# Joint Uplink and Downlink Resource Allocation for D2D Communications System
## 1 Introduction  
With the rapid popularity of intelligent devices, the cellular systems are suffering an unprecedented pressure imposed by the explosive growth of data traffic and a massive increase of interconnected devices [1; 2; 3]. In order to alleviate this pressure, device-to-device (D2D) communication is introduced to improve the spectrum utilization of cellular networks [4]. D2D communication is defined as direct communication between two mobile users without traversing the base station [5; 6], which can potentially increase the cellular capacity, improve the user throughput, and extend the battery lifetime of users [7]. In addition, the access to the spectrum in D2D communication can be done in two ways: Overlay spectrum sharing or underlay spectrum sharing [8; 9]. In the overlay case, D2D transmitters can only access the channels which are not used by nearby cellular users. This method cannot improve spectrum utilization since the D2D pairs use separate resource with the cellular users (CUs). On the other hand, D2D transmitters in underlay case can continuously transmit on all channels subject to tolerable interference to the cellular users. This approach has the advantages of not affecting the spectrum of the cellular communication but also achieving the reuse gain in D2D communication [10]. Therefore, we focus on the underlay spectrum sharing where the D2D pairs reuse the spectrum of the CUs in this paper. In D2D underlay cellular network, D2D transmitter sends the signal to the D2D receiver by using the same spectrum resource with the cellular links, which can improve the system capacityand spectrum utilization [11]. However, when the spectrum resource is allocated unreasonably, co-channel interference between the cellular users (CUs) and D2D pairs will degrade the system performance. In order to solve this key issue, some resource allocation schemes have been proposed in D2D communications, which are mainly divided into two major categories. One is the uplink resource allocation for D2D communications [12; 13; 14; 15; 16; 17; 18; 19; 20]. Specifically, in order to achieve the maximum total data transmission rate, different types of methods are proposed, such as range division [12], mode selection [13; 14; 15], and power control [14; 15]. In reference [16], the authors focus on power control and channel assignment for interference coordination between D2D pair and CU in uplink phase. In reference [17], a dynamic resource allocation scheme for D2D communications in the cellular network is applied to maximize the number of D2D communications pairs and avoid the strong interference of D2D communications with the cellular communication. A game-theoretic scheme [18] is presented to solve the resource allocation problem of multi-cell D2D communications. An optimization problem is formulated to maximize the effectiveness of the D2D user devices, and a novel algorithm [19] is presented based on the many-to-one matching game with companion effects. In reference [20], the maximization method of the weighted system data rate is developed, which can guarantee the minimum individual CU's data rate and proportional fairness among D2D. The other category is the downlink resource allocation for D2D communications [21; 22; 23; 24; 25; 26; 27; 28]. A distributed resource allocation scheme has been proposed in reference [21] to maximize the number of underlay D2D users. Joint resource allocation and power control are investigated in reference [22] for downlink systems, where multiple D2D pairs are allowed to use the same resource blocks. In references [23; 24; 25; 26], downlink resource allocation schemes maximize the sum data rate via different optimization methods. The original non-convex problem is transformed to a convex problem by the semi-definite relaxation technique and a reformulation of the objective function with first-order approximation in each algorithm iteration [23]. In reference [24], resource allocation problem is modeled as a Stackelberg game with pricing.