Code-division multiple-access techniques in optical fiber networks - Part III: Optical AND logic gate receiver structure with generalized optical orthogonal codes

In this paper, we present a deep insight into the behavior 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 lambda = 1 were considered, we consider generalized OOCs with 1 <= lambda <= w, where w 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 lambda = 1, 2, 3,..., w, 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 lambda >= 1. In particular, we can obtain some simple relations between P-e min (minimum error rate), L-min (minimum required OOC length), and N-max (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 lambda = 2, 3 perform better than OOCs with lambda = 1, while having a much bigger cardinality. Finally, we show that an upper bound on the maximum weight of OOCs are on the order of root 2 lambda L where L is the length of the OOCs.