1776 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 6, JUNE 2009 Performance Degradation of Source Matching in Optical CDMA Due to Source Coherence Effects Mohammad M. Rad, Student Member, IEEE, Leslie A. Rusch, Senior Member, IEEE, and Jean-Yves Chouinard, Senior Member, IEEE Abstract—In this paper we study the performance of source matching technique for an optical code division multiple access (OCDMA) system in the presence of source coherence effects and square law detection process. We use a binary-asymmetric chan- nel (BAC) model for an OCDMA system employing an all-optical passive correlator receiver. Source coherence effects lead to relative-intensity-noise (RIN) and phase-induced-intensity-noise (PIIN), which are included in our analysis. Previous studies only considered multiple access interference (MAI) noise, resulting in a Z-channel (where errors only occur for the transmission of data bit zero) model, and neglected RIN and PIIN. The presence of RIN and PIIN leads to errors occurring for both transmitted data bits one and zero, thus a BAC model. We show that source matching gain depends on the normalized source coherence time, defined as the ratio of the optical source coherence time to the bit duration. Our analysis shows that, while MAI limited analysis predicts that increasing the number of users increases the source matching gain, when taking into account RIN and PIIN, source matching gain is both bit rate and source type dependent, and tends to zero for very high numbers of users. Index Terms—Optical code division multiple access (OCDMA), multiple access interference (MAI), source coherency, relative- intensity-noise (RIN), phase-induced-intensity-noise (PIIN), bi- nary asymmetric channel (BAC), optimal source distribution, capacity, source matching. I. I NTRODUCTION D IRECT detection of optical code division multiple access (CDMA) involves the intensity addition of optical pulses at photodetection, or system positivity [1,2], with each optical pulse contributing a positive quantity. Pulses originating from sources other than the desired user cause multiple access interference (MAI), which limits performance. Detected in- tensity is proportional, in the mean, to the number of pulses from interfering users (MAI). Intensity fluctuates severely around this mean due to relative intensity noise (RIN) and phase induced intensity noise (PIIN), causing much greater signal impairments than first order (in the mean) effects. RIN exists for all sources and quantifies the intensity fluctuation of the optical pulse. In the case of coherent sources (such as lasers), due to their very high damping ratio, RIN is generally neglected [3,4]. Paper approved by I. Andonovic, the Editor for Optical Networks and Devices of the IEEE Communications Society. Manuscript received July 10, 2007; revised February 14, 2008. This paper has been presented in part at the 7 th Canadian Worshop on Information Theory in 2007 (CWIT07), Alberta, Canada. The authors are with the Department of Electrical Enginnering at Laval University, Quebec (QC), Canada G1K7P4 (e-mail: larusch@gelulaval.ca). M. M. Rad and L. A. Rusch are also with the Centre for Optics, Photonics, and Laser (COPL). Digital Object Identifier 10.1109/TCOMM.2009.06.070334 RIN is a severe problem in the case of broadband (in- coherent) thermal sources (such as LEDs). Phase-induced- intensity-noise (PIIN), or beat noise, arises in optical systems detecting more than one pulse whenever the center frequencies of the pulses have separation smaller than the electrical bandwidth of the receiver [4]. PIIN occurs for both coherent and broadband sources when detecting multiple pulses where center frequencies are sufficiently close. The multiple pulses may have the same origin, i.e., be delayed versions of the same sources, or may originate from different sources and/or phys- ical locations. In the simplest case, when all the interfering incident optical pulses at the photodetector surface have the same center wavelength, the power of the electrically filtered PIIN term is a simple function of the number of incident pulses and the normalized optical signal coherence time [4]. The normalized optical signal coherence time is defined as the source coherence time of the optical source divided by the electrical integration time (typically the bit time). Note that PIIN only exists when the number of detected pulses is larger than one, while RIN exists even when only one pulse is detected. Therefore, in the case of broadband sources, both RIN and PIIN exist, while for coherent laser sources RIN can be neglected but PIIN must still be taken into account. As multiple user OCDMA systems always involve detection of more than one optical pulse, PIIN exists for all types of OCDMA systems including time domain (time-spreading), wavelength domain (frequency-hopping) or wavelength-time (λ -t) domain based systems [5]. RIN is also significant when broadband sources are used. RIN and PIIN are often neglected in theoretical studies, but have been identified experimentally as the limiting noise sources for several types of OCDMA, including λ - t [6] and spectral amplitude coded (SAC) OCDMA [7]. The experimental eye-diagrams in Figure 1 were generated for λ - t and SAC-OCDMA systems. In Figure 1 (a), a single user λ - t system, with 8 lasers on different frequencies, is examined at 1.25 Gb/s. Thermal noise is visible for both the logical zero (0) and the logical one (1) signals. However, as only coherent sources are used, no significant RIN is present. Since it is a single user system, no PIIN exists (note that the laser center frequencies are separated by more than the electrical bandwidth of the receiver). In Figure 1 (b), the same system now has three interfering users: each interferer contributes one optical pulse in the detection window. Significant PIIN is visible due to beating of interfering pulses with the desired user pulses. Figures 1 (c) and (d) depict experimental eye diagrams for SAC-OCDMA at 155 Mb/s. As shown in Figure 1 (c), the single user SAC- OCDMA system experiences severe RIN impairments since a 0090-6778/09$25.00 c  2009 IEEE