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We consider GMSK for use in frequency division multiple access (FDMA) satellite communication systems where only limited system bandwidth is available. The demodulator employs maximum likelihood sequence estimation (MLSE) of the GMSK signal using a simplified Viterbi processor. For the case of GMSK having a time-bandwidth product of BT=1/4, a two matched filter approximation gives very good performance, while, for BT=1/6, a two filter approximation is very similar to a four filter approximation. For a convolutional code with rate 1/2 and constraint length 7, simulation shows that soft output Viterbi algorithm (SOVA) decoding using a four-filter demodulator for BT=1/6 and BT=1/8, results in a performance improvement of 2.1 dB and 2.3 dB, respectively, in signal-to-noise ratio (SNR), compared to hard decision Viterbi algorithm (HOVA) decoding, at a bit error probability (BEP) of 10-5. When compared to a BPSK system that employs a similar soft decision decoder, the BEP power penalty for these schemes is 2.3 dB and 4.1 dB respectively. The spectral efficiency, relative the 95% RF power containment bandwidth, is 1.88 bits per sec per Hz (bps/Hz) and 2.1 bps/Hz of bandwidth for BT=1/6 and 1/8 GMSK respectively, and only 0.35 bps/Hz for BPSK. As ratios, the spectral efficiency improvement factor is 5.37 and 6.0 respectively.