1148 IEEE COMMUNICATIONS LETTERS, VOL. 17, NO. 6, JUNE 2013 Resource Sharing of Underlaying Device-to-Device and Uplink Cellular Communications Jiaheng Wang, Daohua Zhu, Chunming Zhao, James C. F. Li, and Ming Lei Abstract—The benefit of device-to-device (D2D) communica- tion hinges on intelligent resource sharing between cellular and D2D users. This letter aims to optimize resource sharing for D2D communication to better utilize uplink resources in a multi- user cellular system with guaranteed quality of normal cellular communications. Despite the nonconvex difficulty, we provide an analytical characterization of the globally optimal resource shar- ing strategy, and furthermore propose two suboptimal strategies with less complexity. The superiority of the proposed resource sharing strategies is demonstrated through numerical examples. Index Terms—Cellular system, device-to-device (D2D), non- convexity, uplink resource sharing. I. I NTRODUCTION D EVICE-TO-DEVICE (D2D) communication has been regarded as an effective technique to provide better wireless services in local areas. By allowing two physically close users to communicate directly, instead of being relayed by a base station (BS), D2D communication may achieve higher data rates, lower power consumption, and more efficient resource (e.g., spectrum) utilization [1]. Such a concept has recently been incorporated into existing and future cellular systems as an important supplement for local wireless services [2]. D2D communication as an underlay of cellular systems may share resources with cellular users in an either orthogonal or nonorthogonal manner [1]. In the orthogonal case, dedicated resources are allocated to D2D users, which, though easy to implement, cannot exploit the full potential of D2D communi- cation to improve spectral efficiency. Therefore, nonorthogonal resource sharing has also received much attention [1]–[7]. In the nonorthogonal case, intra-cell interference is in general not negligible, which, therefore, calls for appropriate resource sharing designs with effective interference management. Conceptually, D2D communication can exploit either up- link or downlink resources of a cellular system. In practice, however, uplink resources are more likely to be shared than downlink resources as a result of asymmetric uplink and down- link service loads. Additionally, D2D communication using uplink resources only causes interference at base stations, which generally have stronger processing abilities than user equipments. Therefore, uplink resource sharing has been a subject of a number of D2D system designs [1]–[6]. Optimizing resource sharing of D2D communication under- laying cellular systems is an intensively scrutinized subject. Manuscript received January 30, 2013. The associate editor coordinating the review of this letter and approving it for publication was I. Guvenc. J. Wang, D. Zhu, and C. Zhao are with the National Mobile Communi- cations Research Laboratory, Southeast University, Nanjing, China (e-mail: {jhwang, zhudaohua, cmzhao}@seu.edu.cn). J. Li and M. Lei are with the NEC Laboratory, Beijing, China (e-mail: {li_chaofeng, lei_ming}@nec.cn). Digital Object Identifier 10.1109/LCOMM.2013.042313.130239 Cellular user 1 Cellular user 2 Cellular user N c N h D2D Rx D2D Tx BS 2 c h d i g 1 c h c i g 2 d h 1 d h d N h Fig. 1. One D2D link as an uderlay shares uplink resources of multiple cellular users. In particular, [4] studied resource block allocation among cellular and D2D users in a single-cell system, while a power minimization problem for D2D communication underlying a multiple-cell system was considered in [5]. To suppress the interference between D2D and cellular users, multi-antenna techniques were also introduced into underlying D2D commu- nication [6], [7]. However, due to lack of convexity, only [3] provided optimal resource sharing between one cellular user and one D2D link, whereas globally optimal sharing strategies are generally unknown in other cases. In this letter, we consider D2D communication as an underlay sharing uplink resources of a multi-user cellular system. Our goal is to design proper nonorthogonal resource sharing strategies, applicable to common cellular systems, such that the D2D link can maximally utilize all possible cellular resources and meanwhile the quality of normal cellular communications is guaranteed. In contrast to most existing works (e.g., [1], [2], [4]–[6]) based on heuristic or suboptimal methods, we characterize the globally optimal resource sharing strategy by a closed-form solution with some insights. Further- more, we also propose two suboptimal resource sharing strate- gies with less complexity and signaling overheads. Finally, the effect of the proposed D2D resource sharing strategies is verified by proper numerical examples. II. PROBLEM STATEMENT We consider underlying D2D communication sharing uplink resources in a cellular system that consists of one BS and N orthogonal users as shown in Fig. 1, where each cellular user occupies a frequency band indexed by i =1,...,N (it could also be a TDMA or synchronous CDMA mode). Without loss of generality, we assume that the D2D link may reuse all cellular users’ frequency bands for direct transmission. Denote the channel from the cellular user i to the BS by h c i , and the channel from the cellular user i to the D2D receiver by h d i . Denote the channel from the D2D transmitter to its receiver on frequency band i by g d i , and the channel from the 1089-7798/13$31.00 c  2013 IEEE