Recursive HMM probability distribution computation and its application to the demodulation of CPM signals.

摘要

A method for information recovery from signals transmitted over time varying channels is presented. The method computes a conditional probability distribution function (i.e. PDF) of the received signal. Demodulation occurs by using the computed PDF to recover information contained in the received waveform. The method is optimal in the sense that a MAP estimate of the information at time k, is computed conditioned on the measurement filtration up to time k. Upon the receipt of new measurements at time k + 1, the PDF is updated to incorporate the new measurements. The received signal in the time varying channel is modeled as a combined-process which represents both the transmitter and channel. Development of the combined-signal model begins by showing that the phase generated by the transmitter for CPM systems can be represented as a discrete time finite state Markov chain. The channel on the other hand imparts a continuum of time varying amplitude and phase changes onto the transmitted signal before arriving at the receiver. The effects of the channel are modeled as the output of a stochastic differential equation whose spectral properties are known. Given the combined-signal representation of the measurements to be processed by the receiver, a Girsanov transformation is used to create a new measure under which the PDF for the combined-signal is computed. A gaussian sum approximation is used to approximate a solution to an integral equation relating the combined-signal PDF at time k to the combined-signal PDF at time k + 1 when new measurements arrive. It is shown that information recovery can take place in the presence of a time varying channel without the benefit of training sequences. Recursions and performance are illustrated for gaussian minimum shift key (i.e. GMSK) modulations. Performance in the AWGN shows that the effects of inter-symbol-inteference (i.e. ISI) introduced by transmitter can be eliminated. For the time varying channel, simultaneous information recovery and channel estimation can take place from the computed combined-signal PDF for the received signal.