The M.Sc. degree project, whose one major part is explained in this paper, has been accomplished at the University of Surrey by the financial support of TUBITAK-BILTEN inclusive to the remote sensing satellite project BILSAT-1*, which was carried out by Surrey Satellite Technology Limited in UK, collaboration with TUBITAK-BILTEN. This paper explains the methodology and the simulation results of the performances of advanced modulation techniques under the implications of highly dynamic LEO satellite downlink. Modulation schemes that can possibly serve the objectives are the phase shift keying type modulations. Hence, the performance of binary phase shift keying (BPSK), quadriphase shift keying (QPSK), offset QPSK (OQPSK), pi/4 shifted QPSK, octaphase shift keying (8PSK), and 3pi/8 shifted 8PSK have been deeply investigated through simulations considering the LEO satellite communication downlink channel properties. The modulators and demodulators were synthesised using computer programs. The simulations demonstrated the necessity of applying non-coherent demodulators in order to fight with the multipath fading present in the downlink channel. The non-coherent limiter discriminator demodulator of pi/4 shifted QPSK, which turned out to have the best performance in fading simulations, was an evidence of the above observation. 3pi/8 shifted 8PSK was also demodulated with a similar system. However, implementation of 3pi/8 shifted 8PSK is not recommended because of the fact that higher power with respect to pi/4 shifted QPSK modulation is necessary to have identical BER performances. Although the data rate could be increased even more with implementation of 3pi/8 shifted 8PSK than pi/4 shifted QPSK scheme, power limited 'little' LEO satellites prevent using this higher order modulation for downlink.