MSK and Offset QPSK Modulation with Bandlimiting Filters

It is considered by some that minimum shift keying (MSK) is spectrally more efficient than quaternary phase-shift keying/offset quadrature phase-shift keying (QPSK/OQPSK). An analytical method is presented here for determining the detection efficiencies of MSK and QPSK/OQPSK when the constant-envelope signal is passed through a set of filters and when the resulting signal is corrupted by Gaussian noise. The detection efficiency of MSK is compared with that of QPSK/OQPSK when a four-pole Butterworth filter is used as a transmit filter and for two different receive filter functions. When the two-sided 3-dB bandwidth of the transmit filter is between approximately 1.00/T and 1.50/T, it is shown that the detection efficiency of MSK is not substantially different from that of QPSK/OQPSK. For more severe bandlimiting of the signal, the performance of MSK is shown to be inferior to that of QPSK/OQPSK. It is, therefore, concluded that MSK does not have significantly better detection efficiency when the effect of bandlimiting filters is taken into account.