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This paper presents comparisons of the achievable throughput between the star 32/64QAM and square 32/64QAM schemes based on mutual information (MI) considering the peak-to-average power ratio (PAPR) of the modulated signal. As a PAPR criterion, we use a cubic metric (CM) that directly corresponds to the transmission back-off of a power amplifier. In the analysis, we present the best ring ratio for the star 32 or 64QAM scheme from the viewpoint of minimizing the required received signal-to-noise power ratio (SNR) considering the CM that achieves the peak throughput, i.e., maximum error-free transmission rate. We show that the required received SNR considering the CM at the peak throughput is minimized with the number of rings of M = 3 and 4 for star 32QAM and star 64QAM, respectively. Then, we show with the best ring ratios, that the (4, 12, 16) star 32QAM scheme with M = 3 achieves a lower required received SNR considering the CM compared to that for the square 32QAM scheme. Similarly, we show that the (4, 12, 20, 28) star 64QAM scheme with M = 4 achieves almost the same required received SNR considering the CM as that for the square 64QAM scheme.