Performance of asynchronous fiber-optic code division multiple access system based on three-dimensional wavelength/time/space codes and its link analysis

Jaswinder Singh

doi:10.1364/AO.49.001355

Applied Optics
Vol. 49,
Issue 8,
pp. 1355-1363
(2010)
•https://doi.org/10.1364/AO.49.001355

Performance of asynchronous fiber-optic code division multiple access system based on three-dimensional wavelength/time/space codes and its link analysis

Jaswinder Singh

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Jaswinder Singh, "Performance of asynchronous fiber-optic code division multiple access system based on three-dimensional wavelength/time/space codes and its link analysis," Appl. Opt. 49, 1355-1363 (2010)

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- Fiber Optics and Optical Communications
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About this Article
History
- Original Manuscript: August 3, 2009
- Revised Manuscript: December 20, 2009
- Manuscript Accepted: January 24, 2010
- Published: March 8, 2010

Abstract

A novel family of three-dimensional (3-D) wavelength/time/space codes for asynchronous optical code-division-multiple-access (CDMA) systems with “zero” off-peak autocorrelation and “unity” cross correlation is reported. Antipodal signaling and differential detection is employed in the system. A maximum of $[(W \times T + 1) \times W]$ codes are generated for unity cross correlation, where W and T are the number of wavelengths and time chips used in the code and are prime. The conditions for violation of the cross-correlation constraint are discussed. The expressions for number of generated codes are determined for various code dimensions. It is found that the maximum number of codes are generated for $S \leq \min (W, T)$ , where W and T are prime and S is the number of space channels. The performance of these codes is compared to the earlier reported two-dimensional (2-D)/3-D codes for asynchronous systems. The codes have a code-set-size to code-size ratio greater than $W / S$ . For instance, with a code size of 2065 ( $59 \times 7 \times 5$ ), a total of 12,213 users can be supported, and 130 simultaneous users at a bit-error rate (BER) of $10^{- 9}$ . An arrayed-waveguide-grating-based reconfigurable encoder/decoder design for 2-D implementation for the 3-D codes is presented so that the need for multiple star couplers and fiber ribbons is eliminated. The hardware requirements of the coders used for various modulation/detection schemes are given. The effect of insertion loss in the coders is shown to be significantly reduced with loss compensation by using an amplifier after encoding. An optical CDMA system for four users is simulated and the results presented show the improvement in performance with the use of loss compensation.

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No. of Space Channels, S	$r_{v}$	No. of Codes Generated
$S \leq \min (W, T)$	$W \times T$	$W^{2} T + W$
$\min (W, T) < S \leq \max (W, T)$	$\max (W, T)$	$[\max (W, T) \times W] + W$
$\max (W, T) < S$	$\min (W, T)$	$[\min (W, T) \times W] + W$

Code Name	Code Size	Users Supported	Simultaneous Users at $10^{- 9}$
3-D T-W-P	$11 \times 4 \times 2 = 88$	25	4
3-D GRZI-BCDD	$13 \times 3 \times 2 = 78$	$0.5 \times (W^{2} \times T + W) = 260$	$\sim 10$

Code Family	Code Dimensions	Code Size ( $wavelengths \times time-chips$ )	$λ_{c}$	Simultaneous Users at $10^{- 9}$ (Approx.)	Users Supported	Users Supported/ Code Size
2-D PCBD	$(L \times p) \times p$	$(7 \times 17) \times 17 = 2023$	$4 (= w)$	$(p - 1) = 6$ (worst case)	$2 \times L \times p = 238$	$\frac{2}{p} = 0.117$
2-D code of U.S. Patent 0100338 A1	$M \times N$	$64 \times 4 = 256$	0	126	$2 \times (M - 1) = 126$	$\frac{2 \times (M - 1)}{M \times N} = 0.49$
3-D W-T-S (GRZI-BCDD)	$W \times T \times S$ where $S \leq \min (W, T)$	$59 \times 7 \times 5 = 2065$	1	130	$0.5 \times [(W \times T + 1) \times W] = 12213$	$\frac{0.5 \times [(W \times T + 1) \times W]}{W \times T \times S} = 5.914$

Code Name	Modulation/Detection Scheme	Code Size	AWGs, Filters, Delay Lines in Encoder and Decoder		Users Supported
2-D W-T [2]	OOK/Direct Detection	$W \times T = 4 \times 520$	--, W, T	--, W, T	$T = 520$
2-D W-T [7] (Code $size = 128$ )	OOK/Differential Detection	$W \times T = 64 \times 4$	--, W, $2 T$	--, W, $2 T$	$2 \times (M - 1) = 126$
2-D W-T [3]	OOK/Differential Detection	$W \times T = (17 \times 7) \times 17$	--, $T \times (L + 1) / 2$ , T	--, W, $2 T$	$2 \times L \times p = 238$
3-D S-W-T [9]	OOK/Direct Detection	$(S \times W) \times T = 8 \times 127 \times 2$	01, --, S	01, --, S	$W \times T = 254$
3-D W-T-S (GRZI-BCDD)	Antipodal Signaling/ Differential Detection	$(W \times S) \times T = 59 \times 5 \times 7$	02, --, $2 S$	02, --, $2 S$	$0.5 \times [(W \times T + 1) \times W] = 12213$

No. of Space Channels, S	$r_{v}$	No. of Codes Generated
$S \leq \min (W, T)$	$W \times T$	$W^{2} T + W$
$\min (W, T) < S \leq \max (W, T)$	$\max (W, T)$	$[\max (W, T) \times W] + W$
$\max (W, T) < S$	$\min (W, T)$	$[\min (W, T) \times W] + W$

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Applied Optics