## 4 Results and Discussion
### Results of Different Modulations  
Finally, we used the proposed scheme with four modulation methods to investigate the performance in terms of its universality. The BER values of the demodulation results were calculated and are shown in Figure 8. The four different modulation methods were BPSK, quadrature phase-shift keying (QPSK), differential QPSK (DQPSK), and 16-bit quadrature amplitude modulation (16 QAM). According to the data, the demodulation results with 16 QAM were similar to those of the QPSK cases analyzed above. The DE algorithm was used to estimate the CFO value for each OFDM block before the received signal was compensated with the values. A comparison of the curves shows that its demodulation was significantly better than the case of direct demodulation without compensation. Moreover, the compensation results with the DE estimated values were consistent with those obtained using actual CFO values. This means that the actual TVCFO value could be obtained  
Figure 7: Constellations of demodulations in three cases: (**a**) without CFO compensation, (**b**) with actual CFO compensation, (**c**) with DE estimation values compensation and (**d**) comparison of the three. using the DE estimator. In the case of BPSK, the DE algorithm with estimation value compensation performed better than that without the TVCFO, which was clear in the high SNR situation. This was because there was less pressure to make a correct BPSK judgment compared to QPSK with the same estimation accuracy, which was affected by the fewer decision options of BPSK. The effect of noise on the OFDM block was considered to be part of the CFO. Therefore, the possibility of a mismatch was smaller because BPSK has fewer decision options. This was also the reason that the demodulation results based on the estimated values were slightly better. For DQPSK, the demodulation effect of the DE estimated values were worse than that of the compensation executed using the actual CFO values, which was also due to the effect of noise being regarded as carrier frequency deviation. Phase changes on adjacent subcarriers are employed to transmit information in the DQPSK modulation. However, the original information is destroyed by the equivalent CFO introduced when dealing with noise in the DE estimator. Therefore, the demodulation results deteriorated with the compensation of the actual TVCFO values. In general, it was relatively acceptable to use the DE algorithm to estimate the TVCFO in DQPSK. In summary, the TVCFO estimation using the DE algorithm was very effective in the PSK and QAM modulation modes. Although the performance of the DE algorithm in the DQPSK modulation mode was not the same as those with the PSK and QAM, the demodulation result after compensation based on the estimated value is significantly better than that without compensation. Moreover, as the SNR increases, the gain after compensation is also more obvious. This section showed how three estimators (the SAMGA, GA, and DE algorithms) were adopted for the TVCFO estimation on the improved OFDM model. A comparison of the results in terms of the RMSE of the estimated values and the BER of demodulation showed that the mechanism of the DE algorithm, which considers the dependencies among adjacent variables, was very suitable for solving the TVCFO estimation problem. The demodulation performances for the received signal without compensation, with actual CFO values, and with estimated values obtained by the DE compensation were determined. The results demonstrated that the proposed scheme could achieve real TVCFO values, and the effect of noise on the demodulation could also be considered in the QPSK modulation. Ultimately, the performances of the DE estimator with four modulation schemes, BPSK, QPSK, DQPSK, and 16 QAM, were tested. The proposed scheme correctly estimated the TVCFO values under the QPSK and 16 QAM modulation. The performance under BPSK modulation was the best of the four, and it was easier to reduce the influence of noise under a high SNR.