Theoretical analysis of modified repeated unequally spaced frequency allocations in FDM lightwave transmission systems

In long-haul frequency-division-multiplexing (FDM) lightwave transmission systems, transmission characteristics are degraded by four-wave mixing (FWM) generated in optical fibers. To date, equally spaced (ES), unequally spaced (US), and repeated unequally spaced (RUS) allocations have been demonstrated in FDM lightwave transmission systems. It has been already revealed theoretically and experimentally that intensities of generated FWM lights with f_FWM=f_i for RUS are lower than those for ES, and a total bandwidth of signal lights for RUS is comparable to that for US, where f_FWM is a frequency of an FWM light and f_i is a frequency of a signal light with a channel index i. In this paper, equally spaced RUS (ERUS) and unequally spaced RUS (URUS) are proposed as modified RUS and are theoretically analyzed. Efficiencies of generated FWM lights and total bandwidths of signal lights for ERUS and URUS are compared with those for RUS. As a result, it is found that efficiencies of generated FWM lights with f_FWM=f_i for URUS are lower than those for RUS, and total bandwidths of signal lights for ERUS and URUS are comparable to those for RUS. A bit error rate (BER) for URUS is also comparable to that for US (without FWM) at 2.5, 5.0, and 10.0 Gb/s. Because URUS simultaneously satisfies low FWM light efficiencies with f_FWM=f_i, narrow total bandwidths of signal lights, and low BER, it is concluded that URUS is superior to RUS in FDM lightwave transmission systems.