## 5 Performance Analysis
### Experiment Setup  
We used MATLAB to simulate the system. The proposed model has been simulated for a microcell environment. The focus of the model is to consider the scenario of local scattering giving rise to multipaths. These multipaths and the resulting fading are modeled as stochastic processes and channel characteristics like time-variation, amplitude, and angular spread are modeled using GBSBEM. We consider a cluster-based model with N sensor nodes randomly scattered over a large area. These nodes collect a common message and transmit it towards the cluster head. The information received at the cluster head is filtered and modulated and transmitted to the receiving station. The cluster head is located within a range of 2 meters from this receiving station. In this case both the cluster head and the receiver are surrounded by scatterers and the receiving antenna array is not well above the surrounding objects. The model parameters were chosen to fit the scenario. Table 1 shows the set of parameters used for simulations to develop the channel and the system model. The transmitted sequence is a BPSK modulated signal and the sequence length is \(10^{7}\). The whole sequence is divided into frames of length 100 symbols and the total number of frames are \(10^{5}\). The channel considered here is a quasi-static channel; _i.e._, the channel remains constant over the entire frame and changes from one frame to other. \begin{table}
\begin{tabular}{l l} \hline \multicolumn{1}{c}{**Fixed Parameters**} & \multicolumn{1}{c}{**Values**} \\ \hline No of frames & 100,000 \\ Frame Length & 100 \\ Path Loss (Lr) & 6 dB \\ Path loss exponent (n) & 3 \\ Number of multipaths (L) & 5 \\ Carrier frequency (fc) & 900 MHz \\ Distance between cluster head and receiver (D) & 1,000 m \\ \hline \end{tabular}
\end{table} 
Table 1: Parametric Values for the System Model. Figure 3: Cont. Table 2 compares the performance of the three receive diversity techniques. The table demonstrates that the BER of the system increases by increasing the antenna elements and decreases with the increase in SNR. At higher SNR, the BER goes to zero. The performance of EGC is only marginally inferior to MRC. The implementation complexity for EGC is significantly less than the MRC because of the requirement of correct weighing factors. Hence, the basic idea of diversity reception is that, if two or more independent samples of a signal are taken, then these samples will fade in an uncorrelated manner. This means that the probability of all the samples being simultaneously below a given level is much less than the probability of any individual sample being below that level. Thus, a signal composed of a suitable combination of various samples will have much less severe fading properties than any individual sample alone. 2.2 Performance of the system with single receives antenna and varying receiver height, maximum multipath delay, and transmits power  
In this section we analyze the performance when there is a single antenna in the receive array. The simulations were carried with different varying parameters. First, we perform the simulations based on varying receiver height. If the receiver height is low, there is a possibility that it may suffer from deep fades due to dense environment surrounding the receiver hence degrading the performance of the system. On the other hand, if the receiver is mounted on a higher ground, it will be less susceptible to fading and hence will collect the signal more efficiently. Figure 4(a) shows the variations in the BER as the height of the receiver is increased from 2 meters to 10 meters. It can be seen that the receivers closer to ground have higher BER whereas as the height of the receiver is raised from the ground, the BER improves. Figure 4(b) shows the BER when the maximum multipath delay is varied.