Wireless Communications and Mobile Computing

Volume 2018 (2018), Article ID 8342156, 11 pages

https://doi.org/10.1155/2018/8342156

## A Stochastic Geometry Approach to Full-Duplex MIMO Relay Network

Correspondence should be addressed to Iraj Sadegh Amiri

Received 24 June 2017; Revised 26 August 2017; Accepted 10 September 2017; Published 3 January 2018

Academic Editor: Patrick Seeling

Copyright © 2018 Mhd Nour Hindia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Cellular networks are extensively modeled by placing the base stations on a grid, with relays and destinations being placed deterministically. These networks are idealized for not considering the interferences when evaluating the coverage/outage and capacity. Realistic models that can overcome such limitation are desirable. Specifically, in a cellular downlink environment, the full-duplex (FD) relaying and destination are prone to interferences from unintended sources and relays. However, this paper considered two-hop cellular network in which the mobile nodes aid the sources by relaying the signal to the dead zone. Further, we model the locations of the sources, relays, and destination nodes as a point process on the plane and analyze the performance of two different hops in the downlink. Then, we obtain the success probability and the ergodic capacity of the two-hop MIMO relay scheme, accounting for the interference from all other adjacent cells. We deploy stochastic geometry and point process theory to rigorously analyze the two-hop scheme with/without interference cancellation. These attained expressions are amenable to numerical evaluation and are corroborated by simulation results.

#### 1. Introduction

Currently, the demand for the high capacity and low latency is dramatically increasing, corresponding to advancements in communication devices such as smartphones. It is expected that the wireless traffic volume of these communication devices will have a 1000-fold increase over the next decade which will be driven by the expected billions of connected devices by 2020 to access and share data anywhere and anytime [1]. The bottom line is that the technology has to move to higher frequency bands of millimeter wave to adapt the 5G future mobile communications, where a very large bandwidth in frequency band is available. With rapid increase in the number of connected devices, some challenges appear such as the capacity shortage, cost, and cochannel, and intercell interference especially at high dense network is rapidly increased [2]. Hence, the fifth-generation (5G) wireless systems should be able to support the ultradense networks to adopt the exponential growth in mobile users and high data demand. To satisfy the quality of service (QoS), it is expected that the 5G network deployment will be much denser compared to that of 4G. However, as the network density increases, the interference will degrade the system’s performance especially at cell edges (dead zone). One of these efficient solutions that allow the 5G network to meet its QoS requirements is to use relay to improve the ultradense network performance (capacity enhancement and coverage extension). Cooperative communication is an alternative way to achieve spatial diversity and multiplexing gain through Multiple-Input Multiple-Output (MIMO). MIMO attracted a lot of attention due to its potential for interference mitigation and capacity increase. FD relaying equipped with MIMO is able to perform spatial self-interference suppression [2–5]. The FD relaying looks to be an alternative solution to satisfy the high capacity demands of these wireless systems. The FD communication has attracted considerable attention of many researchers and it is expected to be integrated into the 5G wireless systems. Most used cooperative protocols are the amplify-and-forward (AF) and the decode-and-forward (DF); the DF cooperative protocols can operate in either a half-duplex (HD) or full-duplex (FD) mode. Multiplexing loss occurred when implementing the HD mode in the DF protocol; this is attributed to the fact that, in the first time/frequency slot, the relay has to wait for the source’s message and then forward the message in the next time slot to the destination. However, FD cooperative protocols can overcome the HD spectral loss via simultaneous transmission from source to relay and from relay to destination; this enables frequency reuse, higher throughput, and lower transmission delay [6]. However, there are two main issues hardening the implementation of FD system in cellular network: the self-interference, that is, the relay’s signal leakage from its transmit and receive antennas, and the fact that the simultaneous transmission creates intercell interference [7].

However, cellular networks are usually modeled by placing the sources on a grid (with a regular shape) or arranging them on a line or circle as in the Wyner model with the relay and destination being either deterministically or randomly placed across the network to determine the signal-to-interference-and-noise ratio (SINR). The resulting SINR is complex and depends on multiple random variables. Hence, this fails to account for the randomness in the cellular network distribution [8] and the intercell interference [9]. Such models, however, are highly idealized and not tractable; hence, complex system level simulation is used to evaluate the outage/success probability and ergodic capacity. In order to reduce the dependence on simulations, the closed-form SINR was derived using stochastic geometry [10].

