## 4 Performance Evaluation
### Numerical Results
#### 4.1.2 Detection Performance
ROC Curves  
Retaining the earlier settings, the receiver operating characteristic (ROC) curves for different fusion methods are depicted in Figure 11. By tuning the nominal \(P_{fa}\) in the CFAR detector, the detection performance is obtained under different nominal \(P_{fa}\). In Figure 11, the green, black, blue, and red curves indicate the MF-NCI-EL, MF-NCI-UEL, MF-RFT-NCI, and the proposed MF-RFT-QCI, respectively. From Figure 11, we can find that the proposed method shows a reliable detection performance given a low \(P_{fa}\), which is much better than that of MF-NCI-EL, and approximately up to 20% improvement as compared with MF-RFT-NCI when \(P_{fa}\) is less than \(10^{-5}\). Detection Performance vs. Channel Number \(M\)  
Figure 12 gives the curve of the required minimum detectable input SNR as a function of the channel number M. The simulation settings are as follows: the starting frequency of the channel is 12.395 GHz, the 3 dB bandwidth of the channel is 36 MHz, the carrier frequencies of the adjacent channels are as shown in Table 1, the speed of the target is set to 16 m/s, the CPIs are all the same as 0.1678 s, and the false alarm rate is \(10^{-5}\). In addition, the minimum detectable input SNR is defined when PD achieves 90%. As we know, the lower the required minimum detectable input SNR, the better the detection performance of the method. From Figure 12, we can draw two conclusions as follows: (1) the detection performance of both the proposed algorithm and the MF-RFT-NCI can be improved as the channel number M increases, while the MF-NCI-EL fails to take advantage of MF due to MF-DFM; and (2) the performance gain between the proposed algorithm and the MF-RFT-NCI gradually increases as M increases. When \(M=5\), the required input \(SNR_{SC}\) of the proposed method for detection is 1.0 dB lower than that of the MF-RFT-NCI. This result reveals that the proposed method is more favorable in the cases of extremely low SNR conditions, as the channel number \(M\) increases. Figure 11: The estimated ROC curves for different fusion detectors. Detection Range Analysis  
In this section, the detection range of the proposed method will be given via a link budget analysis. Investigating the maximum detection range of the proposed method is the main objective of this analysis. According to the bistatic radar equation [49], the input SNR of the echo signal is obtained as,  
\[SNR_{int} =\frac{S}{P_{n}} \tag{34}\] \[=\frac{P_{T}G_{T}G_{R}\lambda^{2}\sigma_{B}L_{s}}{kB_{n}T(4\pi)^{3 }R_{T}^{2}R_{R}^{2}},\]  
where \(R_{R}\) is the range of the target from the receiver. Table 2 provides the definitions and values of the other parameters and symbols. Next, we consider the processing gain. The whole signal processing gain can be obtained as,  
\[G_{p}=MB_{s}\tau_{p}, \tag{35}\]  
where \(M\) is the channel number for fusion, \(B_{s}\) is the signal bandwidth, and \(\tau_{p}\) denotes the coherent processing interval. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Setting Value** \\ \hline Transmit effective isotropic & \(P_{T}G_{T}\) & 56 dBw \\ radiated power (EIRP) & \(P_{T}G_{T}\) & 56 dBw \\ Transmit range & \(R_{R}\) & 36,979.1 km \\ Receiver antenna gain & \(G_{R}\) & 34.1 dB \\ Target RCS & \(\sigma_{B}\) & 10 dBsm (10 m\({}^{2}\)) \\ [PERSON]’s constant & \(k\) & \(1.3807\times 10^{-23}\) J/K \\ Noise temperature & \(T\) & 300 K \\ Noise bandwidth & \(B_{n}\) & 37.125 MHz \\ Signal bandwidth & \(B_{s}\) & 37.125 MHz \\ Wavelength in Ku-band & \(\lambda\) & 2.42 cm \\ Coherent processing interval & \(\tau_{p}\) & 0.1678 s \\ System loss & \(L_{S}\) & 5 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters for analyzing the detection range. Figure 12: Required input \(SNR_{SC}\) vs. channel number \(M\).