# Smart Beamforming for Direct LEO Satellite Access of Future IoT
## 5 Numerical Results
### Signal-to-Interference-Plus-Noise Ratio  
To complete the experimental validation we evaluate the SINR. With the aim of using the results obtained in Figure 7, we compute the average SINR after applying the proposed beamforming technique in the direction of the detected users. Hence, we evaluate a subset of the \(N_{\rm U}\) concurrent users. As a benchmark, we have represented the SINR of the MV beamformer with perfect CSIR. As Figure 8 highlights, the degradation is almost not noticeable when perfect CSIR is available. This confirms that the asymptotic orthogonality exists for large antenna arrays. As the number of users increases, the SINR gap is widened between the beamformer envisaged in this paper and the benchmark. The fundamental reason is that the number of symbols \(N_{\rm S}\) and the number of users \(N_{\rm U}\) have an impact on the SINR. Having more samples results in more accurate sample-covariance matrices, which is crucial to successfully separating users. As a general statement, high user density scenarios suffer from SINR degradation, unless a sufficiently high number of symbols \(N_{\rm S}\) are transmitted. Regarding the antenna configuration, the scheme with \(N_{\rm R}=1024\) achieves the best performance. As expected, the array gain and the interference mitigation capability depend on the number of antenna elements. For \(M=64\) and \(P=4\), the performance loss with \(N_{\rm U}\) is remarkable. The results provided in Figure 8 intend to study the impact of \(N_{\rm S}\) and \(N_{\rm U}\) into the SINR. Unfortunately, the full potential of the beamforming technique is not seen. Towards this end, we carry out an assessment under ideal conditions. That is, we assume that the receiver is able to perfectly estimate the number of active users \(N_{\rm U}\) and the covariance matrices formulated in (18)-(20). To gain a better insight we consider different frame configurations. Now, the number of repetition patterns is not kept constant, i.e., \(P\in\{4,8,16,32\}\). The average SINR is depicted in Figure 9. In alignment with the analysis conducted in Section 4, the results reveal that the performance enhances as \(P\) increases. The slope of the curve is more pronounced with \(P=4\) than in the rest of the cases. To justify the results we  
Figure 8: SINR versus \(N_{\rm U}\) for different values of \(N_{\rm S}\) and \(N_{x},N_{y}\). include Figures 10 and 11. For \(P=8,16,32\), we have not analyzed the impact of \(N_{\text{S}}\) on the SINR. The \(N_{\text{S}}\) value that leads to the best complexity/performance trade-off is left for the future work. When users are in close proximity and in addition choose the same repetition pattern, a cluster is created. Then, the proposed beamforming technique is not able to mitigate the unwanted signals that come from the cluster. This is clearly seen in Figure 10, where we have represented the beam pattern and the position of users at a given time instant. This situation can be improved to a high extent if nearby users are associated to orthogonal repetition patterns. The probability of this event occurring is increased with \(P\). This can be appreciated in Figure 10. Interestingly, when there are \(P=32\) orthogonal repetition patterns, we achieve a finer spatial resolution than in the \(P=8\) counterpart. The digital beamforming technique described in this work is compared to a fixed beamforming network that divides the coverage area into 161 beams. The beam pattern is represented in Figure 11. The position of users coincides with those of Figure 10. The downside of the fixed beamforming stems from the fact that beams point towards grid points that do not match with user positions. Another adverse effect is that the beamforming network is not designed to mitigate unwanted user positions. For this reason the SINR suffers the highest degradation in Figure 9. To carry out a fair comparison with the digital beamforming, we have assumed ideal conditions as well.