A stochastic geometrical approach for full-duplex MIMO relaying model of high-density network

Abstract

In a high-density wireless communication network, users suffer from low-performance gains due to multiple path loss and scattering issues. Relay nodes, a significant multi-hop communication approach, provide a decent cost-effective solution, which not only provides better spectral efficiency but also enhances the cell coverage area. In this approach, full-duplex topology is the most efficient way in order to provide maximum throughput at the destination, however, it also leads to undesired relay self-interference. In this paper, we formulated a new Poisson point process approach including a wide variety of interferences by considering a multi-hop high-density cooperative network (source-to-relay and relay-to-destination). Performance evaluation is carried out by using stochastic geometric approach for full-duplex MIMO relaying network to model signal-to-interference-plus-noise ratio (SINR) and success probability followed by average capacity and outage probability of the system. The obtained expressions are amenable and provide better performance as compared to conventional multiple antenna ultra-density network approach.

Introduction

The latest demands on wireless networks applications are forcing researchers to move ahead in the evolution of 3GPP radio access technology. These demands need cost-effective solutions with high system performance and greater spectral efficiency [1]. The key motivation includes more bandwidth and high capacity to provide higher user data rates. It requires greater throughput to run various advance multimedia services, provide reduced network complexity and high quality of service (QoS) by ensuring low latency [2]. In a wireless high-density network, user suffers from high interference by other nearby devices as these devices are sharing the same frequency spectrum to communicate with the base station (BS). Similarly, scattering becomes an issue in a metropolitan area where a number of buildings are high and no line of sight (LOS) link is possible [3], [4]. It will affect more on millimeter wave (mm-wave) frequency spectrum for the 5 G network because scattering mostly occurs when the medium through the wave is traveling contains objects which are much smaller than the wavelength of the electromagnetic wave [5]. Furthermore, in the source (Base station) to destination (User) communication, the desired signal may not be detected because the received signal strength is too weak to detect the actual transmitted signal. However, deploying a base station (BS) within a cell to fulfill the demands is not an efficient approach, due to the interference handling, coordinated scheduling and high-cost issues [6], [7]. One effective solution to solve this problem is to place an infrastructure-based transceiver by creating a multi-hop communication network such as Relay Nodes (RNs), which provides an efficient solution in a very cost-effective manner [8]. It is one of the major innovations of LTE-A, to meet the growing demand for coverage extension and diversity improvement as shown in Fig. 1 [9], [10]. The coverage extension depends on the radial position of RNs in a cell because its location affects the signal to noise ratio (SNR) of the received signal on the evolved-nodeB (eNB) and RN-user equipment (UE) link [11]. On the other hand, diversity improvement can be achieved by deploying multiple RNs, so the received signal coming from both relay and source is maximized, to achieve better modulation and coding (MCS) that gives high user data rates [12], [13].

In the conventional relay communication systems, the relay operates in half-duplex (HD) mode, where the relay utilizes either time-division duplex (TDD) or frequency division duplex (FDD) [14], [15] to transfer information in both directions on the same physical channel but at different timeslots. While, in full-duplex (FD) mode, the BS to UE share a common time-frequency signal-spectrum for transmission and reception simultaneously on the same physical channel [16]. Both modes have different applications [17] like, FD RNs are useful in the urban environment with limited frequency spectrum because it is able to receive and transmit the actual transmitted data with high transparency on the same frequency signal [18]. FD can ideally render up to double spectral efficiency and larger gains when compared to conventional HD operation [19]. It can provide equal requested source–relay and relay–destination data rates to avoid data overflow or congestion at the relay, however, achieved data rates can be unequal due to channel imbalance [16]. Furthermore, FD mode suffers from undesired relay self-interference (RSI), because of the relay's receiver and transmitter are equipped at the same place on a single access point, and using the same frequency band for simultaneous reception and transmission [20], [21], [22]. Sometimes this is descriptively referred as single-frequency “simultaneous transmit and receive” (STAR) [23]. Three different FD communication scenarios can be possible. The first is the multi-hop relay link, where traffic is symmetric but channels are asymmetric, the second is bidirectional communication link, where traffic is typically asymmetric but channels are symmetric, and the third is simultaneous downlink and uplink, where both the traffic and channels are asymmetric [24], [25].

