Bounds on the performance of binary CPFSK type of signaling with input data symbol pulse shaping

In recent years, continuous phase frequency shift keying (CPFSK) with linear phase in the bit intervals has gained interest mostly because of its spectral properties. It is also well known that for certain values of the modulation index, an error probability superior to that of BPSK can be obtained when the receiver makes decisions over 3 bits. This paper studies modulation systems of the CPFSK type with constant envelope and with additional data input symbol pulse shaping. Attention is restricted to binary systems with the same pulse shaping for all bit time intervals. Systems have been found which have better error probability and spectral properties than linear phase CPFSK. An upper bound has been derived on the minimum Euclidean distance which determines the error probability.