# 6G Goal-Oriented Communications: How to Coexist with Legacy Systems?
## 5 Numerical Evaluation
We compare three strategies: _(i)_ the fixed (i.e., non-adaptive) strategy of Figure 7 (black curve), _(ii)_ a strategy with fixed PER, with our adaptive algorithm only controlling \(P_{d,t}\) (red curve), and _(iii)_ our adaptive strategy for both PER and \(P_{d}\) (blue pentagram). First, we can notice how strategy _(i)_ (i.e., fixed PER and adaptive \(P_{d,t}\)) is shown only for a subset of possible PERs, i.e., only the feasible ones, given the target goal effectiveness. Then, from the red curve, we can notice how the proposed optimization method (although without adaptive PER control) is able to follow the profile of the non-optimized case, however slightly enlarging the feasibility region for some values of PER (e.g., \(\gamma=10^{-4}\)), i.e., achieving lower goal costs, thanks to power control and adaptation. However, this gain is negligible in most of the cases. On the other hand, the full optimization strategy (i.e., the adaptive PER and \(P_{d}\) method), which is the main novelty of this work, achieves the lowest goal cost (around 6% vs. 12% of the fixed PER strategy), with a different resulting average PER. Similar considerations can be made for Figure 9b (with \(\Theta_{\text{th}}=-0.5\)), however with a much larger gain obtained by our strategy with respect to the two benchmarks. In addition, in Figure 9c, the two non-adaptive solutions do not provide feasible points for \(\Theta_{\text{th}}=-0.4\), while our strategy is able to guarantee the target goal effectiveness with a goal cost around 8.5%, to be compared with the optimal value obtained by the genie (6.5%). From Figure 9, we can conclude that it is highly beneficial to adapt the target PER (i.e., communication reliability of GO communication) to higher layer performance (i.e., application performance) rather than adapting communication parameters to keep, e.g., a fixed target PER. This can have a huge consequence in adaptive MCS mechanisms, whose aim would be to guarantee application performance (adapting PER and interference tolerance) rather than guaranteeing a target PER a priori, in the case of GO communications. Figure 8: Trade-off between goal cost and goal effectiveness, with our method and with genie, against bandwidth splitting scenario. Figure 9: Goal-effectiveness heat maps as a function of goal cost (DO user data rate loss) and target PER of GO system, with and without optimization, for fixed E2E delay threshold (\(D_{\text{max}}=45\) ms) and different goal value thresholds \(\Theta_{\text{th}}\). Let us now focus on the adaptation capabilities of our proposed optimization. In particular, in Figure 10, we show a moving version of the goal effectiveness (i.e., the goal effectiveness estimated over the past 2000 slots--Figure 10a) and moving average goal cost (Figure 10b) as functions of time, introducing two unexpected events that need the algorithm to adapt to new conditions. Namely, at the beginning, the system requirements are \(D_{\text{max}}=45\) ms, \(\Theta_{\text{th}}=-0.4\) and \(\mathcal{E}_{g}=0.8\). Then, after 10,000 iterations, we switch from \(\Theta_{\text{th}}=-0.4\) to \(\Theta_{\text{th}}=-0.5\), keeping the same target E2E delay and goal effectiveness. After another 10,000 iterations (i.e., at slot 20,000), we switch from \(\mathcal{E}_{g}=0.8\) to \(\mathcal{E}_{g}=0.85\), while keeping the same goal value target and E2E delay requirement (i.e., \(\Theta_{\text{th}}=-0.5\) and \(D_{\text{max}}=45\) ms). First, from Figure 10a, we can notice how, from a goal-effectiveness perspective, the method is able to keep the desired value, switching to the new requirement after \(t=20000\). In addition, looking at Figure 10b, we can appreciate how the method always seeks the optimal solution in terms of goal cost. Indeed, when switching from \(\Theta_{\text{th}}=-0.4\) to \(\Theta_{\text{th}}=-0.5\), the goal cost reduces, thanks to the more relaxed goal value threshold. Then, when imposing a stricter goal-effectiveness constraint (\(t=20\),000), the goal cost increases again to attain the desired performance.