# Location-Based Relay Selection in Full-Duplex Random Relay Networks
## 1 Introduction  
Relay networks are considered an efficient method for expanding coverage and ensuring reliable communication by utilizing multiple relay nodes for data transmission, thereby achieving spatial diversity [1; 2; 3; 4]. Specifically, relay nodes can provide reliable channel links for users who suffer from severe channel impairment or fading due to unexpected interference or obstacles. In addition, by amplifying or regenerating weak signals, relay nodes enable these signals to reach remote users, which extends network coverage. In particular, relay networks have been widely adopted in interference-limited environments, such as cognitive radio networks [5; 6; 7; 8] and non-orthogonal multiple-access systems [9; 10; 11], to mitigate the effects of interference. Additionally, recent research on 6G systems has explored cooperative techniques to enhance coverage for non-terrestrial networks, including satellite communications [12], unmanned aerial vehicle networks [13; 14; 15], and device-to-device relaying [16]. However, these studies on relay systems focus on half-duplex (HD) mode, where each relay hop uses different temporal and spectral resources due to its simplicity. In other words, half-duplex relay (HDR) systems gain benefits at the expense of inefficient resource utilization. To address the limitations of HDR, full-duplex relay (FDR) has attracted considerable attention across various fields [17; 18]. In FDR, a relay node can transmit and receive signals simultaneously using the same frequency band, ideally doubling the spectral efficiency compared to HDR. One of the main hurdles in implementing FDR is managing strong self-interference (SI), which is induced at a node by its own transmitted signal while it receives another signal simultaneously. With the help of recent advances in self-interference cancellation (SIC), however, it has been demonstrated that SI on the same frequency band can be reduced to the noise level, thereby facilitating full-duplex (FD) transmission at the node [19; 20; 21; 22; 23; 24]. Motivated by the progress of SIC techniques, extensive research on FDR has been conducted [25; 26; 27; 28; 29]. Specifically, the transceiver design for multiple-input multiple-output (MIMO) systems in FDR with amplify-and-forward (AF) relay mode was examined in [25]. In [26], the power control algorithm for FDR under various channel environments was studied. Additionally, a comparison between HDR and FDR was conducted in terms of latency in [27] and energy efficiency in [28]. In [29], a buffer-aware rate allocation and antenna selection algorithm was investigated to enhance the scheduling performance of FDR. However, the aforementioned works only consider channel variation while assuming that the locations and number of relay nodes are fixed. In practical networks, on the other hand, the locations and number of available relay nodes can vary and are difficult to determine accurately due to the mobility of nodes. To capture the random nature of real networks, the performance of relay networks has been analyzed using stochastic geometry, where the relay nodes are randomly distributed within a finite two-dimensional plane [30; 31; 32; 33]. In [30; 31], the outage probabilities of the AF and decode-and-forward (DF) relay transmission protocols were explored when relay nodes were randomly distributed. [PERSON] et al. [32] analyzed the statistical performance of the distances among relay nodes under the generalized Gamma fading model. In addition, relay selection algorithms considering fairness and algorithms for cognitive relay networks were investigated in [33]. However, these studies were conducted under the assumption of HD mode in relay transmission, and no works considered FD mode in randomly distributed relay networks. In full-duplex random relay networks (FDRRNs), SI is a dominant factor influencing performance. Therefore, along with network interference, SI should be addressed in performance analysis and relay selection algorithms.