Throughput reliability analysis of cloud-radio access networks Fatemeh Ghods *, Abraham Fapojuwo and Fadhel Ghannouchi

Transcription

1 WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 26; 6: Published online 9 September 26 in Wiley Online Library (wileyonlinelibrary.com) RESEARCH ARTICLE Throughput reliability analysis of cloud-radio access networks Fatemeh Ghods *, Abraham Fapojuwo and Fadhel Ghannouchi Department of Electrical and Computer Engineering, University of Calgary, Calgary, Canada ABSTRACT This paper develops a stochastic geometry-based analytical approach for calculating the throughput reliability of a cloudradio access network (C-RAN) comprising randomly distributed remote radio heads (RRHs) and randomly located users. A tunable distance-based RRH transmit power control mechanism along with cooperative joint transmissions by the RRHs is employed to achieve power savings and high throughput reliability. The analytical result for the throughput reliability serves as input to analysis of per user achievable average rate and C-RAN network-level performance metrics of spectral efficiency and energy efficiency. The analytical results are validated by Monte Carlo simulation results with good agreement, thus confirming the accuracy of the developed analytical approach. The key finding from the analysis is that by carefully tuning the RRH transmit power and cooperation parameter (cluster radius), it is possible to realize a threefold improvement in the energy efficiency along with 8% enhancement in the spectral efficiency of C-RANs. Copyright 26 John Wiley & Sons, Ltd. KEYWORDS energy efficiency; C-RAN; spectral efficiency; throughput; performance analysis *Correspondence Fatemeh Ghods, Department of Electrical and Computer Engineering, University of Calgary, Calgary, Canada. fghods@ucalgary.ca. INTRODUCTION Telecommunication industry is preparing to address the projected -fold increase in data traffic over the coming years attributed to the increasing popularity of smart phones and tablets[]. On one hand, the increase in the rate of data traffic has consistently outpaced the rate of increase in new spectrum acquisition; hence, there is a considerable amount of interest to significantly boost the spectral efficiency (SE) performance. On the other hand, recent statistics indicate that the demand for information and communications technology contributes up to 2% of the global energy consumption and 2% in CO 2 emissions [2], hence the need for energy-efficient communication in telecommunication networks. The cloud-radio access network (C-RAN) architecture is considered as a network innovation on the road to fifth generation (5G) wireless networks. It provides capacity enhancement in order to meet the dramatic increase in data traffic demands [3,4]. In the C-RAN, the baseband units (BBUs) act as virtual base stations (BSs) and are responsible for centralized baseband processing and resource allocation, while the remote radio heads (RRHs) are the distributed antennas that transform the baseband signal to radio frequency signal for onward transmission to the users. The BBUs and RRHs are interconnected by high speed optical fiber links in the fronthaul that can support low latency and high bandwidth communications, both of which are critical for the network capacity enhancement [5]. The C-RAN architecture, as an emerging technology, has a high potential to reduce the energy consumption and to increase the network capacity by means of centralized processing and distributed antenna units [6]. As indicated in [7] and [8], centralized processing makes more sense in data-centric infrastructure, and therefore, C-RAN benefits from simple communication infrastructure, increasing the feasibility of having a cheaper deployment. It has been reported in [4] that the C-RAN architecture can provide up to 7% savings in the operational expenditure merely because of moving the cooling operation from the individual BSs to the centralized processing units. Moreover, in comparison with the traditional long-term evolution network, C-RAN saves % to 5% of capital expenditure [9]. Collectively, the increase in data traffic requirement along with the growth in global power consumption underscores the need to achieve high energy efficiency (EE) in cellular networks in addition to the SE. To this end, 2824 Copyright 26 John Wiley & Sons, Ltd.

