## 4 Performance Analysis in the Absence of Non-Idealities
### Numerical Results
The value \(\Delta E_{\rm max}=20\) dB makes the improvement brought by the use of feedback power control strategies noticeable. Obviously, when \(\Delta E_{\rm max}\) decreases, this improvement reduces. The results presented in the following are obtained through computer simulations and collected by considering increasing values of the energy gap \(\delta\): for each value of \(\delta\) we run a set of simulations for both balanced SNR and unbalanced SNR power control schemes. At the end of each simulation, we evaluate the average actual SNR at the sensors (after feedback power control), denoted as \(\overline{E}_{\rm c}/N_{0}\), considering all \(n\) data flows and all fading realizations. Together with \(\overline{E}_{\rm c}/N_{0}\), we also evaluate the average bit error rate (BER) and the outage probability (denoted as \(P_{\rm O}\)). As for the average SNR, the average BER is evaluated by averaging over all \(n\) data flows and all fading generations. Concerning the outage probability, an outage event occurs when at least one bit in at least one of the \(n\) packets from the sources to the AP is in error. The outage probability is thus evaluated by averaging the numbers of outage events over all fading generations. In Figure 5, the average BER is shown, as a function of the average SNR at the sources, considering (a) regular LDPC-coded schemes, (b) DD LDPC-coded schemes, and (c) SCCCed schemes. The performance in the presence of the balanced SNR power control strategy is compared with that associated to the absence of power control. First, one can observe that, as expected, the use of feedback power control allows to significantly improve the performance with respect to scenarios without its use. As expected, when the number of sources increases, the BER reduces, since there exists a large number of communication links and, consequently, the high BER at the output of the strongly faded links can be partially lowered thanks to the reliable a-priori information coming from the soft-output decoders associated with the other sources which experience less faded links. When power control is considered, three different operating regions can be identified. For low values of the SNR, the performance of feedback power control schemes is worse than that without power control, since the transmit power is not sufficient to reduce the BER. Then, there exists an intermediate SNR region, with waterfall-like BER, where the system is able to (almost) completely compensate the faded communication links and, therefore, the performance is mainly limited by the error correction capabilities of the channel code. For large SNR, the slope of the BER curves decreases. In fact, in this operating region the performance is mainly limited by the fading fluctuations which do not allow to achieve the desired SNR, on account of the limited power control dynamics. Hence, the slope of the curves with power control is essentially the same of that with no power control and one can conclude that the unbalanced SNR power control strategy is not effective. In Figure 6, the average BER is shown, as a function of the average SNR at the sources, considering (a) regular LDPC-coded schemes, (b) DD LDPC-coded schemes, and (c) SCCCed schemes. Both balanced SNR and unbalanced SNR power control strategies are considered. Motivated by the derivation in the previous sections, the unbalanced power control strategy is expected to guarantee, at a given SNR, a performance better than that with balanced SNR power control strategy. However, this effect can be slightly perceived when a regular LDPC code is used, whereas the gain becomes more evident when a DD LDPC code and, even more, a SCCC are used. In particular, the SCCC, in the presence of unbalanced SNR power control, allows to achieve a gain of more than 1 dB in the BER waterfall region with respect to the other two coding schemes. This significant impact of the designed channel code is in agreement with the information theoretic results presented in [25].