLE IN PRESS
Optik
Optics
Optik 120 (2009) 959–962 www.elsevier.de/ijleo
A new family of two-dimensional codes for optical CDMA systems Jaswinder Singha,, Maninder Lal Singhb a
Department of Electronics & Communication Engineering, Beant College of Engineering & Technology, Gurdaspur, India Department of Electronics Technology, Guru Nanak Dev University, Amritsar 143005, India
b
Received 30 October 2007; accepted 12 March 2008
Abstract The design of a new family of two-dimensional single pulse per column codes for optical code division multiple access (OCDMA) networks is reported. The 1-D modified pseudo-noise codes have been known to be orthogonal and their generation and system design based on these codes is rather simple. But their performance is limited due to the bandwidth constraints if the code length increases. Hence, using these 1-D modified pseudo-noise codes, modified 2-D pseudo-noise matrix codes (MPMCs) are generated. The system performance is evaluated for two, three and four simultaneous users using the link with all the sources responsible for degradation included: attenuation, chromatic dispersion, non-linear refractive effects, non-linear scattering and four-wave mixing. The effect of the non-linear and lossy dispersive medium over the system performance is shown by plotting the BER with respect to the link length for the systems designed using encoders/decoders base on 1-D modified pseudo-noise codes and our MPMCs. The performance is compared for the two types of codes by finding the crosstalk due to interfering users simultaneously operating in the network. r 2008 Elsevier GmbH. All rights reserved. Keywords: Differential detection; Multi-access interference; Optical code division multiple access (OCDMA); Single pulse per row (SPPR) codes; Two-dimensional W-T codes
1. Introduction For high-speed access and local-area networks, the passive broadcast optical networks have been considered the most promising. Optical code division multiple access (OCDMA) is one such scheme with many attractive features (Fig. 1). The codes used for designing the encoders/decoders for fiber-optic communication systems are the (0, 1) codes because of the nonnegativity of the optical fiber channel.
Corresponding author.
E-mail addresses:
[email protected] (J. Singh),
[email protected] (M.L. Singh). 0030-4026/$ - see front matter r 2008 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2008.03.031
The PN codes like gold codes as well as the maximal length codes suffer from the multi-access interference problem as the number of 0’s and 1’s in these codes are not equal so the modified PN codes have been developed [1], but these belong to the class of one-dimensional codes. Because of the poor performance with the onedimensional codes, many two-dimensional code families have been proposed [2–4] and designed for different kinds of detection schemes such as IM/DD and differential detection [5]. In [2], the prime codes have been used for time-spreading and optical orthogonal codes for frequency hopping patterns to obtain better crosstalk properties. But still the BER performance is not very convincing for 1 Gbps data rates as only a few users can be behaviour accommodated for BER of
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Data user 1
Encoder/Modulator 1
Data user 2
Encoder/Modulator 2 ο Fiber Link
MUX
ο Light Source
ο ο Encoder/Modulator 7
Data user 7
Decoder 1
Receiver 1
Fig. 1. A generalized OCDMA system. Tc λ1
λ2 Nw λ3
λ4
2. Code design
Lt
Fig. 2. Example of unbalanced SPPR code with Nw ¼ 4 and Lt ¼ 4. Tc is duration of a time chip [6]. Stuffing Bit PN code 1 1 0 1
1 1 1 0
Code#1 Code#2 Code#3 Code#4
1 0 1 0
Code#7
1 1 0 0 1 0 1 0
0 1 1 1
0 0 1 1
1 0 0 1
0 1 0 0
0 0 0 0
Fig. 3. Modified PN code of length 8 [1].
11100100 Modified PN Code
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 0 0 1 0 0
(λ1, λ2, λ3, λ6)
MPMC Code
Fig. 4. Deriving the 2-D MPMC code from the 1-D modified PN code. Table 1.
1e9, even with the use of differential detection. In [6,7] one-dimensional and two-dimensional codes have been proposed, but despite their good correlation properties, these have very long temporal lengths. More is the temporal length of the code, i.e. more the number of time chips, more will be the bandwidth expansion or lower the data rates supported. In [1], the one-dimensional modified pseudo-random codes are generated from the pseudo-random codes, by stuffing of a zero bit in the end of each code. The family of the pseudo-random codes is generated by clock-wise shifting of the chips of the first pseudo-random code of the family. In this paper, the generation of the family of twodimensional modified pseudo-noise matrix codes (MPMCs) from the one-dimensional modified pseudonoise code family of [1] is presented and the analysis of this code family is given. These generated codes have a single pulse in each of the columns of the matrix; hence these are suited for designs using fiber gratings. The example of a single pulse per column code is shown in Fig. 2.
