The uplink channel from a terminal to a regenerative satellite repeater is considered in which a digital transmultiplexer (TMUX) is used as a frequency-division multiple-access (FDMA) to time-division-multiplexed (TDM) converter for group demodulation. Linear modulation techniques were considered to determine which would make the most efficient use of this on-board processing (OBP) satellite system. The modulation techniques examined were quadrature phase-shift keying (QPSK), /spl pi//4-QPSK, and offset QPSK (OQPSK), all with Nyquist pulse shaping, and minimum-phase keying (MSK). The search for the optimum linear modulation technique took into account the performance criteria of power efficiency, bandwidth efficiency, and especially the complexity of the TMUX algorithm for OBP.