An Investigation of an Optical Multiple Pulse Position Modulation Link over a Dispersive Optical Channel

Digital Pulse Position Modulation (digital PPM) is a modulation format that codes n bits of PCM into a single pulse that occupies one of 2n time slots. Various studies over the last three decades have shown that such a scheme can offer an improvement in receiver sensitivity of 5-11 dB when compared to Pulse Code Modulation (PCM). Such
an increase in sensitivity can be exploited beneficially in both long haul applications and
the multi-user environment. However, this improvement results in a considerable increase
in the final data rate of the original PCM, and this makes implementation difficult.

Alternative methods have been proposed, such as multiple PPM, dicode PPM, differential PPM and overlapping PPM, that reduce transmission bandwidth while maintaining an increased sensitivity. Dicode and multiple PPM (MPPM) are the most bandwidth efficient of these formats and MPPM, the subject of this thesis, offers the best
sensitivity without the large bandwidth increase. In this scheme, multiple pulses per frame are used, with the pulse positions being determined by the original PCM word.

The main concern of this thesis is a full and detailed investigation of an Optical MPPM link operating over a dispersive optical channel. As the analysis of any (X/Y) multiple PPM system, in which X denotes the number of data slots and Y the number of pulses, is extremely time-consuming, a novel automated solution was designed to predict the equivalent PCM error rates of specific sequences and simplify the task. An original mathematical formulation is developed using the Maximum Likelihood Sequence
Detection (MLSD) scheme. Using the equivalent PCM error rates of specific sequences generated from software, a full simulation of an MPPM optical link can be produced and the results show the effectiveness of the MPPM format over PPM. A measure of coding quality is proposed that accounts for efficiency of coding and bandwidth expansion. Original results are presented for a (12/Y) MPPM system, considered as very efficient and examined by many authors, showing that the most efficient systems are in the middle of
the family. A methodology to predict the Bit Error Rate (BER) of any MPPM system is also proposed. The results obtained confirmed the results obtained from the full mathematical analysis.

The effects of linear increment, linear decrement, Gray code and random mapping of data on ther performance of a (12/Y) multiple PPM system are also examined. Simulations show that the Gray code is the most effective as it minimizes the Hamming distance between adjacent multiple PPM words.

Further experiments showed that system performance can be obtained exclusively with the use of software making the analysis simpler and minimizing the time consumption. A novel algorithm is presented and results obtained using this method, agree with those obtained using a full mathematical model.

Certain mappings can either enhance or degrade the final total error probability of the system and hence affect the sensitivity of the MLSD scheme. In this thesis the author also suggests a methodology of how to predict and generate an optimum or close to optimum mapping. The methodology is based on minimizing the occurrence of dominant error sequences. Detailed results show the effectiveness of this mapping routine.

For the first time also, high order MPPM codes are considered for analysis. All the experiments completed for the (12/Y) MPPM system are repeated for a range of MPPM systems (with 4, 7, 15, 17, 22, 28 and 33 slots operating over a plastic optical fibre (POF) channel showing again that the most efficient systems are in the middle of
the family. Close to optimum mappings are also presented for these MPPM systems. The estimated mappings were found to be far superior to the efficient Gray codes, linear coding and a series of random mappings. To measure these optimum mappings a very efficient mapping is also considered. This mapping minimises the Hamming distance between all MPPM codewords. This mapping allows repetitions of MPPM codewords and cannot be used in a MLSD scheme. Therefore, it is only used for comparisons with the (close to) optimum mappings. It is shown that the optimum mappings are close to ideal.

Other correlation techniques are also considered for optimised detection in the MLSD scheme. Results obtained showed that raised cosine filtering can enhance detection.