Code-Division Multiple-Access Techniques in Optical Fiber Networks - Part III: Optical AND 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 (CDMA) 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 $1 leq lambda leq w$ , where $w$ is the weight of the corresponding codes. To enhance the performance of such systems, we propose that use of optical AND gate receiver, which, in an ideal case, e.g., in the absence of any noise source except the optical multiple-access noise, is optimum. Using some basic laws on probability, we present direct and exact solutions for OOCs with $lambda = 1,2,3,ldots,w$ , with optical AND 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 $lambdageq 1$ . 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 optical CDMA system design. Furthermore, we show that in most practical cases, OOCs with $lambda = 2$ or $3$ 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 $sqrt2lambda L$ where L is the length of the OOCs used in systems.