Joint User and Beam Selection in Millimeter Wave Networks

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.

Node Cardinality Estimation in a Heterogeneous Wireless Network Deployed Over a Large Region Using a Mobile Base Station

We consider the problem of estimation of the node cardinality of each node type in a heterogeneous wireless network with $T$ types of nodes deployed over a large region, where $T \ge 2$ is an integer. A mobile base station (MBS), such as that mounted on an unmanned aerial vehicle, is used in such cases since a single static base station is not sufficient to cover such a large region. The MBS moves around in the region and makes multiple stops, and at the last stop, it is able to estimate the node cardinalities for the entire region. In this paper, we propose two schemes, viz., HSRC-M1 and HSRC-M2, to rapidly estimate the number of nodes of each type. Both schemes have two phases, and they are performed at each stop. We prove that the node cardinality estimates computed using our proposed schemes are equal to, and hence as accurate as, the estimates that would have been obtained if a well-known estimation protocol designed for homogeneous networks in prior work were separately executed $T$ times. We compute closed-form expressions for the expected number of slots required by HSRC-M1 to execute and the expected energy consumption of a node under HSRC-M1. We formulate the problem of finding the optimal tour of the MBS around the region, which covers all the nodes and minimizes the travel cost of the MBS, show that it is NP-complete, and provide a greedy algorithm to solve it. Using simulations, we show that the numbers of slots required by the proposed schemes, HSRC-M1 and HSRC-M2, for computing node cardinality estimates are significantly less than the number of slots required for $T$ separate executions of the above estimation protocol for homogeneous networks.