Spectral Efficiency Study of QC-CHPCs in Multirate Optical CDMA System

Quadratic-congruence carrier-hopping prime codes (QC-CHPCs) with zero autocorrelation sidelobes, cross-correlation values of at most two, and expanded cardinality were recently constructed for wavelength-time "multicode-keying" optical code division multiple access (O-CDMA) for improved data throughput and code obscurity. To support multimedia services with different discrete bit-rate requirements, "multiple-length" QC-CHPCs are constructed algebraically in this paper. In contrary to conventional single-length codes, our analysis shows that the performance of these multiple-length codes improves as the code length decreases, thus supporting services prioritization in O-CDMA. Moreover, the relationship of the normalized spectral efficiency (NSE) and code lengths of the multiple-length QC-CHPCs is studied. Our results show that the NSE improves as the number of simultaneous users with short code matrices increases, which, however, decreases the total number of simultaneous users in the system. The choice of which code-length distribution to use depends on whether system efficiency or total number of simultaneous users is more important.