Modulation loss analysis for amplitude modulated FSK signal

The satellite control uplink waveform known as SGLS (Space-to-Ground Link System) for commanding satellites currently used by the U.S. Department of Defense (DOD), uses ternary frequency shift keying (FSK), which is amplitude modulated using a triangular waveform. Although this has been in use for a half-century, we are unaware of any reference that rigorously describes its fundamental performance characteristics - specifically, its ideal bit error rate as a function of uplink power. This requires knowing the ideal baseband bit error rate as well as the allocation of total power into the command channel. A frequent alternative for the allocation of power in the command channel is to use the allocation given by the lowest-order terms of an analytic Bessel function expansion, in which the command channel is modeled as a single phase-modulated subcarrier. This alternative is also compromised by the neglect of amplitude modulation (AM). A rigorous characterization of SGLS is necessary in order to quantify the relative performance of new uplink waveforms that are being contemplated by DOD. In this paper, rigorous equations for use in the evaluation of the effect of AM on SGLS uplink modulation losses are presented. It is shown in this paper that the triangular wave amplitude modulation is well approximated as a single sinusoid normalized in terms of power. Analytical expressions are provided for the modulation losses that include AM effects supported by simulation results. For the typical SGLS uplink with a value of modulation envelope factor equal to 0.5, the effect of AM is to reduce the power in each spectral component of the uplink by less than 10%. This amount corresponds to less than a dB in most cases. It is shown in this paper that for the purpose of link margin calculations, it is adequate to conservatively allow an additional 1 dB for the modulation losses and ignore the AM in the modulation loss equations.