## 5 Performance Analysis
### Experiment Setup
As can be seen from Equation (1) and Equation (2) that the semi-major and the semi-minor axis of the ellipse, respectively, is dependent on the maximum multipath delay, \(\tau_{\max}\), therefore, as we change \(\tau_{\max}\), the geometry of the ellipse also changes. The results show that as \(\tau_{\max}\) is decreased, the system gives better \begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline \multicolumn{2}{|c|}{**No. of Antenna**} & \multicolumn{2}{c|}{**SNR**} & \multicolumn{2}{c|}{**Bit Error Rate**} \\ \cline{3-5} \multicolumn{1}{|c|}{**Elements**} & \multicolumn{1}{c|}{**(dB)**} & \multicolumn{1}{c|}{**EGC**} & \multicolumn{1}{c|}{**MRC**} & \multicolumn{1}{c|}{**SMC**} \\ \hline \multirow{3}{*}{2} & 1 & 0.0018 & 0.0014 & 0.0016 \\  & 5 & 0.0002 & 0.0001 & 0.0001 \\  & 10 & 0.0000 & 0.0000 & 0.0000 \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{3} & 1.0e–003 * & \multirow{3}{*}{0.0001} & 1.0e–003 * \\  & 1 & [0.5900 & 0.0006 & [0.2240 \\  & 5 & 0.0200 & 0.0001 & 0.0080 \\  & 10 & 0.0000] & 0.0000 & 0.0000] \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{4} & 1.0e–003 * & \multirow{3}{*}{1.0}e–003 * & \multirow{3}{*}{1.0}e–003 * \\  & & 1 & [0.2300 & [0.1320 & [0.1520 \\  & 5 & 0.0100 & 0.0100 & 0.0120 \\  & 10 & 0.0000] & 0.0000] & 0.0000] \\ \hline \end{tabular}
\end{table} 
Table 2: BER at various SNR for different number of receive antennasperformance. It can be explained in terms of the geometry of the ellipse. As \(\tau_{\max}\) increases, \(a_{\mathrm{m}}\) and \(b_{\mathrm{m}}\) also increases, thus making the ellipse larger, and vice-versa. Larger ellipse means increase in the propagation delays, hence poorer performance. Smaller ellipse means lesser propagation delays, hence better performance. Figure 4: **(a)** BER _vs._ SNR with varying receiver height, \(H_{R}(m)\). **(b)** BER _vs._ SNR with varying maximum multipath delay, \(\tau_{max}\left(\,\mathrm{\mu s}\right)\). **(c)** BER _vs._ SNR with varying transmit power, \(P_{T}(W)\). Figure 4(c) shows the BER performance of the model as a function of SNR under different values of transmission power based on numerical simulation. It can be seen that the use of smart antennas can help significantly in reducing the sensor nodes' power consumption. However, the performance of the system increases with increase in transmission power. It is evident that the performance of the system varies with variation in transmission power. 2.3 Performance of the system with MRC and varying receiver height, maximum multipath delay, and transmit power  
In this section, we repeat the simulations for different \(\mathrm{H_{R}}\) and \(\mathrm{\tau_{max}}\) when we have multiple antennas at the receiver. As seen from the table, MRC gives the best performance, thus, for our further simulations we have focused on the system model with MRC at the receiver only and the implementation of EGC and SC is straight forward. Figure 5(a) shows that the performance of the system increase with receiver height irrespective of the number of the receive antenna elements. Figure 5(b) shows the performance based on \(\mathrm{\tau_{max}}\) and proves that BER improves with smaller \(\mathrm{\tau_{max}}\). The simulations have been performed with number of receive antennas up to four but it is not limited and can be extended for higher numbers of receive antennas. Figure 4: _Cont._  
Figure 5: **(a)** BER _vs._ SNR with different receiver height, \(H_{R}(m)\) and \(\rm{N_{R}}=\) 1,2,3, and 4. **(b)** BER _vs._ SNR with varying maximum multipath delay, \(\tau_{max}\) (\(\,\upmu\)s) and \(N_{R}=\) 1,2,3, 4. The BER values for multiple receive antennas at different receiver height with different maximum multipath delay have been summarized in Table 3.