2 F. Ghods, A. O. Fapojuwo and F. Ghannouchi Throughput reliability analysis of cloud-radio access networks the use of cooperative joint transmissions by the RRHs along with the downlink power control technique in the C- RAN architecture is expected to address the SE and EE crunch problem. As such, not only energy is utilized more efficiently because of power control but also spectrum is used more efficiently as evidenced by the improvement in achievable data rate and mitigation of interference. Intrinsically, like any other techniques that bring forth advantages and benefits, cooperative joint processing and power control come with a cost/overhead along with the complexity of transmitting control and bearer traffic information by the RRHs to the centralized baseband processing units. Currently, C-RAN is a work-in-progress as a network architecture that requires more in-depth investigations in order to fully understand its capabilities and limitations. While a majority of recent works are on the performance of heterogeneous and homogeneous cellular networks, only a limited number of studies have been concerned with C-RANs. Furthermore, the existing C-RAN studies lean towards enhancing the performance by using optimization techniques, such as finding optimal RRH placement, fronthaul capacity, and BBU processing of resources to ensure energy efficiency [5,]. These prior works lack clear insights into the impact of multiple C-RAN operating conditions/parameters on SE and EE performance, as most of the investigations are typically carried out for a specific C-RAN operating condition/parameter. This paper tackles the problem of assuring user s quality of service (QoS) in C-RANs, considering the C-RAN operating conditions of RRH cooperation and RRH power control. The QoS metric is the per user achievable throughput (i.e., achievable data rate), and the probability that the achievable throughput exceeds a specified throughput threshold, referred to as throughput reliability in this paper, is derived. Knowledge of the throughput reliability enables the calculation of the per user achievable average rate that, in turn, is used for computing the EE and SE. The paper adopts a stochastic geometry-based approach that incorporates interference mitigation via cooperative joint processing and power control to enhance the SE and EE performance in C-RAN. Under the settings considered, cooperation and power control enable the RRHs to be opportunistically operated in accordance with the interference and load conditions such that both the SE and EE are maintained at a high level at all times. Specifically, the contributions of this paper are twofold: (i) Analytical derivation of throughput complementary cumulative distribution function, referred to henceforth as throughput reliability, in C-RAN under RRH cooperation along with power controlled transmissions. (ii) Derivation of analytical results for SE and EE, also with RRH cooperation and power control. The novelty of our approach is the consideration of both the RRH cooperation and power control in C-RAN performance analysis, using tools from stochastic geometry. To the authors best knowledge, this is the first work in the literature that combines both RRH cooperation and power control in the context of C-RAN and analyzes the C-RAN performance using the stochastic geometry framework. The rest of this paper is organized as follows. Section 2 summarizes the previous related works, which are compared and contrasted with the proposed work. Section 3 describes the C-RAN model assumed in the paper, covering the different aspects of C-RAN design and operation. This is followed by C-RAN throughput reliability analysis in Section 4 that serves as input to EE and SE analysis presented in Section 5. In Section 6, numerical and simulation results are presented and discussed. Finally, Section 7 concludes the paper and points out some areas for future work. 2. RELATED WORK The concept of cooperative transmission has been used in traditional cellular networks by the previous researchers to enhance the outage probability performance. Using the stochastic geometry framework, reference [] analyzed the outage probability of a cellular network where a group of BSs inside a cluster area cooperatively transmits to a user equipment located near the cluster edge or cluster center. To alleviate strong interference at the user equipments near the cluster edge, the frequency subchannels assigned to the cluster edge BSs are different than those assigned to the cluster-interior BSs. In addition, reference [] uses the channel inversion power control policy at each BS. The work by Tanbourgi et al. [2] also adopted the stochastic geometry tool to characterize the signal-to-interference-plus noise ratio (SINR) distribution