RNs are infrastructure-based transceivers that facilitate multi-hop communication by receiving and forwarding the desired signals at single access point [26], [27]. In general, relaying techniques are usually classified into two different relaying protocols, i.e., decode-and-forward (DF) or amplify-and-forward (AF) [28], [29]. DF protocol first decodes the received message signal, then generates a copy of the same signal to be transmitted, eliminating noise in the process due to decoding, quantization and encoding of the signal [30]. However, DF consumes more time in the process and require complex circuitry which is absent in AF protocol [31]. AF protocol would simply amplify the received signal and transmit it to the destination, but is prone to noise which is also amplified in the process and may lead to undesired signal at the destination [32], [33].

In recent time, the analysis of cellular communication systems has been attractive from the perspective of stochastic geometry, because of the irregular BS location [34]. Poisson Point Process (PPP) is the fundamental of the stochastic geometry modeling tool for communication networks. The main idea of stochastic modeling consists of considering the configuration of the destinations and the transmitters as realizations of stochastic point processes [35]. In many applications, these processes can be taken independent and Poisson. The main advantage of the PPP is its simplicity because the distribution of a Poisson process is completely defined by the intensity measure, representing the mean density of points [36]. On the other hand, some more realistic models are needed, specifically 2-D network of BSs on a square or hexagonal lattice. Signal-to-interference-plus-noise ratio (SINR), user location, relay position and cell corner are some of the few tractable analyses, which can be achieved for a small number of BSs placed in an interference-limited environment. A grid-based model is often referenced to present an ideal scenario where grid size of all the BSs in the network is fixed, BS is always located in the center of the cell with fixed transmit power and therefore, there are no variations in SINR and channel conditions [37]. Though the grid-based model is not practical due to variations in user densities in different cells over a specific region, and therefore ultra-dense network (UDN) model is often used when analyzing the performance of the network. Small cells can be used in UDN to increase the BS to UE throughput as well as save the power consumption of the BS [38]. However, users’ QoS is badly affected due to the random fluctuations in channel conditions, shadowing and fading effects which cause abrupt changes in average user's data rate and SINR values. There are several parameters which can cause variation in cell radius, such as BS height, transmitting antenna power and user's density.

In this paper, we study multi-hop communication networks by using the stochastic geometrical approach for high-density networks. The FD relaying model has been considered and the location of the source, relays and destination nodes are modeled as point processes on the grid. A new proposed PPP approach considering a wide variety of interferences including Inter-Relay Interference (IRI), Source-Relay Interference (SRI), Relay Self Interference (RSI) and Source-Destination Interference (SDI). As per our research, no one has considered all of these interferences in a single model and this is the first time that all the mentioned interferences are incorporated in a single model base on PPP. Here, we proposed a new PPP approach which includes: i) analyzing the received SINR by including all the interference faced by the relay node and the destination separately, ii) success probability which defines the minimum SINR threshold required to detect the transmit messages successfully, iii) Outage probability that explained the probability of received signal that falls below a given threshold level and the average capacity, which states the maximum number of users whose probability of success is higher than the set threshold. The remainder of this paper is organized as follows. In Section 1, we first discuss the related work present in the literature. Section 2 evaluates the signal-to-interference-plus-noise ratio calculations for the Source-to-Relay (SR) and Relay-to-Destination (RD) links separately. Furthermore, Section 3 estimates the success probability of the received signal at both the relay and the destination. Section 4 investigates the outage probability along with the average capacity of the overall network. After this, all numerical results and discussion describe in Section 5. Finally, the conclusions are drawn in Section 6.