Maximum likelihood double differential detection clarified

The maximum likelihood detector (MLD) for single differential modulation is easy to derive. On the other hand, the MLD problem associated with double differential modulation is much more complicated and solving it was deemed to require a computationally unattractive nonlinear search. Consequently a simple heuristical detector was usually preferred to the MLD, on computational grounds. In this paper we prove the somewhat unexpected result that the aforementioned heuristical detector coincides with the exact MLD.