at a typical user in a traditional cellular network with noncoherent joint transmissions by cooperating BSs, considering cooperating mechanisms of user-centric clustering and channel-dependent cooperation activation. The key insights from [2] are that BS cooperation improves the SINR gain, which is better at large path loss exponent, and the SINR outage probability decreases exponentially with increasing BS density. The cooperative transmission concept is implicit in C-RANs, and its impact has been studied in the literature. Ha et al. [5] developed optimal and low-complexity algorithms that minimize the total transmission power of cooperative RRHs in a C-RAN under the constraints of processing power at the BBUs, fronthaul capacity, and required QoS of users. Two related problems were solved iteratively: fronthaul constrained power minimization problem and power and fronthaul capacity trade-off problem, with the goal of determining the RRHs that can cooperatively and efficiently transmit to the users with the requested service. Previous studies have also been conducted on the power control and EE of C-RANs. The authors in [] analyzed the EE expressed in Joules per bit, of C-RAN under specified QoS constraints, accounting for the circuitry energy consumption. In addition, [] determined the optimal size (radius) of the cooperating region at which the Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd. 2825

3 Throughput reliability analysis of cloud-radio access networks F. Ghods, A. O. Fapojuwo and F. Ghannouchi energy consumed per bit is minimized. Liu and Lau [3] tackled the problem of optimal joint power and antenna selection to achieve energy-efficient large distributed multiple input, multiple output (MIMO) C-RANs. It is shown that the capacity of a very large distributed MIMO C-RAN scales according to the order of a factor equal to the product of the number of users, path loss exponent, and logarithm of the number of antennas [3]. The transmit power in the uplink and downlink must be controlled to avoid significant interference, maximize system capacity and EE. Currently, there are very few power control algorithms to adapt to the centralized management structure of the C-RANs [4]. The authors in [4] proposed a power allocation algorithm for uplink transmissions in C-RANs, where the proposed algorithm is applied to solving a capacity optimization problem. Liu el al. [5] proposed algorithms for the joint wireless power control and fronthaul rate allocation in the uplink that maximize the throughput in orthogonal frequency division multiple access (OFDMA)-based C-RAN. The proposed joint optimization algorithms exhibit significant performance gain relative to individually optimizing wireless power control or fronthaul rate allocation. Compared with the aforementioned works, this paper exhibits similarities. The paper is similar to [5,,2] in terms of RRH (or multicell) cooperation and studies the power control and EE of C-RANs as in [4,5] and [,3], respectively. In terms of the analysis tool, this paper adopts the stochastic geometry framework for C-RAN performance analysis, the same tool as used in [,2] for the SE performance analysis of traditional cellular networks with multicell cooperation. This paper distinguishes from the previous works in four respects. First, the paper combines RRH cooperation with a power control policy to analyze the throughput reliability, energy efficiency, and spectral efficiency of C-RANs. While [3 5] also involve cooperation and power control, their analysis focus is on the system-level performance metrics of SE and sum-rate [5], sum-rate [3], and system capacity [4], whereas this paper addresses in a holistic manner both the user-level and network-level performance metrics of throughput reliability, and EE and SE, respectively. Second, unlike [4] and [5] that focused on the uplink transmissions, the current paper studies the downlink transmissions with a goal to reduce the RRH transmission power, thus increase network EE and simultaneously enhance the user data rate; this somewhat conflicting objective is achieved through joint RRH cooperation and power control. Third, this paper adopts a predefined distance-based power control policy and studies its impact on C-RAN performance. The works [3 5] determine the transmission power as a solution to the formulated resource allocation problem, without explicit specification of a power control policy as performed in this paper. Finally, in order to manage the analysis complexity arising because of the combined RRH cooperation and power control, this paper studies the single input, single output C-RAN to determine the throughput reliability, EE and SE, different from [3] that studied the maximum average weighted sum-rate of a MIMO C-RAN. 3. C-RAN MODEL As the C-RAN operating conditions of RRH cooperation and RRH transmit power control are of interest in this paper, the C-RAN model developed in this section is on the radio access segment of C-RAN. Transmissions in the downlink (i.e., from RRHs to users) are studied where each RRH is equipped with one antenna and each user equipment also has a single antenna (i.e., single input, single output downlink transmission model is studied). The radio access segment is governed by the assumptions listed in the following subsections. 