Fractional Frequency Reuse in Ultra Dense Networks

Abstract

Ultra Dense Network (UDN) in which Base Stations (BSs) are deployed at an ultra high density is a promising network model of the future wireless generation. Due to ultra densification, reuse of frequency bands with an ultra high density is compulsory for this network. Conventionally, the research on frequency reuse technique such as Fractional Frequency Reuse (FFR) classifies the active users into only two groups. However, this approach is not suitable for UDNs where the signal experiences a huge amount of power loss over distances. Thus, this paper proposes a generalized model of FFR for UDNs where the active users are classified into more than two groups The paper introduces a simple approach to obtain the coverage probability of a typical user in the case of a general path loss model. In the case of stretched path loss model for UDNs, the closed-form expression of user coverage probability is derived. From the analytical and simulation results, it is stated that the proposed model can improve user performance without increasing BS power consumption. Furthermore, two additional interesting conclusions are found in this paper: (i) the user coverage probability increases to a peak before passing a decline when the density of BSs increases; (ii) an increase in BS transmission power may decrease the user performance.

Introduction

In recent years, the number of networked devices has risen critically. According to Cisco report [1], the number of networked devices in 2023 will reach 29.3 billion which are about 3 times greater than the world population. This will make the mobile data traffic increase by 8 times in the next few years. The explosive growth has encouraged the development of new generations of mobile networks, particularly 5G, to provide the ultra-high data rate, ultra-low latency, ultra-high number of connections as well as ultra-wide coverage area [2], [3]. To meet the requirements of 5G networks, Ultra Dense Networks (UDNs) in which the distance between two adjacent Base Stations (BSs) is around 10 m has been introduced as a promising solution [4], [5], [6]. The millimeter wave (mmWave) is recognized as the ideal operational frequency bands for UDNs.

However, the deployment of BSs with an ultra-high density introduces new challenges. Specifically, the power loss of the transmitted signal should be carefully investigated since the mmWave is extremely sensitive to the transmission environment. Moreover, the interference between cells cannot be ignored when the BSs are very close together. Therefore, a large number of research works have been conducted to investigate UDN performance through path loss modeling and intercell interference coordination technique.

The performance of wireless systems strongly depends on the power loss of the radio signal. To analyze the network performance, the path loss model should be studied first. The multi-slope path loss model in which the signal experiences more than one path loss exponents was widely studied [7], [8], [9], [10]. For each slope, the power loss follows the conventional model which is formulated as $Loss=r^{-\alpha }$, where $r$ and $\alpha$ are the horizontal distance and the path loss exponent, respectively. The authors based on the probability of Line-of-Sight (LoS) and non-Line-of-Sight (nLoS) to compute the power loss over the wireless link. The coverage probability and spectrum efficiency were analyzed. The impacts of the density of BSs and their heights were examined [11], [12], [13]. Other related works modeled the power loss as a exponential function of the distance such as [14], [15]. Recently, the Stretched Path Loss Model (SPLM) was introduced in Ref. [16]. In this model, the power loss over a distance of $r$ is determined as $\alpha r^{\beta }$ in which $\alpha$ and $\beta$ are turnable parameters. This model is considered a simplified model of a multi-slop model with a finite number of slopes. Through experimental measurements, the authors proved that the SPLM is more suitable for UDNs than previous models in the literature. Thus, we utilize this model to analyze the UDNs.

Frequency Reuse is a popular technique in wireless communications that allows two BSs to share their frequency bands. The demand for reuse of frequencies became more necessary in the 4G networks since these systems require much more BSs to cover the service area than its previous generations. Thus, the Frequency Reuse technique has been improved to allow adjacent BSs to transmit on the same frequency bands at the same time. This technique is known as Fractional Frequency Reuse (FFR). FFR was originally used to define reuse of frequency between cells where each BS is allowed to utilize a part of whole frequency bands. For such definition, FFR with reuse factor of $N$ means that every $N$ adjacent BSs employ the same frequency reuse pattern and each BS is allocated $1/N$ of whole frequency bands. It is reminded that the term frequency reuse pattern is used to describe the approach that the sub-bands are used in a group of $N$ adjacent BSs. This term is commonly used in the documents of European Telecommunications Standards Institute (ESTI) such as in Ref. [17]. This original FFR scheme could not optimize radio spectrum efficiency. Thus, new FFR schemes such as Soft FFR, Strict FFR, and distributed FFR [18], [19] have been introduced to allow each BS to utilize whole frequency bands. Due to the new introduction of FFR, the concept of FFR with reuse factor $N$ is explained as following aspects: (i) each BS is allowed to utilize full bandwidth; (ii) every $N$ adjacent BSs use the same frequency reuse pattern. Conventionally, FFR scheme divides the associated users and allocated frequency resources into 2 groups respectively so that each group of users is served by a group of frequency resources. By this way, the Intercell Interference (ICI) can be minimized and the user performance can be improved.

