# A Light Signaling Approach to Node Grouping for Massive MIMO IoT Networks
## 1 Introduction  
It is clear by now that massive multiple-input multiple-output (MIMO) is a key technology for achieving high capacity in broadband wireless networks, and it is currently being deployed to this end in expanding 5G networks. The use of many electronically steerable service antennas at the base station facilitates aggressive spatial multiplexing to tens of user equipment nodes. This enables a substantial increase in the link reliability experienced by a particular node. In situations where the massive MIMO array is required to simultaneously serve a very large number of nodes, there arises the challenge of first grouping and then scheduling these nodes for transmission. This is particularly important for the massive machine-type communication (mMTC) use case, where extremely large numbers of nodes may be present within the same geographical area served by the base station [1].  
In this paper, we propose a node grouping method based on directional properties of the nodes' channels that are stable over long periods and so do not need to be updated at the rate of the coherence time of the channel. This reduces the signaling overhead and makes our method suitable for use as a precursor to node scheduling for energy-constrained Internet of Things (IoT) nodes with infrequent transmissions. We formulate this as an optimization problem using mixed-integer programming. We then develop an efficientapproximation algorithm to solve this problem much faster than is possible using the optimization process. Our results show that both our optimization and approximation provide superior performance in terms of the minimum signal-to-interference-plus-noise ratio (SINR) in comparison to a reference method based on grouping nodes by their instantaneous signal strength, that is, received power, taking into account both small and large-scale fading. The reference method requires full small-scale channel state information (CSI); however, the dominant power consumption of IoT nodes is due to transmission, as shown in [2]. Hence, sending pilot sequences to learn small-scale CSI, prior to data, would consume too much energy. In contrast, less time-varying information could be reused without the need to relearn the channel for each uplink message.  
The contributions of this paper are:  
* A node partitioning method for massive MIMO systems based on simple directional characteristics of the nodes' channels, namely, dominant direction and angular spectrum spread, allowing for stable partitioning over a long time period with minimal signaling by the node devices. The partitioning is complete in the sense that every node belongs to a group, so that all nodes are served.
* A formulation of the node partitioning problem using directional channel characteristics as an optimization problem using mixed integer programming.
* An efficient approximation algorithm to solve the problem that runs in \(O(n\text{log}n)\) time, where \(n\) is the number of nodes.
* A numerical evaluation of the optimization problem and the approximation algorithm using network examples generated with a suitable channel model, showing similar performance for our partitioning method compared to using full channel information.  
The rest of this paper is organized as follows. Section 2 introduces and motivates our node grouping approach. Section 3 then discusses related work on node partitioning and scheduling in massive MIMO systems. Next, Section 4 details our problem setting and defines the node partitioning problem. The partitioning problem is then formulated as a mixed-integer optimization problem in Section 5, and our approximation algorithm to solve this problem more efficiently is given in Section 6. We present our numerical evaluation of the optimization problem and the approximation algorithm in Section 7. Finally, in Section 8, we conclude this paper and discuss future work.