Performance of a MAP Clock Recovery Scheme for GMSK Modulations with Tracking Capabilities

The GMSK (Gaussian Minimum Shift Keying) modulation is currently being considered as a possible standard for space missions [3], due to its compact power spectrum, high immunity against interference and capacity to support various receiver structures. The objective of the overall framework in which the work described in this manuscript has been developed (the work was performed for the ESOC/ESA Contract 14295/00/DCS, End-to-End Study of GMSK Modulation), is to define realistic GMSK transmitter and receiver structures, taking into account implementation issues. In this manuscript we deal in particular with the practical implementation of a Maximum A Posteriori (MAP) symbol synchroniser [1], with the aim of analysing the clock recovery subsystem performance in presence of some relevant system parameters, to be settled in a real implementation of this receiver function. The relevant system parameters that have been considered are the number of samples per bit (symbol) used at the receiver side Nsr, and the number of quantisation bits used at the receiver side to represent the synchronization path metrics, Nqr. Moreover, the performance evaluation of the symbol timing subsystem takes into account the working conditions of the system, in terms of signalto- noise ratio Es/N0 and possible presence of timing drifts. In [1] the theoretical derivation of the synchronisation rule is presented, as well as a generic scheme to implement the derived Maximum A Posteriori (MAP) synchronisation rule. A simplified version of the MAP synchroniser is also shown in [2]. Both schemes are, in reality, not well suited to a practical implementation since they do not consider quantisation and normalisation problems, nor the presence of a finite duration observation window. Furthermore, they require the symbol duration to be almost constant, and they do not take particular counter-measures against drift phenomena. In this paper we recall the main steps of the theoretical derivation, then we identify some critical issues that must be considered when dealing with a finite precision practical realisation of the algorithm, and we describe the performance of a quantised and finite window duration version of the symbol epoch estimator, suitable for hardware implementation.