Joint User and Beam Selection in Millimeter Wave Networks

TL;DR

This work tackles the problem of jointly selecting a user and a beam for each mmWave AP to maximize the weighted sum rate across multiple APs and UEs. It proves NP-completeness of the optimal joint UE-beam selection and introduces two offline, asymptotically optimal benchmarks: a Markov Chain Monte Carlo (MCMC) method and a Local Interaction Game (LIG) approach, each guaranteeing convergence to the global optimum under appropriate parameter limits. To enable fast operation, the paper also proposes two greedy heuristics, NGUB1 and NGUB2, which jointly select UE-beam pairs and demonstrate performance close to the asymptotically optimal schemes while outperforming prior methods in extensive simulations. The results establish a principled benchmark framework for offline-optimal and online-learning-based UE/beam selection in mmWave networks, with practical implications for robust, scalable network design and scheduling under blockage and mobility. Future work includes extending the framework to scenarios where APs can serve multiple UEs concurrently and integrating the benchmarks with online learning algorithms.

Abstract

We study the problem of selecting a user equipment (UE) and a beam for each access point (AP) for concurrent transmissions in a millimeter wave (mmWave) network, such that the sum of weighted rates of UEs is maximized. We prove that this problem is NP-complete. We propose two algorithms -- Markov Chain Monte Carlo (MCMC) based and local interaction game (LIG) based UE and beam selection -- and prove that both of them asymptotically achieve the optimal solution. Also, we propose two fast greedy algorithms -- NGUB1 and NGUB2 -- for UE and beam selection. Through extensive simulations, we show that our proposed greedy algorithms outperform the most relevant algorithms proposed in prior work and perform close to the asymptotically optimal algorithms.

Figures (3)

• Figure 1: This is an illustration of our system model for an example scenario in which there are two APs and five UEs. $\operatorname{UE_{3}}$ and $\operatorname{UE_{5}}$ are concurrent users.
• Figure 2: The plots show a performance comparison in terms of the per-user average throughput metric under different algorithms for different mmWave network scenarios. The common parameters used in Fig. \ref{['Fig: Motivation for new heuristics']} and Fig. \ref{['Fig: vScen']} are operating frequency= 60 GHz and number of schedules per slot (SPS)=1. The other parameters used in Fig. \ref{['Fig: Motivation for new heuristics']} (respectively, Fig. \ref{['Fig: vScen']}) are $N_A$ =4, $N_U$ = 10 (respectively, $N_A$ =9, $N_U$ = 25).
• Figure 3: The plots show a performance comparison in terms of the per-user average throughput metric (respectively, Jain's Fairness Index (JFI)) in Fig. \ref{['Fig: vAPUE']}, Fig. \ref{['Fig: vFE']}, Fig. \ref{['Fig: vSPS']} (respectively, Fig. \ref{['Fig: vJFI']}) under different algorithms for a mmWave network. In Fig. \ref{['Fig: vAPUE']}, Fig. \ref{['Fig: vFE']}, and Fig. \ref{['Fig: vSPS']} UMi scenario is considered. In Fig. \ref{['Fig: vAPUE']}, the parameter used are $(N_A,N_U)=(4,10), (9,25), (16,40)$, operating frequency= 60 GHz, number of SPS=1. In Fig. \ref{['Fig: vFE']}, the parameters used are $N_A=9$, $N_U=25$, operating frequency= 28 GHz, 60 GHz, 73 GHz, number of SPS=1. In Fig. \ref{['Fig: vSPS']}, the parameters used are $N_A=9$, $N_U=25$, operating frequency= 60 GHz, number of SPS=1, 5, 10. In Fig. \ref{['Fig: vJFI']}, the parameters used are $N_A=9$, $N_U=25$, operating frequency= 60 GHz, number of SPS=10.

Theorems & Definitions (19)

• Theorem 1
• Lemma 1
• Lemma 2
• Theorem 2
• Definition 1: Pure Strategy Nash Equilibrium (NE)
• Definition 2: Potential Game
• Theorem 3
• Definition 3: Mutually Independent Set of Players
• Lemma 3
• Theorem 4