# Device Free Detection in Impulse Radio Ultrawide Bandwidth Systems
## 7 Conclusions  
In this paper, a novel device-free detection method is proposed for an indoor STH-PPM UWB system. Our method relies solely on calculating the characteristic function (CF) of the device. 1 st and 2 nd moments are calculated using this CF, to develop decision statistics which are employed to design and develop the receiver operating characteristics (ROC)s. Particularly, it was shown that \(P_{FA}\) can be reduced by increasing the detection threshold and/or frame length. Furthermore, probability of detection approaches 1 for an interference-to-noise ratio greater than \(-5\) dB, even for a very low probability of false alarm. Through numerical simulations, it is shown that the proposed detection method  
Figure 5: Simulated and calculated Probability of miss detection curve comparison for STH \(M-\)ary PPM System. The curves labelled as “Exact” are plotted using (27) where as the markers denote the simulation performance using (16).  
is able to detect the presence of the device and results in satisfactory performance with a reduced probability of false alarm. Moreover, the simulation results corroborated the derived performance expressions. The proposed detector can be implemented in a real time system. As a future work, similar to [17], we are planning to implement and test this algorithm on a UWB kit and carry out the measurements in an industrial warehouse.  
Conceptualisation, The conceptualization, methodology and original manuscript draft preparation was done by W.B.A., F.C. and Q.Z.A. The validation, supervision, manuscript editing, manuscript review and funding acquisition was done by Q.Z.A., F.A.K. and T.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} AWGN & Added White Gaussian Noise \\ BER & Bit Error Rate \\ BLE & Bluetooth Low Energy \\ CF & Characteristic Function \\ COVID & Coronavirus Disease \\ CRLB & Cramer-Rao Lower Bounds \\ DS & Direct-Sequence \\ DS-TH & Direct-Sequence and Time-Hopping \\ False Alarm & FA \\ GPS & Global Positioning System \\ INR & Interference Noise Ratio \\ IR & Impulse Radio \\ LoRa & Long Range \\ LoS & Line of Sight \\ NLoS & Non Line of Sight \\ NP & Neyman Pearson \\ OOK & On-Off Keying \\ PAM & Pulse Amplitude Modulation \\ PPM & Pulse Position Modulation \\ PSM & Pulse Shape Modulation \\ RFID & Radio Frequency Identification \\ ROC & Receiver Operating Characteristics \\ STH & Slow Time Hopping \\ SV & Saleh Valenzuela \\ TDoA & Time Difference of ArrivalChannel State Information \\ ToA & Time of Arrival \\ UWB & Ultra-wide bandwidth \\ WiFi & Wireless Fidelity \\ \end{tabular}  
List of Symbols  
The following symbols are used in this manuscript:  
\begin{tabular}{l l} \(s(t)\) & Transmitted Signal \\ \(y(t)\) & Received Signal \\ \(n(t)\) & AWGN Noise \\ \(\psi(t)\) & Time domain UWB pulse \\ \(N_{s}\) & Number of pulses \\ \(j\) & index of Frame \\ \(t\) & index of Time \\ \(k\) & index of Device \\ \(h(t)\) & Channel Impulse Response \\ \(V\) & Number of Clusters \\ \(U\) & Number of Rays in Clusters \\ \(T_{f}\) & Frame duration \\ \(L\) & Total Number of multipath \\ \(T_{l}\) & Delay of the \(l\)-th multipath \\ \(K\) & Number of devices \\ \(h_{l}\) & Channel impulse response of \(l\) multipath \\ \(\sigma^{2}\) & AWGN Noise Variance \\ \(\gamma\) & Threshold \\ \(E(X^{m})\) & \(m\)-th moment \\ \(\mu_{a}\) & Mean when Deviceis Absent \\ \(\mu_{p}\) & Mean when Device is Present \\ \(\sigma_{a}\) & Variance when Device is Absent \\ \(\sigma_{p}\) & Variance when Device is Present \\ \(R(\cdot)\) & Autocorrelation of the UWB pulse \\ \(\delta(\cdot)\) & Dirac delta Function \\ \end{tabular}