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The performance of turbo-coded Amplitude-Phase Shift Keying (APSK) in an aeronautical telemetry system with a non-linear power amplifier is investigated. The AM/AM curves for four L-band power amplifiers are modeled and used to simulate the performance the turbo-coded APSK system over a non-linear channel, Spectral efficiency and bit error rate performance as a function of back-off are quantified and compared with a system based on the existing aeronautical telemetry standard using uncoded SOQPSK. The results show that the -50 dBc bandwidth can be matched with 2.5 to 4.1 dB of back-off, the -60dBc bandwidth can be matched with 4.3 to 6.6 dB of back-off, and the 99%. bandwidth can be matched with 0.8 to 1.6 dB of back-off. The bit error rate results show that each power amplifier has an optimal back-off and that this back-off is 3 dB for the four amplifiers used in this study. When put together, this system is capable of outperforming an uncoded system based on SOQPSK by matching (or exceeding) the detection efficiency while simultaneously achieving a spectral efficiency in excess of three times that of SOQPSK.