## 3 Results and Discussion
### Interference Limited Communication Range Regions  
In this section we present our simulation results for the d\({}_{\mathrm{LIR}}\) which is the maximum distance from which a transmitter can successfully send data to the centrally positioned receiver with a specific rate. We compare our simulation results with the results from calculations based on the theoretical analysis presented previously. Figure 7 illustrates, the mean interference limited communication range with the confidence intervals (standard deviation) _versus_ the number of interfering nodes, using different transmission data rates, r\({}_{\mathrm{min}}\) = 0.4 m and path loss exponent equal to 2 and 4 in plots (a) and (b) respectively. By adapting the transmission rate (lowering in this case) we can control the size of the region (enlarge it) and allow more transmitters to be able to successfully communicate with the receiver of interest. This result implies that we can use an upper layer communication parameter to easily adapt (using the proposed method) to the experienced interference. The theoretical and simulation results are in better agreement as the number of interfering nodes increases. We can see that using a higher path loss exponent assumption reveals how much the exhibited interference affect communication and that is the reason that the region is restricted to smaller sizes. We observe (Figure 7) that the theoretical  
Figure 6: _Cont._  
calculations give a lower value (worst case scenario) but are within the deviation interval of the simulation results, for a = 2 (plot (a)), but not for a = 4 (plot (b)). The reason of this discrepancy lies in the way we use the interference measurements to calculate \(\mathrm{d}_{\mathrm{ILR}}\). A different approach for measuring the value of \(\mathrm{d}_{\mathrm{ILR}}\), is to first measure the mean interference level, repeating the experiment (random placement of transmitting nodes) a large number of times, and then compute the \(\mathrm{d}_{\mathrm{ILR}}\) using this mean value of interference. In this case (Figure 8) the results are in accordance with the ones found from the theoretical calculations. This corresponds to a situation where a receiving node monitors the varying (due to changes in the network) interference for a period of time and calculates the mean interference levels in order to find the \(\mathrm{d}_{\mathrm{ILR}}\). Figure 7: \(\mathrm{d}_{\mathrm{ILR}}\) for different transmission rates. Comparison of simulation and theoretical results. In the final set of simulations the procedure described at the beginning of this section is employed (we measure the value of the \(\mathrm{d}_{\mathrm{ILR}}\) for each placement of the transmitting nodes and then calculate its mean value). Changing the distance \(\mathrm{r}_{\mathrm{min}}\) (exclusion region) the interference limited communication range is not significantly affected, as shown in Figure 9. As was noted before, for a higher path loss exponent there is a discrepancy between the simulation and calculation results for the \(\mathrm{d}_{\mathrm{ILR}}\), which is reduced as the number of interfering nodes increases. This agrees with the results presented in [24] where it is noted that for small number of interfering nodes the theoretical and simulation results don't seem to  
Figure 8: \(\mathrm{d}_{\mathrm{ILR}}\) values calculated using the mean interference value found by Monte-Carlo simulations. Plots (**a**) and (**b**) are derived using different transmission rate. Comparison of simulation and theoretical results. converge. In the same figure we can see that for path loss exponent \(a=4\) the calculated \(d_{ILR}\) values are smaller than those for \(a=2\).