## 4 Performance Evaluation
### Field Test Results
From Figure 18b, the target's energy is suppressed to a relatively low level and even the MF-DFM is not evident, as compared with that in Figure 18a. Thanks to the high-SNR results in Figure 16, the scope of the range search can be narrowed down to several range bins. By picking the maximum output of the MF-DFB, the estimation of the target's velocity \(\hat{V}_{b}\) = 14.6 m/s, which is negative since the target was moving away from our system, as shown in Figure 19. Following the MF-DFB, the PSO-based  
Figure 16: Different frequency bands of RDM without adding Gaussian noise: (**a**) SF1; (**b**) SF2; (**c**) SF3. Figure 17: Different frequency bands of RDM after adding Gaussian noise: (**a**) SF1; (**b**) SF2; (**c**) SF3. Figure 18: Doppler profile data: (**a**) without adding noise; (**b**) with adding noise. phase estimation is then performed. The bounds of phase (i.e., \([\theta_{1},\theta_{2},\theta_{3}]\) are all set as \([0,2\pi]\). The solving processing of the PSO-based phase estimation algorithm is shown in Figure 20. It can be seen that the entropy-based fitness value gradually converges as the iterative step increases. The final estimated results are found to be \([\hat{\theta}_{1},\hat{\theta}_{2},\hat{\theta}_{3}]\) = [0, 5.203, 4.751] (in radian). The estimate of the target phases obtained by the data without adding noise are considered as the ground truth, which are \([\theta_{1},\theta_{2},\theta_{3}]\) = [0, 5.348,4.199] (in radian), and target velocity \(V_{b}=-14.2\) m/s, as shown in Table 4. Compared with the true values, the accuracy of the parameter estimation is arguably acceptable since the relative error in the velocity estimation is 2.82%, while the root-mean-squared error (RMSE) of the phase estimation is 0.32 radian. Based on the estimation of the target's velocity and phase, the integrated RDMs of the moving target are then achieved. The comparison of the integrated RDMs using four different methods is given in Figure 21, where the MF-NCI-EL, MF-RFT-NCI, MF-RFT without PSO, and MF-RFT-QCI are, respectively, given in Figure 21a-d. The output SNRs of the MF-NCI-EL, MF-RFT-NCI, MF-RFT without ME-PSO, and MF-RFT-QCI are 4.37, 9.07, 12.53, and 14.80 dB. From Figure 21a, we can see that the target's energy cannot be well focused in the same Doppler unit using MF-NCI-EL because of the MF-DFM. However, by employing the MF-DFB in the non-coherent mode, the MF-RFT-NCI can concentrate the target's energy at a single range-Doppler unit, the range of which is 36 m and the Doppler frequency is \(-\)631.37 Hz (see Figure 21b). For the NCI-based methods, MF-RFT-NCI achieves a processing gain of 4.70 dB over the MF-NCI-EL, which indicates the effectiveness of the MF-DFB in non-coherent mode. For a fair comparison, we do not compare the output SNR between the NCI- and CI-based detectors. Instead, the performance comparison between the CI-based detectors is given in Figure 21c,d, showing that the proposed MF-RFT-QCI significantly outperforms the MF-RFT without PSO-based phase estimation with a 2.27 dB performance gain. These results indicate the importance of the joint parameter search of the unknown velocity and target's phase, showing consistency with earlier numerical results. Finally, based on the integrated RDM, the final detection results can be achieved after selecting a proper CFAR detector. For the NCI-based methods, including the MF-RFT-NCI and MF-NCI-EL, the generalized gamma-based CFAR in [38] is employed. Meanwhile, the biparameter CFAR in [42] is used for the case of CI-based methods. The number of training cells and guard cells are 60 and 5, respectively. In this setting, the CFAR loss can be limited below 0.3 dB. According to the _Radar Handbook_[50], the detection threshold depends on the pre-set false alarm rate. If the detection threshold is set too high, there will be very few  
Figure 21: The integrated RDMs using different fusion methods: (**a**) MF-NCI-EL; (**b**) MF-RFT-NCI; (**c**) MF-RFT without ME-PSO; (**d**) MF-RFT-QCI (proposed).