# A Light Signaling Approach to Node Grouping for Massive MIMO IoT Networks
## 3 Related Work
### Node Selection for Massive MIMO  
When selecting nodes for transmission, many approaches rely on full CSI, such as [12; 13; 14; 15]. However, this is not suitable for our use case since this would require all nodes to first wake up from sleep and then transmit a pilot signal in order for the base station to gather the CSI. For low-power IoT devices, such an approach would consume too much energy to be viable, and does not allow the schedule to be set in advance to provide a defined sleep opportunity and wake-up time. There is, however, a body of work that performs node grouping based on reduced channel information, which is usually more stable over time. This is often carried out in the context of two-stage beamforming, where pre-beamforming groups are first formed using coarse channel information, and then full precoding takes place after collecting the full CSI for a subset of nodes. Some examples of reduced information that can be used for this purpose are channel quality indicators [16], directional information collected from downlink probing [17], and the covariance matrices of node channels [16; 18; 19], which can be determined over time by recording statistical channel information. Of particular interest to us are spatial clustering methods [20], sometimes also used in combination with the above techniques. Joint spatial division and multiplexing (JSDM) [19; 21] is one approach that has similarities to ours, although it is not aimed at node partitioning for scheduling. In this method, artificial covariance matrices are constructed based on a set of angles of arrival and angular spreads. Nodes are then clustered into sectors based on the similarity of their channels, for example, by computing the chordal distances of the eigenspaces of nodes' channel covariance matrices to those of the constructed ones. One key result, proven in [21], is thatfor a uniformly spaced linear array, JSDM approaches optimality, in terms of maximizing the sum rate, as the number of antennas grows. This is because the node channels, when grouped according to their angles of arrival and angular spreads, form near-orthogonal subspaces. Although the objective of JSDM is different to that of our work, and thus results from JSDM and our method are not comparable, this nonetheless demonstrates the value of node grouping based on directional characteristics, which we also use in our approach. A key difference between the above work and ours is that we do not wish to select a subset of nodes for service to maximize the sum rate, but rather to serve all nodes over time. An optimal partitioning of nodes where only a subset will be served may be quite different to one where all nodes must be served. In our scenario, nodes with a low signal-to-noise ratio (SNR) or that interfere significantly with other nodes cannot be simply dropped to improve overall performance, but must be accommodated in some group. A few existing works on node grouping consider other objectives. The authors in [13] grouped nodes into multicast groups according to their interests, with the objective of maximizing minimum throughput. However, in that study, the full CSI was used, which is not feasible for low-power IoT. The authors in [12] focused on IoT, primarily considering the aspect of serving a large number of nodes, rather than low energy usage, since again the full CSI was used and the objective was the maximal sum rate. One interesting aspect of that work was the observation that node groups may overlap, such that each node can be served by more than one group, helping to ensure full coverage. In our work, we use disjoint node groups, but this could be extended to overlapping groups in the future, for example, for nodes that have a higher traffic demand or poor SINR. The authors in [16] performed node selection as in the other work above; however, this was carried out in combination with fair scheduling, to avoid the starvation of nodes that would otherwise be repeatedly not selected.