3.. Network model The locations of the RRHs are distributed over the C-RAN service area as a Poisson point process (PPP) denoted by with intensity. The PPP is assumed for analytic tractability, consistent with previous works, for example, [6 8]. The C-RAN service area is assumed to be partitioned into cluster areas, where a cluster contains the set of cooperating RRHs. The cluster area is assumed to be circular in shape, for analytic simplicity, with a radius of R c.torepresent the worst case analysis, all RRHs are assumed to be active with at least one user to serve in their respective coverage areas that, for analytic tractability, is also assumed to be circular in shape with radius R cell. The locations of users are assumed to be distributed over the C-RAN service area as a PPP with intensity u, which implies that the users are uniformly distributed across the cluster area as well as the RRH coverage area (PPP becomes uniform when the area is bounded [9]). Without loss of generality, the desired user is located at the origin of a cluster area Channel model The channel is modeled by a distance-dependent path loss and small-scale fading. Similar to [2], large-scale shadow fading is neglected as it is assumed to be overcome with slow power control. The distance-dependent path loss is modeled by ri,where is the path loss exponent and r i is the distance between the desired user and each cooperating RRH i, i D, 2, 3, :::, K, in the cluster of radius R c, whose locations are denoted by A, A 2, A 3, :::, A K, respectively, and K is a random variable. Given that the K RRHs in the cluster are uniformly distributed over the cluster area (Section 3.), the mean number of RRHs in the cluster is calculated by, EŒK D R 2 c. The small-scale fading amplitude (envelope) is assumed to be Rayleigh distributed, and thus, h, the Rayleigh fading channel power gain (i.e.,amplitude squared) is an exponentially distributed random variable with unit mean. In addition to path loss and small-scale fading, additive white Gaussian noise (AWGN) is considered whose power is symbolized by N Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd.

4 F. Ghods, A. O. Fapojuwo and F. Ghannouchi Throughput reliability analysis of cloud-radio access networks 3.3. Spectrum allocation Orthogonal frequency division multiple access is assumed as the spectrum allocation scheme for the C-RAN. For the OFDMA-based C-RAN considered in this paper, the total available spectrum BHz is divided into a finite number of equal bandwidth subcarriers. OFDMA, the de facto access technique in the current 4G standards, is selected because of its efficient spectral usage and zero or negligible co-channel interference (users are allocated orthogonal subcarriers). The total spectrum is available to each cluster of cooperating RRHs and equally allocated to all the users within each cluster area. The BBU associated with the cooperating RRHs in a cluster controls the subcarrier allocation such that each subcarrier is only allocated to one user, thus eliminating intra-cluster interference Power control model For the downlink transmission model, it is assumed that all the RRHs utilize the distance-proportional fractional power control (FPC) model given by r i,where is the power control coefficient, 2 Œ, [2,22]. Based on the assumed power control model, the transmit power of each RRH is assigned such that a certain minimum power p min can be received by the user. Thus, the transmit power by RRH i is given by [23]: pmin p i D p r max i < r i R cell () p max where p max denotes the maximum transmit power by an RRH. The cases D and D correspond to no power control and full power control (i.e., full path loss inversion), respectively and < < correspond to FPC. In the no power control scenario, each RRH transmits at maximum power (i.e. p i D p max ), whereas for FPC, lower transmit power i.e. p i D pmaxr R i < p max,for< r i < R cell is assigned, cell and RRH i in full power control transmits at the lowest power i.e. p i D p min rį. Clearly, pmin rį < p max or equivalently p minrį p max <. Hence, for given values of p min, p max, and, the value of R cell should be selected such that the inequality is always satisfied. In this way, it is guaranteed that the transmit