裝置對裝置間通訊透過短距離傳輸的優勢，不僅能增加資源使用率，更能減少傳輸時間延遲以及降低能量消耗。然而，我們必須特別注意，引入裝置與裝置間通訊會對傳統蜂巢網路的使用者造成額外干擾。因此，本文中我們研究了在傳統蜂巢網路下裝置與裝置間通訊的基本問題，也就是如何進行連線，不論是透過傳統蜂巢網路通訊，亦或是藉由區域內裝置與裝置間通訊的傳輸方式。透過新型的模式選擇機制，希望能達到最大的平均區域頻譜效率。因此我們使用新型的隨機幾何模型，來分析我們提出的模式選擇機制的效能。透過真實蜂巢網路的特徵，使用者將會連線到最近的基地台，因而形成Voronoi 鑲嵌圖形。我們更進一步得出可靠性與區域頻譜效率間的權衡。透過結果顯示，我們可將其作為對於分析裝置與裝置間模式選擇的一種有力且有效的工具。

Taking the advantages of short transmission distance, Device-to-Device (D2D) communication increases resource utilization as well as reduces transmission delay and power consumption. However, the introduction of D2D communication incurs extra interference to the user equipments (UEs) who make the traditional cellular connection with the base station (BS), which shall be carefully considered. This paper, therefore, investigates the very beginning and fundamental problem in D2D communications underlaying cellular networks, that is, either establishing local D2D communications or make a traditional communication with BS. A novel mode selection mechanism is proposed to control the number of UEs performing D2D communications to achieve maximum average area spectral efficiency (ASE). We apply the recent innovation, stochastic geometry, to analyze the performance of the proposed mode selection mechanism. By including the realistic feature in a cellular network, that is, UEs will associate the closet BS, a Voronoi tessellation is comprised. We further derive a tractable result on the tradeoff between link reliability and ASE. As a result, this work serves as a powerful and efficient tool for analyzing the effects of D2D mode selection.

[1] M. Ni, L. Zheng, F. Tong, J. Pan, and L. Cai, “A geometricalbased throughput bound analysis for D2D communications in cellular networks,” IEEE J. Sel. Areas Commun., vol. 33, no. 1, pp. 100 – 110, Jan. 2015.
[2] X. Lin, J. G. Andrews, A. Ghosh, and R. Ratasuk, “An overview of 3GPP device-to-device proximity services,” IEEE Commun. Mag., vol. 52, no. 4, pp. 40–48, Apr. 2014.
[3] A. Asadi, Q. Wang, and V. Mancuso, “A survey on device-to-device communication in cellular networks,” IEEE Commun. Surveys & Tutorials, vol. 16, no. 4, pp. 1801–1819, Fourth quarter 2014.
[4] L. Wei, R. Q. Hu, Y. Qian, and G. Wu, “Enable device-to-device communications underlaying cellular networks: Challenges and research aspects,” IEEE Commun. Mag., vol. 52, no. 6, pp. 90–96, Jun. 2014.
[5] A. H. Sakr and E. Hossain, “Cognitive and energy harvesting-based D2D communication in cellular networks: Stochastic geometry modeling and analysis,” IEEE Trans. Commun., 2015 accepted.
[6] C. Ma, J. Liu, X. Tian, H. Yu, Y. Cui, and X. Wang, “Interference exploitation in D2D-enabled cellular networks: A secrecy perspective,” IEEE Trans. Commun., vol. 63, no. 1, pp. 229–242, Jan. 2015.
[7] Q. Ye, M. Al-Shalash, C. Caramanis, and J. G. Andrews, “Resource optimization in device-to-device cellular systems using time-frequency hopping,” IEEE Trans. Wireless Commun., vol. 13, no. 10, pp. 5467–5480, Oct. 2014.
[8] B. Kaufman, J. Lilleberg, and B. Aazhang, “Spectrum sharing scheme between cellular users and ad-hoc device-to-device users,” IEEE Trans. Wireless Commun., vol. 12, no. 3, pp. 1038–1049, Mar. 2013.
[9] A. Orsino, L. Militano, G. Araniti, A. Molinaro, and A. Iera, “Efficient data uploading supported by D2D communications in lte-a systems,” in European Wireless, 2015 jan, pp. 81–99.
[10] 3GPP TR 36.843, “Study on LTE device to device proximity services,”
Mar. 2014.
[11] F. Malandrino, C. Casetti, C.-F. Chiasserini, and Z. Limani, “Fast resource scheduling in HetNets with D2D support,” in Proc. IEEE INFOCOM 2014, Apr. 2014, pp. 1536 – 1544.
[12] E. Zihan, K. W. Choi, and D. I. Kim, “Distributed random access scheme for collision avoidance in cellular device-to-device communication,” IEEE Trans. Wireless Commun., vol. 14, no. 7, pp. 3571–3585, Jul. 2015.
[13] Q. Ye, M. Al-Shalash, C. Caramanis, and J. G. Andrews, “A tractable model for optimizing device-to-device communications in downlink cellular networks,” in Proc. IEEE ICC 2014, Jun. 2014, pp. 2039–2044.
[14] X. Lin, J. G. Andrews, and A. Ghosh, “Spectrum sharing for deviceto-device communication in cellular networks,” IEEE Trans. Wireless Commun., vol. 13, no. 12, pp. 6727–6740, Dec. 2014.
[15] S. Andreev, O. Galinina, A. Pyattaev, K. Johnsson, and Y. Koucheryavy, “Analyzing assisted offloading of cellular user sessions onto D2D links in unlicensed bands,” IEEE J. Sel. Areas Commun., vol. 33, no. 1, pp. 67 – 80, Jan. 2015.
