## 5 Numerical Simulation Results and Reception Performance Analysis  
In this section, the numerical simulation results are presented to illustrate the reception performance of time hopping pulse position modulation impulse-based ultra-wide band wireless sensors and the performance enhancement provided by the complex-coefficient adaptive notch filter narrow band interference suppression algorithm developed in this paper under different channel propagation environments. We consider a second derivative of the Gaussian monocycle transmitted impulse waveform with \(\tau_{p}=0.0625\) ns. The frame length \(T_{f}=512\) ns; the duration of the chip \(T_{c}=0.25\) ns; the number of time slots per frame is 2048; the number of transmitted base band pulses  
Figure 5: Normalized frequency response of the \(K\) order complex-coefficient cyclic cascaded matrix adaptive notch filter. per symbol \(N_{s}=4\); and the number of active users \(N_{u}=8\). We suppose the time hopping codes for different users are orthogonal. We first observe the reception performance of the time hopping pulse position modulation impulse ultra-wide band signal in the present of narrow band interferences under additive white Gaussian noise (unfaded scenario) channel. Figure 6 shows the simulated average bit error probability (BEP) versus average signal to noise ratio (SNR) for different values of the narrow band interference to signal ratio (ISR). We can find that the narrow band interference will deteriorate the system performance, especially when the ISR is more than 10 dB. Figure 6: Average bit error probability of the TH-pulse position modulation (PPM) UWB wireless sensors in the unfaded scenario with the narrow band interferences under different power levels. Figure 7: Normalized impulse response of the IEEE 802.15.4a CM1 channel model for the indoor residential line of sight scenario. The practical ultra-wide band radio propagation environment is a dense multipath fading channel. A number of UWB channel models have been proposed in the last decade: [58] suggested a model for the frequency range below 1 GHz. The IEEE 802.15.3a group developed a channel model that is valid from 3 GHz to 10 GHz, but is designed only for indoor residential and office environments, and the distance between transmitter and receiver is restricted to 10 m [59]. The IEEE 802.15.3a channel model is parameterized for line of sight (LOS), as well as non-line of sight (NLOS) circumstances in residential, industrial, office, farm and open outdoor environments. Based on more practical measurements than the IEEE 802.15.3a channel model, the IEEE 802.15.4a work groups provided a more general parameterized ultra-wide band channel model from 2 GHz to 10 GHz. The standard ultra-wide band channel model also covers office, farm, residential, industrial, open outdoor environments and body-area networks with both LOS and NLOS cases [50; 60]. In this place, we first consider the IEEE 802.15.4a CM1 channel model for the indoor residential environment under the line of sight case. The normalized impulse response in the IEEE 802.15.4a CM1 channel model is depicted in Figure 7. The impulse response of the ultra-wide band CM1 channel consists of hundreds of resolvable multi-path components. It is not difficult to notice that the channel impulse response of CM1 is the sum of attenuated, delayed and distorted multipath components, and in this case, well-known Rake receivers can be used to collect the dispersive energy of multipath components. A Rake receiver can consist of a matched filter with a tapped delay line matching the impulse response of the practical ultra-wide band channel. It also can be replaced by a set of time delay correlators that are sampled at the delays related to specific multipath components. We next consider the case in which the time hopping ultra-wide band wireless signal undergoes multipath fading. More specifically, the IEEE 802.15.4a CM1 channel model for the indoor residential environment under line of sight case is considered.