Received: 27 December 2018 Revised: 3 May 2019 Accepted: 12 June 2019 DOI: 10.1002/ett.3687 SPECIAL ISSUE ARTICLE Supervised learning and graph signal processing strategies for beam tracking in highly directional mobile communications Yosbel R. Ortega 1 Igor M. Guerreiro 1 Dennis Hui 2 Charles C. Cavalcante 1 F. Rodrigo P. Cavalcanti 1 1 Wireless Telecommunications Research Group, Federal University of Ceará, Fortaleza, Brazil 2 Ericsson AB, Stockholm, Sweden Correspondence Yosbel R. Ortega, Wireless Telecommunications Research Group, Federal University of Ceará, Fortaleza-CE 60455-760, Brazil. Email: yosbel@gtel.ufc.br Funding information Ericsson Research, Grant/Award Number: UFC.46; CNPq, Grant/Award Number: 408609/2016-8, 309472/2017-2 and 151004/2017-0; CAPES, Grant/Award Number: 001 Abstract The use of efficient beam tracking mechanisms becomes necessary in highly directional communication of the fifth-generation systems. In this context, this paper analyzes the tracking problem and proposes a framework that exploits the samples in the user equipment (UE) dataset (historical UE dataset) to efficiently estimate and predict the channel state at the base station. The framework is com- posed of two steps. First, a supervised learning algorithm, namely, K-nearest neighbors (K-NN), is evaluated as a mean of (i) finding the most similar histori- cal samples to some beam measurements reported by the UE and (ii) predicting the corresponding channel state. As a second step, a sampling and reconstruc- tion strategy based on graph signal processing (GSP) called K-nearest neighbors with reconstruction (K-NN-R) is introduced in order to reduce the beam search space during the beam measurement stage, which allows a more efficient usage of the feedback channel. Simulation results illustrate the performance of the proposal in terms of normalized mean square error in comparison with three traditional/baseline prediction techniques. The K-NN technique provides a bet- ter performance than the baseline approaches for any length of the observed temporal window and with full beam sweep. Meanwhile, the K-NN-R frame- work outperforms the baseline approaches with only half of the beam pairs and throughout a significantly low length of observed temporal window. 1 INTRODUCTION Capacity demand in mobile communications has been continuously increasing and this trend is expected to continue. To improve system capacity, the use of millimeter wave (mm-Wave) bands are envisioned as a feasible solution in fifth-generation (5G) systems, incorporating mm-Wave small cells into current fourth-generation systems. Millimeter waves make possible the usage of a large number of antenna elements, which allows highly directional communications through the use of beams with very narrow beamwidth (called pencil beams). Pencil beams offer high array gain, provid- ing mm-Wave small cell base station (BS) with the capability of achieving the desired link budget targets and enabling energy-efficient communication. However, the use of mm-Wave frequencies also brings new challenges caused by severe path loss due to the communication channel, blockage, and other environmental obstructions. Link establishment and maintenance between a BS and a user equipment (UE) in highly directional communications are often rather difficult processes. Especially, in scenarios with mobility, any environmental change such as device rotation, link blockage, or a Trans Emerging Tel Tech. 2019;e3687. wileyonlinelibrary.com/journal/ett © 2019 John Wiley & Sons, Ltd. 1 of 24 https://doi.org/10.1002/ett.3687