# Performance Analysis of D2D Communication with Retransmission Mechanism in Cellular Networks
## 1 Introduction  
With the rapid growth of wireless multimedia traffic, there is an urgent need to develop new techniques that transmit diverse data types to realize information exchange among various types of devices. Device-to-device (D2D) communication permits mobile terminals to communicate directly with each other in a licensed spectrum under the control of evolved Node B (eNB) [1, 2]. In the last few years, D2D communication has been regarded as a key technology in 5G cellular networks, which could provide higher data rates and quality of service (QoS) provisioning [3, 4]. Furthermore, D2D communication has been extensively studied in sensor networks [5, 6], ad-hoc networks [7], and mobile health systems [8]. D2D communication in cellular networks can significantly strengthen the network architecture and the reliability of transmission among devices. However, the advantages of D2D communication are based on several challenges, including device discovery, mode selection, interference management, and so on. In contrast to traditional cellular networks, D2D heterogeneousnetworks have overlay and underlay scenarios. In overlay D2D communications, there is no interference between D2D and cellular users (CUs) because parts of the cellular channel spectrum are dedicated to D2D users. In D2D underlay cellular networks, more complex interferences are introduced by D2D links reusing cellular spectrum resources. Thus, addressing the co-channel interference issue by developing a reasonable interference management scheme is crucial for maintaining the QoS of D2D underlay cellular networks. Stochastic geometry has been proven to be a powerful mathematical tool to model randomly distributed devices and numerically analyze the network performances [9]. It was used to solve various problems for D2D networks in [10; 11; 12; 13]. The common point of these works is that D2D transmitters (DTs) are modeled as a Poisson point process (PPP). However, these works were not concerned with random data generation and the queuing behavior of users. In that way, some substantive performance parameters were ignored, such as the overflow dropping caused by a saturated buffer and delays caused by an empty buffer. Several studies on performance analysis of D2D communications using the queuing model have been reported in the literature [14; 15; 16]. Existing works have also built the spatiotemporal model simultaneously based on the queuing theory and stochastic geometry (e.g., [17; 18; 19]). However, in these works, the transmitter sends packet in order; if the packet is not correctly received due to interference and an intrinsically unreliable channel, it is dropped. The dropping probability would rise significantly in a severe interference scenario. The authors did not consider retransmission schemes to improve the transmission reliability and lower the dropping probability. As we all know, when digital data need to be transmitted from a transmitter to a receiver, some packets may be corrupted or even lost entirely because of the time-varying characteristics of the channel and the indeterminacy of the communication distance. Automatic repeat request (ARQ) is a well-known protocol used to cope with this problem, which has been extensively employed in next-generation wireless packet data networks to provide reliable communication [20]. Stop-and-wait (SW-ARQ) is one of the classic ARQ schemes [21]. In SW-ARQ, the transmitter waits for feedback acknowledgment after it sends a data packet to the corresponding receiver. According to the error detection results, if the packet is received correctly (ACK), the transmitter sends the next packet in the queue. Otherwise, the transmitter receives a negative acknowledgment (NACK), and the same packet is scheduled and retransmitted immediately. This process continues until the packet is positively acknowledged. SW-ARQ is easily implemented and ensures that packets are received in the same order, so no resequencing is needed.