power with full power control (and also with FPC) will not exceed p max. This paper proposes to improve the C-RAN energy efficiency by tuning the transmission power using the effects of the wireless propagation mechanism (e.g., path loss, fading) without any direct involvement of the BBU in managing the RRH power allocation. In this paper, only the path loss effect is considered for simplicity and generality of the FPC model. We note that some other works in the literature on FPC applied to traditional cellular networks, for example, [22] have considered small-scale fading in their FPC model, but this lacks generality because the transmit power may be undefined under the channel inversion scenario for some small-scale fading distributions such as Rayleigh fading Cooperation model A random number K of RRHs in a cluster (of radius R c ) cooperates by jointly transmitting to the desired user. This cooperation model is identical to joint transmission, the most advanced coordinated multi-point scenario of longterm evolution advanced systems [24]. The larger the value of R c, the larger the value of K. Hence, the cooperation model parameter is R c, the cluster radius. Now, the locations of the cooperating RRHs in a cluster, say cluster A, are represented by A, :::, A K, where, without loss of generality, A denotes the nearest RRH to the desired user and A j, j D 2, 3, :::, K are the other cooperating RRHs in the cluster. Similarly, the other clusters in the C-RAN service area will each have K cooperating RRHs. Hence, we focus on one cluster where the desired user resides as the cluster of interest and treat the other clusters in the C-RAN service area as sources of out-of-cluster interference (also referred to as inter-cluster interference). Recall from Section 3.3 that there is no intra-cluster interference; thus, the desired user only suffers from inter-cluster interference, denoted by I, from RRHs in the neighboring clusters to its own cluster. In this model, there are four different distances of interest which are defined in the following and depicted in Figure : r D r: distance of the desired user to its nearest RRH in its cluster. r i : distance between a cooperating RRH i and the desired user.for i 2f2, 3, :::, Kg/. R j : distance between an interfering RRH and the desired user (for j 2 nfa, :::, A K g/. x j : distance between an interfering RRH j and its own user within RRH j s coverage area. For illustration, cluster A, the cluster of interest, in Figure contains three cooperating RRHs that jointly and coherently transmit to the desired user. Figure also shows four RRHs that are located outside of cluster A belonging to some other clusters in the service area. These RRHs are potential sources of inter-cluster interference to all the users in cluster A. 4. THROUGHPUT RELIABILITY ANALYSIS The objective of the analysis is to derive the expression for throughput reliability, defined as the probability that Thr, the per user achievable throughput exceeds, a desired throughput threshold in a C-RAN with RRH cooperation and RRH transmit power control. The starting point is the expression for Thr. By Shannon s capacity law, Thr D log 2 C S D I C N ln 2 ln C S I C N D ln. C SINR/ ln 2 (2) Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd. 2827

5 Throughput reliability analysis of cloud-radio access networks F. Ghods, A. O. Fapojuwo and F. Ghannouchi Figure. An illustrative cloud-radio access network architecture. where Thr is in bits=sec=hz or nats=sec=hz accordingly, S is the total received power at the desired user from all the K cooperating RRHs inside the cluster of radius R c, I is the received aggregate out-of-cluster interference from all the RRHs located outside the boundary of the cluster of interest (i.e., cluster where the desired user resides), and SINR is the received signal-to-interference plus noise ratio at the desired user. Making use of Figure and the assumed propagation channel model (Section 3.2), the expressions for SINR is given by SINR D S I C N D p h r C P K id2 p i h i ri Pj2nfA,:::,A K g p jh j R j C N Because, the RRH locations in the C-RAN service area follow the PPP with RRH density (Section 3.), clearly S, I, SINR, and, hence, Thr are random variables. Without loss of generality, assume that RRH (whose location is A ) is the closest RRH to the desired user. Given that the desired user is at a distance r D r from its closest RRH in the cluster (Figure ), the conditional throughput reliability is defined mathematically by (3) ThrReliab.,, R c, jr/ D Pr.Thr >jr/ (4) By unconditioning with respect to the location of the desired user in the coverage area of its closest RRH, the unconditional throughput reliability is denoted by ThrReliab.,, R c, /. Clearly, the expression ThrReliab.: : :/ requires