## 5 Numerical Simulation Results and Reception Performance Analysis
In the simulations, selective Rake combining is employed, where the number of fingers \(L_{r}\) is chosen big enough. The results are averaged over 1000 channel realizations, each associated with a random TH code. It can be seen from Figure 8 that the performance is severely degraded by the presence of fading on the desired signal comparing the average bit error probability with the previous scenarios. When the ISR is more than 20 dB, the system performance is unsatisfactory if no proper narrow band interference suppression  
Figure 8: Average bit error probability for the TH-PPM UWB wireless sensors with narrow band interferences under the IEEE 802.15.4a CM1 multipath fading channel. is employed. The proposed interference suppression algorithm can greatly improve the reception performance under the strong in-band interferences case. Finally, to validate the practical amount of performance enhancement obtained by the complex-coefficient NBIs scheme proposed in this article, we investigate the average bit error probability of time hopping code division pulse position modulation ultra-wide band wireless reception in the present of multiple narrow band interferences with and without the designed complex-coefficient adaptive notch filters. The simulation is executed under IEEE 802.15.4a CM5 channel model for the outdoor line of sight scenario. The normalized impulse response of IEEE  
Figure 10: Average bit error probability versus SNR of the time hopping ultra-wide band wireless sensors receiver considered with and without the proposed narrow band interference (NBI) scheme. Figure 9: Normalized impulse response of the IEEE 802.15.4a CM5 channel model for the outdoor line of sight scenario. 802.15.4a CM5 channel model is depicted in Figure 9. Compared with the simulation in Figure 7, we can find that the energy of the multipath component is more dispersive in the outdoor environment. The reception performance under the IEEE802.15.4a CM5 channel model is depicted in Figure 10. In this scenario, the UWB wireless sensors suffered from four in-band strong narrow band interferences with four different central frequencies. In the simulation, we suppose that the signal to interference ratio is \(-30\) dB. From the numerical simulation results, we can notice that the reception performance is worst when the receiver consists of the matched filter without the proposed narrow band interferences' suppression; the average bit error probability is larger than \(10^{-2}\) even if the average signal to noise ratio is more than 25 dB through this kind of reception. The performance of Rake combining outperforms the matched filter scheme, and the A-Rake scheme with the proposed NBIs can obtain the best reception performance. In addition, we can find that the reception performance of SRake with NBIs outperforms the case of MRC combining without the proposed NBIs since the proposed NBI algorithm can improve the reception SINR. Both the proposed NBI approach and Rake combining receiver can elevate the reception performance of ultra-wide band wireless sensors, since the complex-coefficient adaptive notch filtering algorithm proposed in this article can remove the strong NBIs with slight distortion and the Rake combining receiver will collect the dispersed energy of the multi-path components due to the large number of resolvable multipath components in cognitive ultra-wide band wireless sensor networks.