# Device Free Detection in Impulse Radio Ultrawide Bandwidth Systems
## 6 Performance Analysis and Discussion
However, as the INR decreases \(P_{D}\) will be reduced significantly to 80% and below depending upon the INR value. With these receiver operating characteristics (ROC)s for STH-UWB radar can be designed. This threshold detection will help increase the \(P_{D}\) and reduce \(P_{FA}\) for a given INR. In Figure 3, it is observed that for a given \(P_{FA}\), the detection performance increases monotonically with the INR. The pulse duration was fixed to \(T_{f}=100\) ns. Figure 3 was simulated using (27), where the value for \(\mu_{p}\) and \(\sigma_{p}\) are calculated using (36) and (41), respectively. From the figure, it becomes obvious that in order to improve the detection performance, either \(P_{FA}\) is increased or the INR is increased. For a fixed \(P_{FA}=1\times 10^{-5}\), we need an improvement of 3 dB in INR to improve the detection probability from 0.3 to 0.8. However, for lower \(P_{FA}=0.1\), we will require an improvement of 8 dB to reach the same detection probability. Therefore, it can be concluded from the figure that for higher \(P_{FA}\), higher increase in INR is required as compared to lower \(P_{FA}\). In order to further clarify this concept, we have plotted Figure 4. Figure 4 shows the effect of increasing the energy of the interference. The pulse duration was fixed to \(T_{f}=100\) ns. Figure 4 was simulated using (27), where the value for \(\mu_{p}\) and \(\sigma_{p}\) are calculated using (36) and (41), respectively. By doubling the interference energy, there is a improvement of 3 dB in INR for a fixed \(P_{FA}=0.1\) and \(P_{D}=0.5\). The other main point of Figure 4 is found when comparing the performance of IR UWB system to DS-UWB system. In IR-UWB, there is only a single transmitted pulse in a frame duration, while for a DS system, \(N_{s}\) pulses are transmitted in each frame, resulting in a decrease of transmitted power. If a DS-UWB  
Figure 2: Receiver operating characteristics for UWB system with different interference to noise ratio (INR). system transmits two pulses in a frame, then there will be a decrease of 3 dB in INR for a fixed \(P_{FA}\) at \(P_{D}=0.5\). Figure 4: Detection performance and effects of interference energy. Figure 3: Detection performance of UWB system on linear \(P_{FA}\) scale. The performance of the proposed detection method is corroborated with the derived analytical expressions of probability of miss-detection. The performance of the simulated algorithm matches exactly with the derived theoretical performance expressions, which indicates that the algorithm achieves benchmark performance. Moreover, the derived expressions of \(P_{FA}\) and \(P_{D}\) can be utilized to plot the ROC and determine the operating point for the algorithm in various environments. Figure 5 corroborates the derived analytical expression of the probability of miss-detection, i.e., \(P_{MD}=1-P_{D}\), through simulation. The probability of miss-detection is plotted with varying the SNR per bit and the parameter \(M\). A general trend observed is that the miss-detection probability reduces as the SNR increases. In addition, it can be observed that as \(M\) increases, the miss-detection probability reduces. This trend is observed because \(M\) indicates that the transmission time is divided into \(M\) orthogonal slots. Each user randomly chooses a slot for transmission and this reduces the collision/interference probability. As a result, as \(M\) increases, the miss-detection probability reduces due to lower interference. Finally, it can be noted that the simulation results match exactly with the derived analytical expression.