On the outage analysis of a D2D network with uniform node distribution in a circular region

Abstract

This paper studies the coverage probability of a device-to-device (D2D) link between a pair of nodes uniformly distributed in a circular region of arbitrary radius, thereby modeling the D2D network operation for a public safety scenario. The expression for the cumulative distribution function (CDF) of the signal-to-interference ratio (SIR) at the destination is derived, where the transmissions are affected by multipath fading, path loss and interference. The analysis involves finding the ratio distribution of two random variables, representing the desired signal and the intra-region interference, respectively. The expression for CDF helps in ascertaining the outage probability at the destination. Hence, given a desired outage probability, a limit on the number of simultaneously active D2D links in a circular region can be determined, thereby allowing interference avoidance. Numerical simulations are conducted to validate the theoretical model. The Kolmogorov–Smirnov (K–S) test is applied to further characterize the matching between simulation and analytical model. Moreover, the results also help in identifying the minimum transmit power that ensures the desired quality-of-service (QoS), providing efficient transmission in energy constrained environments.

Introduction

Fourth generation (4G) communication technology was introduced to accommodate the rising demands of mobile user equipments (UE)s in terms of data rates and network reliability. However, a sharp rise in the number of mobile users has resulted in recent years and is expected to grow exponentially in the years to come, which prompted the need for a futuristic standard which could support a rather complex infrastructure of communication. Moreover, there is a consensus in the research community that in order to realize the concept of future smart cities, new communication technologies are required which provide a resource efficient and reliable connectivity [1]. The concept of 5G technology was introduced as a futuristic solution for applications involving peer-to-peer (P2P) high data rate links. The proposed technologies, which would undergo standardization under the aegis of 5G network development, include heterogeneous networks (HetNets), Machine-to-Machine (M2M) communications, D2D networks and internet of things (IoT) among others.

In D2D communication, the users are able to establish direct links for communication instead of routing transmissions through a base station (BS) [2], allowing energy and resource efficiency due to cellular offloading. D2D networks could be specifically helpful in establishing networks for disaster recovery and public safety networks, utilizing minimum energy and providing reliable connectivity [3]. Several network topologies have been identified in literature for establishing D2D networks, depending upon the role of BS in the transmissions. In the In-coverage D2D networks, the BS is responsible for network setup and other signaling activities. On the other hand, in Out-of-coverage D2D networks, the D2D users form a cluster and sustain transmissions by forming a cooperative network [4]. Cluster-based D2D networks have gained significant importance as 3rd Generation Partnership Project (3GPP) has envisioned cluster-based D2D networks for public safety [5]. It is envisioned that the communication systems that are developed for future smart cities would be resource efficient, providing a green solution for resource constrained environments. The network based on hand-held devices are energy constrained, highlighting the need for energy efficient communication protocols [6]. Public safety is one of the key aspects that is being researched with regards to smart cities [7]. In situations such as a disaster, the initial few hours are very critical for planning a rescue and rehabilitation operation. Due to the destruction of traditional communication infrastructure, the devices need an alternative mechanism to establish communication. The main objective of public safety networks is to transmit initial information such as an SOS message, which helps the government agencies in planning a timely response. The presence of several devices in a close proximity in a smart city makes D2D networks a favorable solution for providing connectivity in case of any unforeseen events such as disasters or security threats.

Out-of-coverage D2D cluster networks could aid the users affected by a safety threat to establish cooperative communication and ensure transmission of information to the government agencies. In this mode, multiple D2D pairs lie in a circular region (CR), and the entire cell is covered using many such regions, as shown in Fig. 1. Each CR may contain a cluster-head that controls various signaling activities [8]. Cluster-based D2D networks allow devices in proximity to enjoy services such as content sharing and social networking [9]. It is important to characterize the impact of interference in D2D public safety networks, as high levels of interference could compromise the end-to-end transmission success [10]. Moreover, the real-time information generated in such scenarios is of sensitive nature, signifying the need for employing an interference avoidance mechanism. The analysis of cluster-based D2D networks strictly depends on the node distribution within an area [11]. Some prior works in literature propose spatial models with fixed distance between D2D pairs [12], however, a more practical approach lies in removing the restriction of fixed D2D distance and assuming a random uniform distribution of nodes [13]. In [14], the authors model the coverage probability and area spectral efficiency (ASE) of a clustered D2D network with random node distribution. The analytical expression of SIR observed between a transmitter–receiver pair in a cluster is derived. The analysis conducted in this work is aimed at identifying the number of simultaneously active D2D transmitters that can ensure content delivery without causing significant interference at the receivers.

In this work, we assume a uniform distribution of nodes in a CR and investigate the coverage probability of a typical D2D pair. It is also assumed that the multiple D2D pairs use the same time-frequency resource block for transmissions, leading to intra-region interference at the destination. Specifically, we derive the expression for the CDF of SIR at the destination node, given that the transmitter and the receiver are uniformly placed in a CR and the transmissions are affected by multipath fading, path loss and intra-region interference. The analysis is divided into three steps. We first derive the expression of the CDF of the received power at the destination node, representing the desired signal. The problem of finding the CDF in this case boils down to finding the distribution of the ratio of two random variables (RVs), i.e., an exponential RV representing the channel fading, and a power function of the Euclidean distance between the D2D pair. Second, this ratio distribution is used to determine the statistics of intra-region interference. Finally, the first two steps of the analysis are used to obtain a closed-form expression of the outage probability at the destination.

The distribution of the ratio of different RVs has been widely studied in the literature, e.g., in econometrics [15], statistics [16] and communications theory. In [17], an ad-hoc single-input-single-output (SISO) network is considered, presenting an analytical model for determining the received power at the destination by finding the ratio of exponential random variable and generalized gamma random variable. Similarly, [18] models a multi-hop network by providing a statistical analysis of the ratio of random variables. The results help in characterizing the impact of co-channel interference and signal fading, which helps in readjusting the network parameters to maintain the desired quality-of-service (QoS). References [19], [20] model the outage probability of maximum ratio combining (MRC) receiver for multi-hop network environment. Analytical expressions for CDF of sum of ratio of $\alpha -\mu$ RVs are derived that help in obtaining the outage probability of the wireless multi-hop network. In [21], authors derive the ratio of the product of two $k-\mu$ random variables and Nakagami-m random variable for a relay based wireless communication system. However, to the best of our knowledge, the ratio of the specific RVs considered in this paper has not been investigated in the literature before.

The rest of the paper is organized as follows. In Section 2, we discuss our system model. Section 3 presents the mathematical modeling, i.e., the derivation of the distribution of $SIR$ at the destination node, which involves finding the ratio distribution of random variables. In Section 4, we validate our analytical model and provide results with regards to network performance. The paper is concluded in Section 5, along with providing some future directions.