A note on the orthogonality of MSK signals

Minimum shift keying (MSK) got is name from its description as the coherent FSK scheme with the “the minimum frequency spacing which allows the two FSK signals to be coherently orthogonal”. This notion is not well defined in the literature. MSK signals are not strictly orthogonal over any bit interval for all frequencies, as a simple calculation shows. The MSK waveform should be observed over two bit intervals instead of one, as Massey (1980) showed with his optimal coherent MSK receiver. Even then, a naive implementation may show degradation due to non-orthogonality at low signal frequencies. We derive expressions for the optimal coherent MSK receiver which show that the signals are orthogonal only for certain values of the centre frequency and initial phase. This is important for demodulator designs which work at low signal frequencies, such as sampled implementations