## 3 Feedback Power Control
### Feedback Power Control Strategies with Unlimited Transmit Power
In this illustrative example, the fading coefficients (depicted in blue) are distributed as follows: the fading coefficients of the first and second links are lower than 1 (\(|\alpha^{(1)}|^{2}=0.3\) and \(|\alpha^{(2)}|^{2}=0.6\), respectively), i.e., the fading affecting these links is strong, whereas the fading coefficients of the third and fourth links are higher than 1 (\(|\alpha^{(3)}|^{2}=1.3\) and \(|\alpha^{(4)}|^{2}=2\), respectively), i.e., the fading affecting these links is \"beneficial.\" At this point, we apply the two proposed power control strategies and we show the obtained target SNRs (at the AP) and the corresponding transmit SNRs at the sensors--in all cases, the SNRs are shown in a linear scale. * In subfigure (a), we show the results obtained by applying the optimized (unbalanced) power control strategy. The target SNRs at the AP (shown as green bars) are the following: \(\gamma_{1}^{(\rm tgt)-unbal}=0.24\), \(\gamma_{2}^{(\rm tgt)-unbal}=0.29\), \(\gamma_{3}^{(\rm tgt)-unbal}=0.37\), and \(\gamma_{4}^{(\rm tgt)-unbal}=1\). At this point, the target SNRs at the transmitters (depicted in red) become  
Figure 3: Illustrative comparison, in terms of target SNRs at the AP and at the transmitters, between (a) ideal unbalanced SNR and (b) ideal balanced SNR feedback power control strategies in a scenario with \(n=4\) sources and \(\rho=0.95\). \[\frac{E_{\rm c-unbal}^{(1)}}{N_{0}}=\frac{\overline{\gamma}_{1}^{( \rm tgt)-unbal}}{|\alpha^{(1)}|^{2}}=0.8 \frac{E_{\rm c-unbal}^{(2)}}{N_{0}}=\frac{\overline{\gamma}_{2}^{(\rm tgt)- unbal}}{|\alpha^{(2)}|^{2}}=0.48\] \[\frac{E_{\rm c-unbal}^{(3)}}{N_{0}}=\frac{\overline{\gamma}_{3}^{ (\rm tgt)-unbal}}{|\alpha^{(3)}|^{2}}=0.28 \frac{E_{\rm c-unbal}^{(4)}}{N_{0}}=\frac{\overline{\gamma}_{4}^{(\rm tgt)- unbal}}{|\alpha^{(4)}|^{2}}=0.5\] The average target SNR \(\overline{E}_{\rm c-unbal}/N_{0}\) at the transmitter is thus equal to 0.51 (dashed horizontal line). * In subfigure (b), we show the results obtained by applying the balanced SNR power control strategy. The minimum common target SNR at the AP, given by (15), is 0.45. Therefore, the target SNRs at the transmitters (depicted in red) are the following: \[\frac{E_{\rm c-bal}^{(1)}}{N_{0}}=\frac{\overline{\gamma}^{(\rm tgt )-bal}}{|\alpha^{(1)}|^{2}}=1.5 \frac{E_{\rm c-bal}^{(2)}}{N_{0}}=\frac{\overline{\gamma}^{(\rm tgt)- bal}}{|\alpha^{(2)}|^{2}}=0.75\] \[\frac{E_{\rm c-bal}^{(3)}}{N_{0}}=\frac{\overline{\gamma}^{(\rm tgt )-bal}}{|\alpha^{(3)}|^{2}}=0.35 \frac{E_{\rm c-bal}^{(4)}}{N_{0}}=\frac{\overline{\gamma}^{(\rm tgt)- bal}}{|\alpha^{(4)}|^{2}}=0.23\] The average SNR \(\overline{E}_{\rm c-bal}/N_{0}\) at the transmitter becomes 0.71 (dashed horizontal line). The proposed illustrative comparison shows the benefits which can be obtained by properly unbalancing the target SNRs in the various links according to the actual channel conditions. In fact, in both power control strategies, setting the target SNRs at the transmitters as indicated makes the network operational point fall in the feasible SNR region, thus allowing theoretically error-free communications. The unbalanced SNR power control strategy, however, guarantees a given performance level at a lower energy cost than that required by the balanced SNR power control strategy.