# Removing False Targets for Cyclic Prefixed OFDM Sensing with Extended Ranging +
## 6 Simulation Results
We also consider single- and multitarget cases. In both cases, target delay, velocities, and amplitudes are randomly generated over \(10^{4}\) independent trials. Moreover, the target delay is in the range of \([N,1.5N]\), where \(N=256\) is the original OFDM length. The target speed is in the range of \([-120,120]\) m/s. Further, the target amplitude conforms to a complex Gaussian distribution with the mean of one and the variance of 0.01. A key parameter of CA-CFAR is the expected false alarm rate. It is used in computing the detecting threshold. Here, we set the expected false alarm rates for Algorithms 1-4 as \(10^{-4}\), \(10^{-5}\)  
Figure 6: RDM of COS in (**a**); RDM of Algorithm 1 in (**b**); RDM of Algorithm 3 in (**c**). Four targets are set, as highlighted in the figures. Please note that the symbol “-” before all numbers, as automatically generated by MATLAB during plotting the figure, denotes the negative sign. Figure 7: RDMs obtained by Algorithm 4 with four targets simulated. The RDMs from the first three iterations in the algorithms are given in (**a**–**c**), respectively. Please note that the symbol “-” before all numbers, as automatically generated by MATLAB during plotting the figure, denotes the negative sign. \(10^{-5}\), and \(10^{-6}\), respectively. In general, the smaller the value, the greater the detecting threshold would be. As a result, the detecting probability would be reduced. Figure 8 plots the detecting performance achieved based on the RDMs obtained using different methods. From Figure 8a, we see that Algorithm 4 achieves the maximum detecting probability. This is mainly because we simply detect the maximum peaks as targets without applying threshold detection, as do the other three algorithms. However, identifying the maximum peak as target is enabled by our proposed Algorithm 4. It effectively remove the impacts of stronger targets and their associated false targets on weaker ones. From Figure 8a, we also see that COS basically fails to detect targets in the whole SNR region. Moreover, we see that Algorithm 1 always achieves higher detecting probabilities than Algorithm 3. This reveals a disadvantage of Algorithm 3. It indeed prevents the false targets from being generated by nullifying CPs, but it also reduces the processing gains on the true targets due to the signal nullification. From Figure 8b, we see that Algorithms 3 and 4, as developed in this work, can reduce the false alarm rate, compared with Algorithm 1, which suffers from false targets. This validates that the proposed algorithms can effectively counteract the impacts of false targets. Moreover, Algorithms 1 and 3 have higher false alarm rate than Algorithm 2, although the former two algorithms actually use a smaller theoretical false alarm rate to calculate the detecting threshold than the third one. This is a consequence of not only false targets but also the virtual CPs introduced in the sensing framework of Algorithm 1. As analysed in [32], the background noise level can be slightly raised by Algorithm 1 compared with the classical COS given in Algorithm 2. Moreover, there can be a fixed noise floor even when the receiver noise is negligibly weak. All these consequences contribute to the slightly increased false alarm rate of Algorithm 1 and its variants Algorithms 3 and 4. In parallel, Figures 8 and 9 presentthe detecting performance achieved based on different RDMs. From Figure 9a, we see that Algorithm 4 substantially outperforms the other three algorithms. This is because Algorithm 4 has the mechanism to reduce interference of strong targets on weaker ones. Again, the feasibility of doing so is enabled by our discovery on false target features in this work. From Figure 9b, we further see that the proposed Algorithms 3 and 4 can effectively reduce the false alarm rate. Figure 8: Detecting performance versus SNR (with respect to \(\mathbf{y}\)), where a single target is set with randomly generated parameters over \(10^{4}\) independent trials.