[16] 3GPP TR 22.803, v. 12.2.0, “Feasible study for proximity services (ProSe),” Jun. 2013.
[17] H. A. U. Mustafa, M. A. Imran, M. Z. Shakir, A. Imran, and R. Tafazolli, “Separation framework: An enabler for cooperative and D2D communication for future 5G networks,” IEEE Communications Surveys Tutorials, vol. 18, no. 1, pp. 419–445, Firstquarter 2016.
[18] N. Cheng, N. Lu, N. Zhang, T. Yang, X. Shen, and J. W. Mark, “Vehicle-assisted device-to-device data delivery for smart grid,” IEEE Transactions on Vehicular Technology, vol. 65, no. 4, pp. 2325–2340, April 2016.
[19] Y. Zhang, C. Y. Wang, and H. Y. Wei, “Incentive compatible mode selection and spectrum partitioning in overlay D2D-enabled network,” in 2015 IEEE Globecom Workshops (GC Wkshps), Dec 2015, pp. 1–6.
[20] D. D. Penda, L. Fu, and M. Johansson, “Mode selection for energy efficient D2D communications in dynamic TDD systems.” in 2015 IEEE International Conference on Communications (ICC), June 2015, pp. 5404–5409.
[21] Y. Huang, A. A. Nasir, S. Durrani, and X. Zhou, “Mode selection, resource allocation and power control for D2D-enabled two-tier cellular network,” vol. PP, no. 99, pp. 1–1, 2015.
[22] R. Wang, J. Zhang, S. H. Song, and K. B. Letaief, “QoS-aware joint mode selection and channel assignment for D2D communications,” CoRR, vol. abs/1602.08908, 2016. [Online]. Available: http://arxiv.org/abs/1602.08908
[23] M. G. Khoshkholgh, Y. Zhang, K.-C. Chen, K. G. Shin, and S. Gjessing, “Connectivity of cognitive device-to-device communications underlying cellular networks,” IEEE J. Sel. Areas Commun., vol. 33, no. 1, pp. 81–99, Jan. 2015.
[24] X. Xu, Y. Zhang, Z. Sun, Y. Hong, and X. Tao, “Analytical modeling of mode selection for moving D2D-enabled cellular networks,” IEEE Communications Letters, vol. 20, no. 6, pp. 1203–1206, June 2016.
[25] S. W. Jeon, S. N. Hong, M. Ji, and G. Caire, “On the capacity of multihop device-to-device caching networks,” in Information Theory Workshop (ITW), 2015 IEEE, April 2015, pp. 1–5.
[26] Y. Liu, “Optimal mode selection in D2D-enabled multibase station systems,” IEEE Communications Letters, vol. 20, no. 3, pp. 470 – 473, March 2016.
[27] J. Kim, S. Kim, J. Bang, and D. Hong, “Adaptive mode selection in D2D communications considering the bursty traffic model,” IEEE Communications Letters, vol. 20, pp. 712–715, April 2016.
[28] P. Mach, Z. Becvar, and T. Vanek, “In-band device-to-device communication in OFDMA cellular networks: A survey and challenges,” IEEE Commun. Surveys & Tutorials, vol. 17, no. 4, pp. 1885–1922, Fourth quarter 2015.
[29] H. Tang and Z. Ding, “Mixed mode transmission and resource allocation for D2D communication,” IEEE Transactions on Wireless Communications, vol. 15, no. 1, pp. 162–175, Jan 2016.
[30] L. Lei, Y. Kuang, N. Cheng, X. S. Shen, Z. Zhong, and C. Lin, “Delayoptimal dynamic mode selection and resource allocation in device-to-device communications; part I: Optimal policy,” IEEE Transactions on Vehicular Technology, vol. 65, no. 5, pp. 3474–3490, May 2016.
[31] L. Lei, Y. Kuang, N. Cheng, X. Shen, Z. Zhong, and C. Lin, “Delayoptimal dynamic mode selection and resource allocation in device-to-device communications; part II: Practical algorithm,” IEEE Transactions on Vehicular Technology, vol. 65, no. 5, pp. 3491–3505, May 2016.
[32] L. Zhang, M. Xiao, G. Wu, and S. Li, “Efficient scheduling and power allocation for D2D-assisted wireless caching networks,” IEEE Transactions on Communications, vol. 64, no. 6, pp. 2438–2452, June 2016.
[33] H. ElSawy, E. Hossain, and M. S. Alouini, “Analytical modeling of mode selection and power control for underlay D2D communication in cellular networks,” IEEE Transactions on Communications, vol. 62, no. 11, pp. 4147–4161, Nov 2014.
[34] A. H. Sakr and E. Hossain, “Cognitive and energy harvesting-based D2D communication in cellular networks: Stochastic geometry modeling and analysis,” IEEE Transactions on Communications, vol. 63, no. 5, pp. 1867–1880, May 2015.
[35] H. H. Yang, J. Lee, and T. Q. S. Quek, “Heterogeneous cellular network with energy harvesting-based D2D communication,” IEEE Transactions on Wireless Communications, vol. 15, no. 2, pp. 1406–1419, Feb 2016.
[36] L. Wang, H. Tang, H. Wu, and G. L. Stuber, “Resource allocation for D2D communications underlay in Rayleigh fading channels,” IEEE Transactions on Vehicular Technology, vol. PP, no. 99, pp. 1–1, Apr 2016.
[37] M. Afshang, H. S. Dhillon, and P. H. J. Chong, “Coverage and area spectral efficiency of clustered device-to-device networks,” in 2015 IEEE
Global Communications Conference (GLOBECOM), Dec 2015, pp. 1–6.