Since characterizing the SINR by the grid model and Wyner model is obviously not practicable, recently stochastic geometry has emerged as a powerful tool to model and quantify the capacity, interference, and success probability in cellular networks that are verified to be approximate to the actual networks [11]. The use of the Poisson point processes (PPP) model simplified the analysis and provided insight into the operation of the network in the form of scaling laws. Base station, relay, and destination parameters (e.g., path-loss exponent and transmit power) become the sign of the node in the PPP. Recently, under homogeneity condition, it was shown that the source positions are agnostic to the radio propagation; this makes the received power at the relay from any population of sources as if it generated from PPP, distributed sources [12, 13]. This justifies the modeling assumption of PPP sources and allows computing some metrics performance such as the success probability and Ergodic capacity [14, 15], while [16] derived an upper bound for the success probability. Obtaining full diversity order using distributed space-time codes is detailed in [17, 18], but a distributed space-time code requires precise signaling and very tight coordination among the relays, which increases the complexity and overhead in the system. This paper is motivated by the benefit of MIMO two-hop system, such as performance benefits and reducing implementation complexity.

Researchers have dealt with the interference in many different ways. For instance, an active method known as analog cancellation, to cancel the interfering signal at the receiving antenna, utilizes additional radio frequency (RF) chains; and there is another active cancellation method known as digital cancellation, where the RSI is removed in the base-band level after the analog-to-digital converter [19]; another simple passive method is known as antenna separation, where the RSI is attenuated due to the path-loss between the transmitting and receiving antennas on the FD node. Further, reducing the FD interference using directional antennas is analyzed in [20]. References [21, 22] quantify the impact of self-interference of a heterogeneous network consisting of FD and HD nodes. They conclude that the capacity can be maximized by operating all nodes in either HD or FD compared to their mixtures, whereas [23] considers a single-cell setting and [22, 24] consider multicell setting. A cellular system comprising an FD source and HD destination has been illustrated in which the throughput gain is analyzed via extensive simulation [25]. In [26], the numbers of base station antennas and users antennas are increasing with a fixed ratio, while the capacity grows by the number of users and SNR. In this paper, however, we use a stochastic geometry tool to characterize the randomly distributed performance of FD MIMO relay nodes and derive bounds for the probability of successful transmission and ergodic capacity with/without interference cancellation. Finally, numerical results corroborate the theoretical findings with baseline scheme.

Next, in Section 2, the network system model is described. The SINR characterization is derived in Section 2.3; the success probability and the ergodic capacity are given in Section 2.4 and Section 2.5, respectively. Section 4 depicts the numerical results, and Section 5 offers the conclusion.

Throughout this paper, boldface lowercase letters (e.g., ) represent vectors, and boldface uppercase letters (e.g., ) represent matrices. is the Frobenius norm. stands for conjugate transpose, and denotes the expectation operator, while denotes the magnitude and the trace of a matrix is denoted by ; is the determinant; is the diagonal matrix with diagonal components ; is the -by- identity matrix; is the -by- zero matrix.

#### 2. System Model

##### 2.1. System Setup

In a downlink relay-assisted cellular network, consider a multiple independent FD dual-hop relaying system. The th source with message equipped with antennas communicates with destinations receiving antennas through relay set , with messages , equipped with and transmitting and receiving antennas, respectively, as in Figure 1. The relay uses DF protocol; hence, decodes the message from and then reencodes the message before sending it to . The relays are equipped with FD capabilities, where the reception and transmission of relay signal happen simultaneously. The main challenge is that relay’s transmitted signal is coupled with its receiver chain, causing relay self-interference (RSI) via channel and source causes interference to other relay known as source-relay interference (SRI) via channel in addition to the interference from the sources to the destinations causing source-destination interference (SDI) via . Space division multiplexing is applied so that the two hops are separated.