The difference of our 2-D MPMCs from the modified PN codes (Fig. 3) is that these 2-D codes carry the optical pulses only in the chip slots which are 1’s, as per their position in the code whereas the modified PN codes carry the wavelengths in the ‘1’ and the complement wavelengths in the ‘0’ bit periods [1,3]. So, although differential detection has been used with modified PN codes, still because of the presence of the signal during the whole of the ‘1’ and ‘0’ bit periods, there is considerable crosstalk interference among the users and hence the performance is limited. Fig. 4 shows the conversion of the 1-D modified PN code into an 8-by-4, 2-D unbalanced MPMC W-T code. After each ‘1’ chip, n zero chips are stuffed. Here, n is equal to the number of wavelengths used and these numbers of wavelengths are equal to the size of the modified PN code or its integral multiple. The elements of the 1-D code are written downwards. Because the addition of any number of zeroes equally in between all the 1’s of the code does not change its correlation properties, so this code also has the same correlation properties as the original 1-D modified PN code. The translation of the 1-D code into the 2-D matrix code of a
Important system parameter values
System parameter
Peak pulse power
Bitrate/user
Optical pulse width
First wavelength
Channel spacing
Chip period
Value used
1 mW
2.5 Gbps
0.02 ns
1548.6 nm
0.4 nm
0.1 ns
ARTICLE IN PRESS J. Singh, M.L. Singh / Optik 120 (2009) 959–962
10-8 10-10 10-12 BER
10-15 10-19 10-24 10-29
user 1_MPMC
10-35
user 1_PN
-43
10 10-52 1
2
3
4
5 6 7 fiber_spans
8
9
10
10-1 10-2 10-3 10-5
BER
size can be selected by selecting the number of rows and hence the number of columns gives the flexibility in choosing the size of the two dimensions. This flexibility increases with the increase in the code size. In this paper, eight wavelengths have been used and hence the 2-D MPMCs have eight rows. The matrix in Fig. 4 can be written as the time positions of the wavelengths as shown on the right in the same figure. A modified PN code can be represented by the positions of 1’s in the sequence. As shown in the figure, code (1,1,1,0,0,1,0,0) can be written as (1,2,3,6) and similarly the other codes of the family can be written. The generated code matrix has only a single ‘1’ chip in all the columns of the matrix, i.e. there will be only a single wavelength present. The size of this family of codes is (number of wavelengths used 1) with a cross-correlation of 2. We call this family of 2-D modified matrix codes as MPMCs.
961
10-9 10-16
3. System design and simulation
10-27 user 1_MPMC
10-47
Fig. 5. BER vs. length of the span for the two schemes when there are (a) two simultaneous users, (b) three simultaneous users, (c) four simultaneous users and (d) four simultaneous users for MPMCs only (shows variation for MPMC scheme on a zoomed scale). User 1 is default user in both cases. PN in the figure is a modified PN code.
user 2_PN
10-80 10-137
1
2
3
4
5 6 7 fiber_spans
10-1
8
9
10
user 1_MPMC user 1_PN
10-2 BER
10-3 10-5 10-8 10-12 10-18 10-27 10-41 1
2
3
4
5 6 7 fiber_spans
8
9
10-25
BER
The link used between the transmitter and the receiver consists of iterated number of fiber spans, each of length 50 km, which is fully loss and dispersion compensated (corning_vascade_l1000 as regular fiber and corning_vascade_s1000 as the DCF fiber and uses amplification after each 50 km). The number of fiber_ spans is iterated to see the effect of link length on BER and signal degradation (due to channel impairments). The non-linear effects that have been considered for the link are attenuation, chromatic dispersion, non-linear refractive effects, non-linear scattering and four-wave mixing (PMD has been assumed to be very small to be ignored). The eight mode-locked laser sources used have wavelengths symmetrically placed around the zero dispersion wavelength of the fiber, i.e. 1550 nm (giving the worst FWM condition in the link) with the first wavelength placed at 1548.6 nm and the higher wavelengths with a uniform spacing of 0.4 nm. The analysis has been carried out assuming that the beat noise is not present. The delay line encoder encodes the data from users with the wavelength pattern given by the code assigned to the corresponding users. For example, user 1 uses the wavelength pattern of (l1, l2, l3, l6) for encoding of the 1’s in the data generated by user 1. The other important system parameter values are given in Table 1.
10-26
10-27
MPMC 4 users
1
2
3
4
5 6 7 fiber_spans
8
9
10
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Crosstalk
102
101
100 MPMC modified PN
10
-1
2
3 4 5 6 No. of simultaneous users
7
Fig. 6. Back-to-back crosstalk vs. number of simultaneous users.
4. Results and discussions Fig. 5 shows the plots of the BER rates vs. the fiberspans in the link, where each fiber-span is 50 km long. RSOFT’s Optsim simulation tool has been used to carry out the simulations to obtain the graphs shown in Fig. 5. The various plots are drawn for two, three and four simultaneous users operating in the network for the cases of our 2-D MPMC and modified PN codes. BER plots for user 1 have been plotted for both the code families for two, three and four simultaneous users. In Fig. 6 is plotted the back-to-back crosstalk in the two systems due to the interfering users simultaneously operating in the network. These figures (Figs. 5 and 6) show that the 2-D MPMCs outperform the 1-D modified PN codes in terms of the BER achieved due to the effect of the increase of link length of the nonlinear and lossy channel and in terms of the back-toback crosstalk. The crosstalk is calculated as Crosstalk ¼
Pall users transmitting Pdesired user transmitting . Pdesired user transmitting
This has been plotted in Fig. 6 for the two codes for different number of simultaneous users.
5. Conclusions We have presented a new and simple way of designing the two-dimensional W/T codes from the one-dimen-
sional modified PN codes and presented the comparative results of our 2-D MPMCs and those of 1-D modified PN codes, showing the system performance for up to four users operating simultaneously in the network. The results indicate that there is a significant improvement in the performance of the system with the 2-D MPMCs. It is also shown that the effect of the non-linear dispersive medium over the performance of the system with MPMCs is insignificant for link length up to 500 km as shown in the BER with respect to the link length plots, and also the back-toback crosstalk is plotted for the two types of codes with respect to the number of users simultaneously accessing the network that shows better performance of 2-D MPMCs.
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