# A Metric for Secrecy-Energy Efficiency Tradeoff Evaluation in 3 GPP Cellular Networks
## 4 Results  
In this section, the results that have been obtained by numerically computing the values of Equations (5)-(7) are discussed. Figure 4 shows the percentage of the secure area \(A_{\mathrm{s}}^{\mathrm{[eff]}}\) and of the complementary unsecure region (\(1-A_{\mathrm{s}}^{\mathrm{[eff]}}\)), referred to as the overall area of the cell sector. The transmit power of Alice ranges from 5 to 40 W, while the distance of [PERSON] varies from 10 to 100 m.  
Some conclusions about secure and unsecure areas can be drawn:  
* If [PERSON] is close to [PERSON] (10 m), a power increase does not imply a proportional enlargement in the secure area;
* When [PERSON] is in the middle of the cell (50 m), a power increase is beneficial from the security point of view: the unsecure area becomes smaller; anyway, continuing to increase the power over and over does not imply a remarkably larger secure area; a sort of saturation in the extension of the secure area can be observed when the power increases over 10 W;
* When [PERSON] is in the boundary of the cell (100 m), a higher power is needed to obtain a secure area of about 50% of the cell sector extension; moreover, a higher than 20 W transmit power gives tiny enlargements of the secure area. Figure 5 shows the values of the metric \(\rho_{1}\) (6) as a function of [PERSON]'s distance and [PERSON]'s transmit power. As it can be seen, there is always an optimum transmit power for [PERSON] for every distance of [PERSON], i.e., the minimum power maximizing the effective secrecy area. Increasing the power over the optimum does not give benefits, i.e., the secure area does not increase considerably, while the power consumption gets higher. Figure 4: Secure and unsecure areas when [PERSON]’s distance is \(\{10,50,100\}\) m and \(P=\{5,10,20,30,40\}\) W.  
Figures 6 and 7 show the values of the metric \(\rho_{2}\) (7) as a function of the [PERSON]'s distance and power consumption \(P_{in}\) for two different BS types that are described in in [15], the Remote Radio Head (RRH) (According to the EARTH Deliverable D2.3 the maximum RRH transmit power is equal to 20 W: nonetheless, in the computation of the Effective Secrecy-Energy Efficiency metric, we have considered higher power values in order to allow a more complete system evaluation). and the Macro BS, respectively. The target secrecy rate is fixed and set to \(\overline{R}_{s}=0.1C_{B}\). As it can be seen, for every distance of [PERSON], there is always an optimum power consumption, i.e., the minimum power that maximizes the effective secrecy area. As in the previous case, if the power is increased over this value, negligible additional benefits are achieved. The Effective Secrecy-Energy Efficiency vs. BS power consumption curves are not monotone: particularly, the maximum of the proposed metric is achieved for different power consumption values that depend on Bob's position; this result confirms that the optimization of the tradeoff between the security area, the afforded date-rate and the power spent by the BS is not a trivial task: particularly, the simple control of the radiated power is not efficient when a target secrecy rate has to be guaranteed to an end-user. This conclusion is enforced by the results that are shown in Figure 8, which presents the percentage of unsecure area (over the total coverage) as a function of the distance of Bob and the target secrecy rate \(\overline{R}_{s}\) to be supported. The target secrecy rate is calculated as the percentage of the capacity of the legitimate link, i.e., \(\overline{R}_{s}=\{1\%,5\%,10\%,20\%,50\%\}\) of \(C_{B}\). The BS power consumption \(P_{in}\) is fixed and, for Macro BSand assuming \(P=20\) and \(N_{TRX}=3\), i.e., one carrier per sector, is set to 291.22 W (This value is obtained by following the recommendations of the EARTH (Energy Aware Radio neTwork tecHnololgies) project). As it can be seen, the higher the target secrecy rate, the wider the unsecure area.