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In regard to the M-ary phase-shift keying (MPSK) modulation and the quadrature amplitude modulation (MQAM), MPSK is preferred up to M = 8, with MQAM being the most common choice for M > 8. In this letter, the modulations two-radii 8-ary and 16-ary amplitude-phase shift keying (APSK), respectively named 2r8APSK and 2r16APSK, are proposed as alternatives to 8PSK and square 16QAM, in this order. The 2r8APSK achieves higher power efficiency than the 8PSK, at the cost of a higher peak-to-average power ratio (PAPR) and a slightly more complex receiver. The 2r16APSK yields lower PAPR than the 16QAM, with roughly the same receiver complexity, but at the cost of a slightly lower power efficiency. Comparisons with other APSK-based modulations are made as well.
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