JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 18, NO. 9, SEPTEMBER 2000 1187 Maximum Achievable Number of Users in Optical PPM-CDMA Local Area Networks Hossam M. H. Shalaby, Senior Member, IEEE Abstract—An optical code-division multiple-access (CDMA) communication network employing optical orthogonal codes is considered. The data symbols of each multiple-access user is encoded, before multiplexing, using pulse-position modulation (PPM) technique with sufficiently large pulse position multiplicity. The concepts of both users rate and users strength are introduced. Using these concepts an achievable number of simultaneous users that can be accommodated by the optical PPM-CDMA channel, while keeping the transmitted information per photon fixed and maintaining the probability of error below some prescribed threshold , is determined. Furthermore, it is shown that the users strength has a simple positive characterization and in turn it is possible to load the entire subscribers simultaneously into the optical channel and embrace arbitrary small error rate. Index Terms—Code division multiple access (CDMA), direct de- tection optical channel, optical CDMA, pulse-position modulation (PPM), spread spectrum. I. INTRODUCTION I N OPTICAL code-division multiple-access (CDMA) systems, users transmit information simultaneously over a common optical channel, Fig. 1. Each user is assigned a code (called the signature code) with length and weight . We focus on optical orthogonal codes (OOCs) with both off-peak autocorrelation and cross-correlation bounded by . Methodologies in the design and analysis of such codes can be found in [1], [2]. An optical pulse (laser on) of duration is transmitted whenever a “1” occurs in the signature code and a “0” is transmitted (laser off) for the same duration, otherwise. Each user generates -ary data symbols . These symbols are encoded with the aid of pulse-position modulation (PPM) schemes. In PPM, a time frame of duration is subdivided into disjoint slots, each slot has a width . The user’s information is conveyed by transmitting a signature code (with optical pulses) in one of the possible slots within the time frame. The relation between the optical pulsewidth and is thus . An example of such format is given in Fig. 2 with , , and . The bit error rate performance of the above system has been studied in [3]–[6] for the case of . We have found in [5], [6] that while keeping the transmitted information per photon ( nats/photon) fixed and maintaining the probability of error Manuscript received July 26, 1999; revised May 23, 2000. The author is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, on leave from the Department of Electrical Engineering, Faculty of Engineering, University of Alexandria, Alexandria 21544, Egypt (e-mail: eshalaby@ieee.org). Publisher Item Identifier S 0733-8724(00)08069-5. below some prescribed threshold , the number of simultaneous users can be increased as desired by increasing the possible number of pulse positions . Of course the price to be paid is the increase in the bandwidth in order to have same throughput per unit time. Another limitation is the maximum available number of subscribers (or signature codes) dictated by the design criteria of OOCs. Indeed for , the number of available code sequences cannot exceed . Obviously this limit can be tolerated by increasing the code length leading to a narrower pulsewidth or increasing with fixed. Other more frequently encountered optical CDMA models [7]–[13] employ ON–OFF keying (OOK) instead of PPM before multiplexing. In this case the number of users cannot be increased freely without destroying the error rate threshold for any given value of . The superiority of PPM-CDMA over OOK-CDMA in that sense makes it an attractive candidate in local area networks (LANs). Moreover, the traditional advan- tages in using PPM rather than OOK add to its preeminence, namely, it does not require a threshold in the detection process and is more efficient in utilizing the laser energy. There have been some variants to the traditional optical CDMA systems in order to enhance its performance. Ohtsuki et al. [10] have proposed a synchronous optical CDMA system with double optical hard-limiters placed before and after the optical correlator. It has been shown that this system introduces an improvement in the performance over the system without optical hard-limiters as long as the number of users is not so large. In the case of asynchronous optical CDMA, Ohtsuki [11], [12] has shown that this improvement continues for all possible number of users. Another optical CDMA technique was introduced by Lam and Hussain [14] and generalized by Kwon [15]. In [15], multibits of the user data are mapped into shifted versions of the signature code allowing nats to be transmitted per sequence period. It has been shown that this system outperforms OOK scheme at the expense of increasing the hardware complexity. In our study of optical PPM-CDMA networks we assume equi-probable data symbols, i.e., , . The transmitted information in nats per channel use is thus equal to For the sake of convenience, we will denote the last piece of information by : nats/channel use Since both the maximum number of simultaneous users and the probability of error depend on (or equivalently ), they may be denoted by and , respectively. 0733–8724/00$10.00 © 2000 IEEE