# Impacts of Diversity Technique Application in Order to Reduce the Fading in IEEE 802.15.4 Networks
## 5 Numerical Results  
All the results are obtained in the form of infinite series, and their truncation is needed. In Table 1, the number of terms to be summed in order to achieve accuracy at the fifth significant digit is depicted for (25), (30) and (36). The calculation was performed for the parameters \(\gamma_{0}=0\), \(L_{c}=32\) chips, \(M=4\), and \(k=4\). The number of terms required to obtain accuracy on the fifth significant digit decreases for higher values of the parameter \(m\) (in the case of the Nakagami-\(m\) model--Equations (25) and (36)). The number of terms required to obtain accuracy at the fifth significant digit is increased for a greater number of branches of the MRC combiner (in the case of the Rayleigh model--Equation (30). In order to obtain accuracy at the fifth significant digit for the SC combiner and the SC combiner, 195 terms are required. By using the calculated analytical expressions (17), (25), (30) and (36), the numerical results of BER depending on the mean value of the received SNR-\(\gamma_{0}\) are presented. Figure 3 shows the BER behavior for fading channels modeled with the Nakagami-\(m\) and Rayleigh distributions, when the signal is processed by the SC and MRC combiners and when there are no combiners (the case analyzed in [18]). The following parameter values were used: \(L_{c}=32\) chips, \(M=4\), \(k=4\) bits, \(m=2\) (for the Nakagami-\(m\) distribution), and \(L=2\) (for the MRC combiner). From Figure 3 it can be seen that the BER values decrease with an increasing parameter \(\gamma_{0}\) and that the Rayleigh fading channel has a better performance than the Nakagami-\(m\) fading channel. The application of SC and MRC combiners has the effect of reducing BER and of improving system performance. Only in the case of using the SC combiner, and for the Nakagami-\(m\) fading channel, is poorer performance obtained when the parameter \(\gamma_{0}\) has lower values. The MRC combiner gives a better performance than the SC combiner. The simulation results fit the numerical \begin{table}
\begin{tabular}{c c c c} \hline  & **m = 1** & **m = 2** & **m = 3** \\ \hline Equation (25) & 223 & 201 & 178 \\ Equation (36) & 225 & 209 & 180 \\ \hline  & **L = 2** & **L = 3** & **L = 4** \\ \hline Equation (30) & 211 & 234 & 255 \\ \hline \end{tabular}
\end{table} 
Table 1: Terms needed to be summed in the expression for cumulative distribution function to achieve accuracy at the fifth significant digit. Figure 3: BER behavior for Nakagami-\(m\) and Rayleigh fading channels with and without SC and MRC combiners. results. Simulation results were obtained using Monte Carlo simulation in the MATLAB R2017b software. Figure 4 shows the BER behavior when using the MRC combiner with a different number of branches. From the given graph it can be seen that the use of MRC combiners gives lower, i.e., better BER values, with better values being significantly more pronounced at lower values of the parameter \(\gamma_{0}\) and Rayleigh fading channels. Figure 5 shows the BER behavior for the case of the Nakagami-\(m\) fading channels when no combiners are used and when SC and MRC combiners are used, for different values of the \(m\) parameter. Increasing the fading parameter \(m\) leads to a decrease in BER. The use of combiners also leads to lower BER values, with the MRC combiner having a greater impact on BER reduction. Figure 4: BER behavior when using MRC diversity combiner. Figure 5: BER behavior for Nakagami-\(m\) fading channels with and without the SC and MRC combiners. A graphical representation of the obtained analytical results in (17) and (30) is given in Figures 6 and 7, where the BER behavior when using SC and MRC combiners with two branches is shown, for different values of the modulation parameter \(M\) for the Rayleigh and Nakagami-\(m\) fading channels, respectively. The given results show that increasing the modulation parameter \(M\) leads to an increase in BER. The increase in BER is significantly more pronounced at lower SNR values.