Recent investigations have shown that it is possible to take a standard communication signal such as an MSK signal and apply techniques associated with nonlinear dynamics to achieve a method of geometric demodulation of the message. These techniques have also been useful for demodulating signals that had suffered degradation from channel effects, and offered some potential for co-channel demodulation. One key difference between the geometric techniques and multi-sensor approaches is that oversampling of the data replaces the need for multiple sensors. This is related to the fact that any signal that has passed through a channel picks up short-term determinism. It is this short-term determinism that makes NLD techniques effective, and the processes that create intersymbol interference become beneficial to the geometric approach. When oversampled, the short-term determinism can allow for error correction in some cases, since the short-term effects extend beyond the boundaries of the data drop-out. The basic approach has been to create what we have called wire-diagrams, which are nothing but loops and transitions in phase space. By studying the pure communication signals before introducing channel effects, we can develop a set of reference wire diagrams. When a signal has been degraded by channel effects, we can compare the geometric reconstruction of the degraded signal with the original to extract the message.
As part of this year's research efforts, we are attempting to automate some of the processes that allow for demodulation of the message signals in the presence of channel effects. The first such approach we are considering is to take the (deformed) reconstruction of the degraded signal and define certain key structures common to the deformed and reference wire diagrams. A mapping is defined which takes the deformed structure onto the reference structure, and the mapping is then extended to the entire wire diagram. Our preliminary results, described below, indicate that such an approach may be promising, but more work must be done and tests must be conducted in more complex cases.