# Multicell Interference Management in Device to Device Underlay Cellular Networks
## 1 Introduction  
Device to Device (D2D) communication has emerged as an add-on communication paradigm to the modern 5G wireless cellular networks [1]. In these networks, two types of users exist. The first type of users are the cellular users who communicate conventionally via the intervention of the evolved nodeB (eNB). The second type of users concerns the D2D users who are able to communicate directly with each other [2].  
D2D communications can take place either overlaying or underlaying inband a cellular network or outband [3]. D2D users can act cooperatively, form clusters and facilitate content dissemination [4; 5]. In the overlay case, D2D communications use dedicated resources, while in the underlay case D2D communications share common resources with the residual cellular network. In this paper, we focus on the underlay policy, where the cellular and the D2D users share common radio resources, organized into resource blocks (RBs). RBs are combinations of frequency and time symbols which are allocated to the users of the network [6]. All users of the network belong to a cell, where the central entity, i.e., the eNB, is in charge of the efficient RBs assignment to the users. RBs assignment and power control are key factors for the efficient operation of the network in terms of spectral and power efficiency. Though significant research efforts have been devoted to the RBs and power allocation ina single-cell environment [7; 8; 9; 10; 11; 12], the impact and consideration of multi-cell environment in the case of D2D underlay cellular network has been considerably neglected.  
In this paper, we aim at closing this gap in the literature and study the joint problem of RB and power allocation in a multicell D2D underlay cellular environment. Multiple neighbouring cells exist serving the users of the network. Every cell is assumed to use the same spectrum band with the other cells for reasons of spectrum economy. In every cell, both cellular and D2D users co-exist and share common RBs. D2D users may share RBs with several other D2D users and with at most one cellular user in a given cell. Though a RB can be used by only one cellular user in a cell, yet interference may occur either by the reuse of the same RB by other cellular users in neighbouring cells, or by several other pairs of D2D users reusing the same RB either in the same cell or neighbouring cells.  
In this setting, efficient RBs assignment and power control are of fundamental importance. On one hand RBs reuse promotes spectrum economy, but on the other hand causes signal to interference and noise ratio (SINR) degradation to the co-sharing users. The users of the network establish connections to either the eNB or their D2D receiver and try to obtain a minimum quality of service (QoS) at their receiver. QoS is expressed at the physical layer via the SINR at the receiver of each link. Users may have multiple different requirements with respect to the SINR at their receiver.  
The rest of the paper is structured as follows. Section 1.1 discusses the related work and Section 1.2 summarizes and introduces our contributions. Section 2 presents the system model adopted, while in Section 3 the problem under consideration is formally presented. Subsequently, Sections 4 and 5 present the first and second stage of the proposed approach respectively, where the problems of RB allocation and power control are described and solved. Finally, in Section 6 detailed numerical results are presented demonstrating the operational effectiveness and efficiency of the proposed methodology, while Section 7 concludes the paper.