Two-Dimensional Optical CDMA Systems Based on MWOOC with Generalized Prime Sequences

Abstract

Two-dimensional (2-D) codes for optical code-division multiple access (O-CDMA) systems can increase the number of subscribers and simultaneous users as compared to one-dimensional time-spreading codes. Multiple-wavelength optical orthogonal code (MWOOC), which is one of the 2-D codes, uses prime sequences as a wavelength-hopping code and an optical orthogonal code (OOC) as a time-spreading code. MWOOCs have some advantages over other 2-D codes especially in high bit-rate O-CDMA systems. The only drawback of MWOOC is that the performance degrades significantly when the number of wavelengths is not prime. Recently a generalized class of modified prime sequence codes (MPSCs), which includes the class of original MPSCs as its subclass, was presented. An important property of generalized MPSCs is that the codes can be constructed over not only prime fields but also extension fields. It has been shown that the correlation property of generalized MPSCs is the same as that of the original MPSCs. This paper investigates MWOOC with generalized prime sequences, which can be obtained in the process of generating the generalized MPSCs, as a wavelength-hopping code. Use of the generalized prime sequences can solve the nonprime problem of MWOOCs. The average error probability of the proposed MWOOCs is formulated theoretically and numerical results are compared with that of the original schemes. It is shown that nonprime numbers, such as 2^m, 3^m and 5^m, can be also taken as the number of wavelengths without degrading the system performance in the proposed systems.