## 4 Simulation and Numerical Results  
Simulation was done using Matlab software R2017b to verify the performance of the LF MISO system. We have considered QPSK modulation and a Rayleigh flat fading channel and perfect phase matching between the transmitter and the receiver. The fixed parameters used in the simulation are shown in Table 1. The values of the variable parameters such as the slot period \(D\) and the carrier frequency \(f\) (i.e., \(\lambda\)) are shown in each figure as appropriate. Figure 4 is generated at carrier frequency 3 GHz. It can be seen that the BER has a periodic fluctuation because of the phase rotating nature of the LF. The lowest BER occurs at a slot period (separation) of 20 mm. Probably, this is the optimal value for the given frequency. However, note that the slot separation has to be practically feasible for a given LF cable (based on its length, loss requirement and other factors). As the ratio between the transmitted and conducted RF energy depends on the slot period, too small separation will cause too much energy to be radiated and vice versa. The general trend of increment in the BER as the slot period increases happens because the amount of energy received by the receiver decreases with high slot spacing. This is probably because of a lesser number of (radiating) slots in a given length (100 m). Essentially, this figure shows that, by appropriately optimizing the slot period of an LF for a given carrier frequency, a very low BER can be achieved. Figures 5 and 6 show a very important outcome. _The leaky feeder provides a significantly lower BER compared to a single antenna for the same SNR_ in both QPSK and M-QAM modulation schemes. It is important to interpret these graphs carefully. In these figures, the SNR of both systems are equal, not the transmission power. The LF has to be fed with more power to achieve the same SNR because of the multiple slots. Nevertheless, the LF system, acting as a distributed transmitter, will have lower RF power density and will cause less (co-channel) interference with neighboring systems while offering much lower BER. This is an interesting observation. Figure 7 is plotted in order to study the effect of RF carrier frequency on BER. Here, the \(x\)-axis is the wavelength (\(\lambda\)) of the RF signal as a function of the slot period \(D\), and \(D\) is fixed at 200 mm. This figure shows that the minimum BER will be achieved whenever \(\lambda=\)\(D/I\), where \(I\) is an integer for \(\lambda\leq D\). This is because, at this wavelength, _constructive interference_ occurs. Since \(D=200\) mm, the corresponding frequency is 0.3 \(<f<\) 30 GHz (i.e., 0.1 \(<\lambda<\) 1 m). We note that the BER also shows a periodic oscillation when \(\lambda<D\) and then steadily decreases for large values of \(\lambda\). Since BER depends on the slot distance \(D\) as well, Figures 4 and 6 have to be jointly used to study the behavior of the LF system. Figure 8 shows the BER of the LF for different values of M in the M-QAM modulation scheme. Note that \(M=4\) gives the best BER, as higher values of \(M\) are affected by larger phase errors, due to the phase rotation in the LF itself. \begin{table}
\begin{tabular}{l c} \hline \hline Carrier Amplitude \(A\) & 15 V \\ \hline Phase velocity \(\beta\) & 0.9 rad/s \\ \hline Number of Paths \(L\) & 3 \\ \hline Noise Power \(N_{0}\) & 0 dB \\ \hline Axial attenuation \(k\) & 0.15 dB/km \\ \hline Bit Duration \(T_{b}\) & 0.1 ms \\ \hline Leaky Feeder’s length & 100 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in the simulation processes. The received power versus the distance is illustrated in Figure 9. Note that the received power was acquired by simulating the LF and a single antenna using Matlab software by assuming the receiver distance up to 50 m. The result shows a stability in the received power when LF is in use, where the received power level is varying from [-15 to -25] (dBm), while, when the single antenna is in use, the received power level is varying from [-5 to -50] (dBm).