Performance of optical time-spread CDMA/PPM with multiple access and multipath interference

Abstract

A novel optical modulation scheme employing ultrashort light pulses, modulated with Pulse Position Modulation (PPM) in conjunction with time-spread Code Division Multiple Access (CDMA) has recently been investigated in a two part paper by Kim, et.al. Mode-locked lasers producing sub-picosecond pulses every few nanoseconds are an excellent communication source, providing many terahertz of coherent bandwidth and a long time interval to spread out the pulse energy. Time-spread CDMA provides asynchronous multiple-access, while M-ary PPM provides enhanced throughput, affording up to several Tb/s of aggregate capacity. In the previous work, Multiple Access Interference (MAI) was the only source of degradation considered, and the impact of propagation through a multipath channel was not addressed. Since PPM is inherently sensitive to multipath interference, any uncompensated stochastic phenomena producing multipath in the channel are likely to be the predominant sources of performance degradation. In this work, we develop a general analysis for the noncoherent detection of PPM with Gaussian MAI transmitted through a channel with two paths. As a specific example, we consider a single-mode, (chromatic) dispersion compensated fiber, where Polarization Mode Dispersion (PMD) is the only significant source of multipath. To a first-order, this produces two distinct paths with a stochastic Differential Group Delay (DGD) that is approximately Maxwellian distributed. Assuming a polarization insensitive receiver, the statistics of the intensity samples at the M possible pulse positions are derived. The sum of the M-1 conditional pairwise error probabilities forms a union bound for the symbol error probability. There are three cases of interest, which are bounded analytically. There is no practical upper bound for the third case, so an approximate solution is obtained by numerically inverting the characteristic function. Lastly, a bound on the total unconditional error probability is obtained. © 2005 Springer Science + Business Media, Inc. Boston.