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This paper presents a novel multiple-access modulation scheme which combines key characteristics of single carrier frequency division multiple access (SC-FDMA) with continuous phase modulation (CPM) in order to generate a power efficient waveform. CPM-SC-FDMA is developed based upon the observation that the samples from a CPM waveform may be treated as "data symbols" taken from a constant-envelope encoder. As with any encoder output, these samples may be precoded using the Discrete Fourier Transform and transmitted using SC-FDMA. Having originated from a constant envelope CPM waveform, CPM-SC-FDMA can potentially retain much of the power efficiency of CPM-thus resulting in a lower peak-to-average power ratio (PAPR) than conventional SC-FDMA. In this paper, we account for the information rate, memory, power efficiency, bit error rate (BER) performance and spectral occupancy of CPM-SC-FDMA. In addition, we investigate the impact of amplifier nonlinearity on BER performance as the number of users increases. Finally, we provide a detailed numerical comparison with a commensurate convolutionally coded QPSK-SC-FDMA scheme (CC-QPSK-SC-FDMA). We show a CPM-SC-FDMA scheme that provides an overall gain of up to 4 dB relative to the CC-QPSK-SC-FDMA scheme over a frequency-selective channel.