## 5 Performance Evaluations
### Simulation Setup and Wireless Channel  
A realistic wireless model is required to make a reliable assessment. The Z-curve simulations [9] consider the modulation, channel model, and coding scheme to obtain the relationship between transmission power and packet receiving rate. Chipcon CC1000 radio module was used in the Z-curve study. Similarly, the H-curve [11] is another study using realistic parameters. For the H-curve wireless model, a wireless node's characteristics with the Chipcon CC1100 radio module [32] were used. This study also used the wireless channel model and its parameters described in [9]. Explanations and specifications for this channel can be found in the following paragraphs. It should also be noted that all the path planning models in this study are run under the same realistic channel conditions.  
The strength of the signal emitted in the physical environment decreases due to wireless propagation. Therefore, path loss and bit error rate should be modeled to analyze the physical layer [35;36]. \(P_{nr}\) packet reception ratio means the possibility of a packet being successfully received. It is expressed by the Bernoulli random variable that takes the value 1 if the packet is received and 0 if not. It is given by:  
\[P_{rr}=(1-P_{be})^{8f}\,(1-P_{be})^{8(f-1)2.0} \tag{4}\]  
where \(f\) = 20 byte is the frame's size related to the TinyOS application after being encoded (the frame consists of a preamble, network payload, and CRC). The Manchester encoding method is used; \(P_{be}\) is the bit error probability, which depends on the modulation type. Here, we chose non-coherent FSK modulation, which is used in MICA2 motes and formulated by [35]:  
\[P_{be}=\frac{1}{2}\mathrm{e}^{\frac{SNR\times B_{N}}{2K}} \tag{5}\]  
where \(B_{N}\) is the noise bandwidth and \(R\) is the data rate in bits. MICA2 motes use the Chipcon CC1000 radio [37] where \(R\) = 19.2 kbps and \(B_{N}\) = 30 kHz. The signal to noise ratio (SNR) at the receiver is calculated by:  
\[SNR^{dB}=P_{rec}{}^{dB}-P_{n}{}^{dB} \tag{6}\]  
\(P_{rec}\) defines the reception power, and \(P_{n}\) expresses the noise floor which is both environmentally- and radio-dependent [38]. It is given by:  
\[P_{n}=(F+1)kT_{0}B_{N} \tag{7}\]  
where \(F\) = 13 dB is the noise figure, and k is the Boltzmann's constant. \(T_{0}\) = 27 \({}^{\circ}\)C is the ambient temperature, and \(B_{N}\) is the equivalent bandwidth. In this study, the average noise floor considered is approximately \(-\)105 dBm, which has a difference of 10 dBm with the analytically calculated value in [36]. On the other hand, \(P_{rec}\) is given as:  
\[P_{rec}{}^{dB}=P_{trans}{}^{dB}-P_{L}{}^{dB} \tag{8}\]  
where \(P_{L}{}^{dB}\) and \(P_{trans}{}^{dB}\) are power loss and transmitting power, respectively. To model the shadow path loss effect, the most commonly used log-normal model [38] is used:  
\[P_{L}(d)^{dB}=P_{L}\left(d_{0}\right)^{dB}+10\gamma\log\left(\frac{d}{d_{0}} \right)+X_{\sigma}{}^{dB} \tag{9}\]  
where \(P_{L}(d)^{dB}\) is the power loss after the signal propagates over distance \(d\), \(P_{L}\left(d_{0}\right)^{dB}\) is the power loss at the reference distance \(d_{0}\), and \(\gamma\) is the path loss exponent. \(X_{\sigma}=N\left(0,\,\sigma^{2}\right)\) is a Gaussian random variable with mean 0 and standard deviation (std) \(\sigma\) (shadowing effect).  
In this paper, the performances of different path planning models are evaluated in a MATLAB environment with 50 runs in an obstacle-presence scenario. It is assumed that there are N = 250 static UNNs in the ROI, a single MA moving on a given path, and theROI is an area of S = 100 \(\times\) 100 m\({}^{2}\). The resolution value (R) is the ratio between the CR and the MA step dx. That is, the resolution is expressed as CR/dx.  
Other parameters used in this study are listed in Table 1.