IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 8, AUGUST 2006 1457 Code-Division Multiple-Access Techniques in Optical Fiber Networks—Part III: Optical AND Logic Gate Receiver Structure With Generalized Optical Orthogonal Codes Saeed Mashhadi, Student Member, IEEE, and Jawad A. Salehi, Member, IEEE Abstract—In this paper, we present a deep insight into the be- havior of optical code-division multiple-access (OCDMA) systems based on an incoherent, intensity encoding/decoding technique using a well-known class of codes, namely, optical orthogonal codes (OOCs). As opposed to parts I and II of this paper, where OOCs with cross-correlation were considered, we consider generalized OOCs with , where is the weight of the corresponding codes. To enhance the performance of such systems, we propose the use of an optical AND logic gate receiver, which, in an ideal case, e.g., in the absence of any noise source, except the optical multiple-access interference, is optimum. Using some basic laws on probability, we present direct and exact solutions for OOCs with , with the optical AND logic gate as receiver. Using the exact solution, we obtain empirical solutions that can be easily used in optimizing the design criteria of such systems. From our optimization scheme, we obtain some fresh insight into the performance of OOCs with . In particular, we can obtain some simple relations between (minimum error rate), (minimum required OOC length), and (maximum number of interfering users to be supported), which are the most desired parameters for any OCDMA system design. Furthermore, we show that in most practical cases, OOCs with perform better than OOCs with , while having a much bigger cardinality. Finally, we show that an upper bound on the maximum weight of OOCs are on the order of where is the length of the OOCs. Index Terms—Generalized OOCs, optical AND logic gate re- ceiver structure, optical code-division multiple-access (OCDMA), optical orthogonal codes (OOCs), optimum auto- and cross-cor- relation value, optimum weight. I. INTRODUCTION E VER SINCE the introduction of fundamental principles of optical code-division multiple-access (OCDMA) using on–off pulses as signature sequences, the search for powerful code structures that can simultaneously satisfy three conditions, namely, minimal auto- and cross- correlation values, while having large cardinality, was unleashed [1]–[3]. Among Paper approved by W. C. Kwong, the Editor for Optical Communication of the IEEE Communications Society. Manuscript received July 12, 2005; revised November 6, 2005. This work was supported in part by the Hi-Technology In- dustries Center of Iran. The authors are with the Optical Network Research Laboratory (ONRL), Electrical Engineering Department, Sharif University of Technology, Tehran, Iran (e-mail: mashhadi@ee.sharif.edu; jasalehi@sharif.edu). Digital Object Identifier 10.1109/TCOMM.2006.878835 the most famous codes introduced to date are optical orthogonal codes (OOCs with its variations), and prime sequences [4], [5]. OOCs, which have captured the attention of many mathe- maticians and sequence designers [3]–[5], enjoy a more superior characteristic than prime sequences, because of their more ro- bust definition and conditions. By definition, a family of OOCs can be designed for any code length ( ), code weight , au- tocorrelation , and cross-correlation values, while for a given code length ( ), prime sequences are designed with weights that are on the order of the square root of its length , and with cross-correlation values that are bounded by two and autocorrelation values that can take on any value between one to code weight , thereby making them more limited in their use. From a multiaccess and synchronization point of view, the most desirable on–off signature sequences are OOCs with . However, these families of codes may suffer from low cardinality in some applications. In [6]–[8], attempts were made to explore the performance of OCDMA systems that employ OOCs with . In particular, in [7], by obtaining lower and upper bounds on the system’s performance, it was hinted that OOCs with could, under certain conditions, outperform OCDMA employing OOCs with , with cardi- nality that could be a hundred to a thousand times bigger. Sim- ilarly, in [9], using a structure based on mimicking a framed time-hopping ultra-wideband CDMA system, it was shown that the system’s performance degrades gradually with respect to OOCs with , while offering many possible sig- nature sequences. In this paper, we first obtain a simple solution on the perfor- mance of OCDMA systems using generalized OOCs, i.e., OOCs with or , and then using the analytical solution, we obtain the best code parameter values and find the most pow- erful codes for three various design scenarios in an OCDMA system. We show that for most practical purposes, OOCs with achieve the best performance, and we find the cor- responding optimum weights that achieve the best performance. These results resemble those of prime sequences, but with major differences in their autocorrelation value and their car- dinality. OOCs with could be designed to have , as opposed to prime sequences autocorrelation value that can take on any value between 1 and . Furthermore, the number of codes for OOCs with is on the order of , while for prime sequences, is on the order of 0090-6778/$20.00 © 2006 IEEE