OQPSK-based approximation to generalized MSK

The authors consider the minimum mean square error (MSE) approximation of an OQPSK (offset quadrature phase-shift keying) waveform to a generalized MSK (minimum shift keying) signal. A closed-form expression is found for the elementary pulse γ(t ) of the minimum MSE approximating signal. It is shown that the filter matched to γ(t) is just the average matched filter, a well-known concept in the context of MSK-like signals. This result is important because it gives a new interpretation of the average matched filter while providing for the first time an analytical expression for the impulse response of such a filter