## 5 On the Robustness of the Proposed Feedback Power Control Strategies
### Non-Orthogonal Links: Multiple Access Interference  
In order to investigate the impact of non-orthogonality between the communication links, we consider the presence of mutual interference between the transmitted signals. Since an accurate characterization of the multiple access interference is beyond the scope of this paper, the residual interference is simply modeled as AWGN. Under this assumption, referring to equation (3), the real observable at the AP after matched filtering and carrier-phase estimation can be expressed as  
\[r_{i}^{(k)}=|\alpha^{(k)}|\sqrt{E_{\mathrm{c}}^{(k)}}y_{i}^{(k)}+\eta_{i}^{(k)}+ z_{i}^{(k)}\hskip 28.452756 pti=0,\ldots,N-1\hskip 28.452756 ptk=1,\ldots,n \tag{27}\]  
where \(z_{i}^{(k)}\) is a Gaussian random variable with zero mean and variance \(I_{k}/2\), where  
\[I_{k}\triangleq\epsilon\times\sum_{j\
eq k}|\alpha^{(j)}|^{2}E_{\mathrm{c}}^{(j)} \tag{28}\]  
and \(\epsilon\in[0,1]\) is a proper interference rejection factor. Note that the Gaussian model for the mutual interference applies accurately to non-orthogonal CDMA multiple access schemes, where \(\epsilon\) is the inverse  
Figure 7: Outage probability, 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 with the absence of power control. of the spreading gain [35] (e.g., see note 6). In general, we use \(\epsilon\) to quantify the level of mutual interference: the higher \(\epsilon\), the higher the multiple access interference, i.e., the less orthogonal the links. In the following, the definition of average SNR at the sources will remain that given by (19), i.e., it will not take into account the interference. Therefore, for very large values of the average SNR, the only surviving noise contribution will be due to the residual interference. In Figure 9, the average BER is shown, as a function of the average SNR at the sources, in a scenario with non-orthogonal links, considering: (a) DD LDPC-coded schemes and (b) SCCCed schemes. Two possible values for \(\epsilon\) are used: (i) 0.1 (moderate interference) and (ii) 0.3 (strong interference). As a reference, the curves relative to the case with orthogonal links (\(\epsilon=0\)) are also shown. As expected, the higher is \(\epsilon\), the worse is the performance, since data transmissions are affected by a larger amount of residual interference. Moreover, the unbalanced SNR power control strategy allows to obtain a performance better than that associated with the balanced SNR power control strategy for all considered values of \(\epsilon\). This effect is clearly visible in the BER waterfall region for the LDPC code, whereas it is evident at all SNRs with the SCCC, in agreement with the observation that this code is more effective  
Figure 8: Outage probability, 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. in JCD schemes [25]. However, a relevant difference, with respect to the ideal case, can be observed in the presence of strong multiple access interference, namely with \(\epsilon=0.3\). In fact, in this case the performance with balanced SNR power control worsens for increasing values of the average SNR. This is due to the fact that for large SNR the noise is basically due only to the multiple access interference. In this scenario, trying to equalize the SNRs in the two links might reverse the levels of mutual interference (from the first source to the second and vice-versa), without eliminating it. On the other hand, in the presence of unbalanced SNR power control this performance degradation, for increasing SNR, is very limited. This means that the unbalanced SNR power control strategy is more robust against multiple access interference.