A generalized formulation of minimum shift keying modulation

The modulator structure consisting of a single-input two-output sequential transducer whose output sequences control the modulated signal in the manner s(t) = x(i)p(t) + y(i)q(t) is considered. Here, iT is less than or equal to t, which is less than iT + T, where T is the modulation bit duration and where x(i) and y(i) take values in /+1, -1, 0/. The behavior of a sequential transducer is characterized by means of a 'trellis'. It is shown that, provided only that the 'carriers' p(t) and q(t) have the same energy in every bit interval, the optimum demodulator for the additive white Gaussian noise channel need process the received signal over only two bit intervals in making each data bit decision. It is demonstrated that particular choices of the sequential transducer yield differential minimum shift keying and differential staggered quadriphase shift keying. Possible generalizations of this approach are discussed.