Although FFR has been well-investigated for 4G systems, the deployment of this technique for future cellular network systems is being at the early stage [20], [21], [22], [23], [24], [25]. The authors in [20], [26] discussed the challenges and approaches of FFR utilization in the these systems. The effects of FFR algorithm on network performance were discussed in [23]. In that work, the optimal frequency reuse factor was derived to optimize energy and spectral efficiency. The authors in [25] introduced an approach to achieve load-balancing between macro and small BSs. Although these works derived important concepts about FFR techniques for future mobile systems, the classification of users into groups has not been well-discussed. The authors in [24] discussed the user classification. However, this work only performed simulation with the mmWave at 26-GHz band. Moreover, in all works discussed above, the two-phase operation of FFR algorithm has not been studied. This motivates us to model and examine the performance of FFR algorithm in UDNs.

The performance analysis of FFR for regular cellular networks with low densities of BSs has been conducted in some interesting works. Ref. [27] introduced an analytical approach and important initial results regarding to the effects of FFR on the cellular networks. In our recent work [28], the uplink performance with power control was considered. The closed-form expressions of performance metrics were given by utilizing Gaussian Quadrature. Recently, the author in [29], [30] presented fully closed-form expression. However, these works only studied regular path loss models in which the received power over a distance of $r$ is $P{r}^{-\alpha }$ (P is the transmission power). In the case of UDNs, as discussed in the previous paragraphs, this path loss model is no longer suitable and should be replaced by SPLM. With the deployment of SPLM, the kernel integral of user performance metric expressions became more complicated [16], [31]. Thus, the approaches in [28], [29], [30] are no longer applicable and the closed-form expressions were only found in the form of Polylogarithm function when $2/\beta$ is an integer number. This paper bases on the Taylor expansions to obtain the simple form of the performance metrics before utilizing confluent hypergeometric function and Gauss–Laguerre quadrature to derive their closed-form expressions for all cases of $\beta$. In the case of $2/\beta$, the closed-form expressions become more simple forms which do not rely on confluent hypergeometric function.

Moreover, the works in the literature only discussed FFR with two user groups and two power levels which is equivalent to FFR with the reuse factor of 3. In our recent works [32], a general FFR algorithm with $N$ user groups was introduced for sparse cellular networks with a low density of BSs and the regular path loss model. Conventionally, sparse cellular networks such as 3G, 4G work with a frequency range from 700 MHz - 4 GHz [33] while UDNs are recommended to work with mmWave radio signals whose frequencies are greater than 24 GHz [34]. Thus, the downlink signal and consequently SINR in sparse networks do not experience so fast attenuation as others in UDNs. Thus, an increase in the number of user groups $N$ did not bring any benefit to the user performance as shown in [32]. In contrast, this paper indicates that the user coverage probability in UDNs is significantly improved when the number of user groups increases from 2 to 3 while the total power consumption remains unchanged.

Generally, compared to the aforementioned works in the literature, the contributions of this work are summarized as follows:

• We propose a generalized model of FFR for UDNs in which the users are classified into more than two groups. The analytical results show the proposed model can improve the user performance without increasing BS’s power consumption.

• We introduce an approach to obtain the simple form of user coverage probability expression under a general path loss model. In the case of a regular path loss model, the user coverage probability is derived as a sum of elementary functions as in Corollary 3.3. In the case of SPLM, the closed-form expression is obtained by following confluent hypergeometric functions and Gauss quadratures as in Section 4.

• The analytical results that are verified by Monte Carlo simulation indicate that an increase in the density of BSs $\lambda$ only improves the user coverage probability if $\lambda$ is in a small regime such as $\lambda <60$ ${\text{BS/km}}^2$ and $SNR=20$ dB. In addition, higher transmission powers may result in a decline in the user coverage probability if both $SNR$ and $\lambda$ are in high regimes such as $SNR>10$ dB and $\lambda =180$ ${\text{BS/km}}^2$. Thus, if an increase in the density of BSs is compulsory for UDNs utilizing FFR, then reducing their transmission power is an effective solution.