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In this paper, SDPSK and 1-bit differential-detected GMSK are proposed for use in a tactical FH-FDMA on-board processing (OBP) satellite communication system. The proposed waveforms are modeled and their respective error performances are simulated under the effects of jamming. Both waveforms, known to be relatively robust for ACI and ISI, are convolutionally encoded and Fast Frequency Hopped (FFH) to mitigate the effects of jamming which is modeled as Partial Band Noise Jamming (PBNJ) or Band Multi-Tone jamming (BMTJ) with AWGN. Simulations are conducted at the modem level as a preliminary step towards assessing their performances in a multichannel FDMA OBP satellite system. Results are presented for the various modem configurations, several of which illustrate the effect of the different BT products on the FFH/GMSK waveform. A comparative assessment of FFH/GMSK and FFH/SDPSK under identical jamming is also presented. Based on the empirical results obtained herein, the feasibility of using FFH/GMSK in a mobile tactical FDMA OBP satellite communication system is strongly dependent on the specific BT product used and the severity of ISI. Furthermore, when considering BMTJ with AWGN impairment the modem performance is highly dependent upon the amount of thermal noise present in the jammed channel. On the contrary, FFH/SDPSK is fairly robust and insensitive to broadband noise and ISI, and is thus tentatively preferred for deployment in a mobile tactical FFH/FDMA OBP satellite communication system.