This paper presents the average block error rate (BLER) performance of circular 32QAM and 64QAM schemes employing a frequency domain equalizer (FDE) for discrete Fourier transform (DFT)-precoded orthogonal frequency division multiplexing (OFDM) in multipath Rayleigh fading channels. The circular QAM scheme has an advantageous feature in that the fluctuation in the amplitude component is smaller than that for the cross or rectangular QAM scheme. Hence, focusing on the actual received signal-to-noise power ratio (SNR) taking into account a realistic peak-to-average power ratio (PAPR) measure called the cubic metric (CM), we compare the average BLER of the circular 32QAM and 64QAM schemes with those of cross 32QAM and rectangular 64QAM schemes, respectively. We investigate the theoretical throughput of various circular 32QAM and 64QAM schemes based on mutual information from the viewpoint of the minimum Euclidean distance. Link-level simulation results show that the circular 32QAM and 64QAM schemes with independent bit mapping for the phase and amplitude modulations achieves a lower required average received SNR considering the CM than that with the minimum Euclidean distance but with composite mapping of the phase and amplitude modulations. Through extensive link-level simulations, we show the potential benefit of the circular 32QAM and 64QAM schemes in terms of reducing the required average received SNR considering the CM that satisfies the target average BLER compared to the cross 32QAM or rectangular 64QAM scheme.