# A Light Signaling Approach to Node Grouping for Massive MIMO IoT Networks
## 7 Numerical Evaluation
### Results  
The minimum, average, and maximum SINRs obtained for each algorithm and number of nodes are shown in Figure 4a-c, and Figure 4d shows the CDFs of the SINRs obtained with each algorithm, over all nodes, in network instances with 36 nodes. In the aggregate figures, the values shown are the averages across all instances for each number of nodes, with 95% confidence intervals. As expected, clumped partitioning performed the worst, with the SINR decreasing as the number of nodes increased. The results even show that a bad grouping of nodes can impact the SINR dramatically, degrading the SINR on average by \(>\)5 dB for 15-20 nodes per group in the considered scenarios. This shows the potential poor performance that may occur if a partition is chosen that does not take into account the directional properties of the nodes' channels. All of the other algorithms substantially outperformed clumped partitioning on all three SINR metrics. The performance of the other three algorithms was similar. Even though the optimization and approximation algorithm used only the two parameters of dominant direction and angular spectrum spread, they were nonetheless able to match the performance of power partitioning, which used the full channel information for each node. This is promising, especially for IoT scenarios, as it demonstrates that an effective node partition can be achieved even with only limited information about the nodes' channels. Moreover, the directional properties we have used will be relatively stable over time for static or slow-moving nodes, meaning that the signaling needed to facilitate node partitioning is reduced, as channel information need only be collected from the nodes occasionally. In the best case, each time nodes transmit, the channel information obtained from their collected pilot signals can be used to compute the next node partition, even in cases where nodes transmit only infrequently, as in many sensor networks and monitoring applications. In many cases, we observed a relatively large variance in the SINRs obtained for all algorithms. This is because, although both our partitioning approaches and power partitioning methods were aimed at reducing inter-node interference, a true optimal partition would require actually computing the instantaneous interference between the nodes. This depends on the correlations between the users' channels, and while both the directional channel properties (for our approach) and the instantaneous power (for power partitioning) correlate with the inter-node interference, they do not perfectly capture it. The variance is greater when the number of nodes is lower, since with fewer nodes the probability of the nodes being more unevenly distributed across the angular spectrum increases, leading to a higher proportion of unusual cases. Figure 4: SINR performance for different numbers of nodes and partitioning methods. (**a**) Minimum SINR for different numbers of nodes and node partitioning methods. (**b**) Average SINR for different numbers of nodes and node partitioning methods. (**c**) Maximum SINR for different numbers of nodes and node partitioning methods. (**d**) CDF over the SINR of all nodes for 36-node network instances. In the figures, we can see that the optimization and approximation algorithms performed similarly, with the approximation algorithm even obtaining a higher SINR in some cases, although the difference between the two was only statistically significant in one case, for the minimum SINR for 33 nodes. The reason that the approximation algorithm was able to achieve better performance than the optimization algorithm is again because here we measured performance in terms of SINR, calculated from the complete node channels, whereas the two algorithms--optimization and approximation--had only reduced channel information available to them in the form of the dominant directions and angular spectrum spreads.