On the power spectral density of quadrature modulated signals

The conventional (no-offset) quadriphase modulation technique suffers from the fact that hardlimiting will restore the frequency sidelobes removed by proper filtering. Thus, offset keyed quadriphase modulation techniques are often proposed for satellite communication with bandpass hardlimiting. A unified theory is developed which is capable of describing the power spectral density before and after the hardlimiting process. Using the in-phase and the quadrature phase channel with arbitrary pulse shaping, analytical results are established for generalized quadriphase modulation. In particular MSK, OPSK or the recently introduced overlapped raised cosine keying all fall into this general category. It is shown that for a linear communication channel, the power spectral density of the modulated signal remains unchanged regardless of the offset delay. Furthermore, if the in phase and the quadrature phase channel have identical pulse shapes without offset, the spectrum after bandpass hardlimiting will be identical to that of the conventional QPSK modulation. Numerical examples are given for various modulation techniques. A case of different pulse shapes in the in phase and the quadrature phase channel is also considered.