# Removing False Targets for Cyclic Prefixed OFDM Sensing with Extended Ranging +
## 6 Simulation Results  
In this section, simulation results are provided to validate the effectiveness of the proposed method. First, we continue the scenario given in Table 1 to illustrate how the proposed methods impact RDMs. Figure 3(a) plots the RDM of MUSF given in Algorithm 3, where parameters given in Table 1 are reused here. We see that, substantially different from USF-RDM in Figure 0(a), the false targets are removed in MUSF-RDM. Figure 3(b) plots the RDM after running Algorithm 4. Since the algorithm removes the strongest target sequentially, the residual RDM would be target-free, if the number of targets is known. This is validated by Figure 3(b). We see that the residual RDM is noise-like without obvious target peaks. Figure 3(b) also confirms the features of false targets derived in Proposition 1, as false targets are reconstructed based on those features. Figure 5 further compares the range and Doppler cuts of different algorithms. From Figure 5a, we see that the proposed Algorithms 3 and 4 can both remove the false targets. From Figure 5b, we see that the two algorithms have negligible impacts on the Doppler spectrum. This is consistent with our analysis in Section 4. Moreover, we can see from Figure 5a that Algorithm 3 has slightly larger sidelobes than the other two algorithms overall. This is actually caused by the reduced peak magnitude of Algorithm 3. Since the peak magnitude is normalised to one in the figure, the sidelobe level is raised as a result. Next, we increase the number of targets to four to validate the proposed methods. With other parameters in Table 1 fixed, the target delays of the four targets are set as 312, 262, 375, and 382. Moreover, their respective Doppler frequencies are 195.06 Hz, \(-\)650.76 Hz, \(-\)476.77 Hz, and 709.80 Hz. These are randomly generated without any special implications. Figure 6a plots the RDM obtained by COS, as given in Algorithm 2. We see that the classical COS, as fully complied with the underlying communication system, fails to generate a normal RDM with peaks at the target locations. Figure 6b plots the RDM of USF, as given in Algorithm 1. Other than the four true targets highlighted, we also see eight false targets (two associated with each true target). Figure 6c presents the RDM of the modified USF given in Algorithm 3. We see that the false targets are effectively removed. Figure 4: RDM of Algorithm 3 in (**a**); RDM of Algorithm 4 in (**b**). A single target is set here. Please note that the symbol “-” before all numbers, as automatically generated by MATLAB during plotting the figure, denotes the negative sign. Figure 5: (**a**) Doppler cuts of the RDMs shown in Figure 4; (**b**) range cuts of the same RDMs. Note that Algorithm 1 as developed in [32], is simulated as a benchmark. It suffers from the false target issue. In contrast, the new algorithms, Algorithms 3 and 4, are able to remove the false targets. Please note that the symbol “-” before all numbers, as automatically generated by MATLAB during plotting the figure, denotes the negative sign. Figure 7 plots the updated RDMs in the first three iterations of Algorithm 4. Note that with four targets set, the algorithm has four iterations in total. From the three RDMs, we can see that each iteration is able to remove one true target along with its associated false targets. This again validates the correctness of our analysis of the features of the false targets. Moreover, this manifests the effectiveness of Algorithm 4 in constructing the RDM of a target and removing it from the overall RDM. Next, we employ the common metrics to further highlight the impacts of false targets and the proposed methods on sensing. In particular, we perform CA-CFAR based on the RDM obtained under different methods, and observe the detecting probability as well as the false alarm rate (when there is no target but the radar detection reports a target, a false alarm happens. The average number of false alarms per unit time is defined as the false alarm rate [39]) against the signal-to-noise ratio (SNR).