Code-Division Multiple-Access Techniques in Optical Fiber Networks—Part III: Optical AND Gate Receiver Structure With Generalized Optical Orthogonal Codes

Abstract

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$lambda = 1$</tex> were considered, we consider generalized OOCs with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1 leq lambda leq w$</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$w$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$lambda = 1,2,3,ldots,w$</tex> , 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$lambdageq 1$</tex> . In particular, we can obtain some simple relations between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$ P_ e min$</tex> (minimum error rate), <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_min$</tex> (minimum required OOC length), and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N_max$</tex> (maximum number of interfering users to be supported), which are the most desired parameters for any optical CDMA system design. Furthermore, we show that in most practical cases, OOCs with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$lambda = 2$</tex> or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3$</tex> perform better than OOCs with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$lambda = 1$</tex> , while having a much bigger cardinality. Finally, we show that an upper bound on the maximum weight of OOCs are on the order of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$sqrt2lambda L$</tex> where L is the length of the OOCs used in systems.