In order to demodulate an optical PPM signal, the receiver must align its slot clock to that of the received waveform to count the number of arrivals within each slot. The large bandwidth expansion factor of PPM, M/log2(M) requires a prohibitively large sample rate when a fixed sample clock N times greater than the slot frequency is used to provide a slot timing resolution of 1/Nth of a slot period. Alternative techniques that achieve slot alignment resolution through adjustment of the phase of the sample clock to align with the slot boundary require custom hardware and are not compatible with post-processing receiver architectures that use fixed-rate analog-to-digital (ADC) sample capture technology.
Demodulating an optical PPM signal transmitted through a photon-starved channel from a time series of unsynchronized slot samples of a photon counting detector output requires the estimation of the number of detector pulses within a sample period, estimates of the received signal slot and symbol timing, and interpolation of the sample counts to produce slot likelihood ratios for information decoding. To achieve this, both new techniques and extensions to existing algorithms are employed. The Sample Decision Photon Counting algorithm is extended to allow a multi-level detection; a technique for detector jitter compensation in LLR generation is extended to include interpolation of a slot sampled detector output; and a novel outlier pruning technique uses constraints on the linear model for linear least squares to estimate the received slot clock frequency and phase.
These algorithms were developed to enable a post-processing receiver architecture that uses a fixed-rate ADC sample capture technology as an alternative to a real-time receiver architecture using custom detector readout circuits that employ sample clock phase feedback control to support the Lunar Laser OCTL (Optical Communication Telescope Laboratory) Terminal (LLOT), a ground terminal for the Lunar Laser Communication Dem onstration (LLCD). LLCD will be the first demonstration of an optical communication link from lunar distances, and this receiver technology is unique in its method for demodulation of the downlink signal.