Differential encoding for multiple amplitude and phase shift keying systems

Because of the symmetry in most two-dimensional signal constellations, ambiguities exist at the receiver as to the exact phase orientation of the received signal set. In PSK systems, this ambiguity is resolved by the use of differential encoding. This paper presents differential encoding techniques which can be used with a variety of symmetric signal sets to remove their phase ambiguity. While not proven to be optimum, the techniques do have low performance penalties relative to the uncoded performance. The key to reducing the performance penalty is to use the minimum amount of differential encoding necessary to resolve the ambiguity. Examples of encoding techniques for several common signal constellations are given, including their performance penalties.