knowledge of the statistics of S, I, SINR, and Thr. Starting with the aggregate interference, generally, the expression for the probability density function (pdf) of aggregate interference in a wireless network is unknown. In essence, for the C-RAN under study, the expression for the pdf of I, the out-of-cluster interference (i.e., aggregate interference from all the RRHs located outside the cluster of interest) is unknown. Hence, in this paper, instead of characterizing by its pdf, we characterize I by L I.s/ D EŒe si the Laplace transform (LT) of the pdf for I, which always exists because I is a strictly positive random variable. Similar to [,2], this paper employs the stochastic geometry framework to obtain, in a systematic way, the LT of the pdf for I as well as evaluating the statistics of SINR and Thr. Section 4. presents semi-closed form results for ThrReliab.: : :/ first under the general case when both RRH cooperation and RRH transmit power control are active and then under cases when only some specific operating conditions are active. Section 4.2 provides per user achievable average throughput results, which are the by-products of the throughput reliability. 4.. Throughput reliability results Proposition 4.. Under the C-RAN operating conditions that both RRH transmit power control (i.e., < ) and RRH cooperation (i.e., < r < R c < ) are active, the conditional throughput reliability ThrReliab.,, R c, jr/ is given by ThrReliab.,, R c, jr/ D e Nı e e r2 (5) where D 2R 2 c =. 2/ 2F, 2 ;2 2 ;, D R r c, # D 2R. C2/r cell, T D e, D.2#=. 2// 2F, 2 ;2 2 ; #. 2/ 2F, 2 ;2 # 2 ;, ı D Tr. / p max p =pmax min, D C2 2T rr cell r R c, and 2 F.a, b; c; d/ is the Gauss-hypergeometric function Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd.

6 F. Ghods, A. O. Fapojuwo and F. Ghannouchi Throughput reliability analysis of cloud-radio access networks Proof: Provided in Appendix A. Equation (5) provides the following insight: the conditional throughput reliability is influenced by the AWGN power (first exponential function in Equation (5)), the aggregate desired signal power received at the desired user from the cooperating RRHs inside the cluster of interest (second exponential function), and the aggregate out-of-cluster interference power at the desired user from all the RRHs outside the cluster of interest (third exponential function). Proposition 4.2. Under the C-RAN operating conditions that both RRH transmit power control (i.e., < ) and RRH cooperation (i.e., < r < R c < ) are active, the unconditional throughput reliability ThrReliab.,, R c, / is given by ThrReliab.,, R c, / D e Nı e e r2 e r2 2rdr. r> where, following the logic in [2], the product e r2 2r is the pdf of the distance r between the desired user and its nearest RRH. The variables and in the exponential terms are each functions of the RRH cooperation parameter (R c ) and the RRH transmit power control parameter via complicated expressions involving special mathematical functions (e.g., the Gauss-hypergeometric function). Proof. Equation (5) is derived given that the desired user is at a distance r from its closest RRH. By unconditioning with respect to e r2 2r the pdf for r, gives Equation (6). Corollary 4.. At a fixed R c and under high RRH density (i.e., tends to a large value), the out-of-cluster interference dominates the AWGN noise power, that is, I >> N, such that.i C N/ IorND and SINR SIR, the signal-to-interference ratio. Setting N D in Equation (6) then gives ThrReliab.,, R c, /D e e r2 e r2 2rdr. r> (7) Equation (7) provides the following insight: the unconditional throughput reliability is influenced by the aggregate desired signal power received at the desired user from the cooperating RRHs inside the cluster of interest of radius R c (first exponential function) and the aggregate out-of-cluster interference power at the desired user from all the RRHs outside the cluster of interest (second exponential function). For a given cluster radius R c,as increases the total received out-of-cluster interference outweighs the aggregate received signal power from the cooperating RRHs such that the received SIR becomes so small and most of the time falling below the desired SIR threshold leading to lower throughput reliability. In the (6) limit when (! ), the throughput reliability tends to zero, as expected. Note that in Equations (6) and (7), the variables and in the exponential terms are each functions of the RRH cooperation parameter (R c ) and the RRH transmit power control parameter () via complicated expressions involving special mathematical functions (e.g., the Gauss-hypergeometric function). Hence, the impact of power control and cooperation on throughput reliability will be demonstrated via numerical computations. Using Corollary 4. as basis, we next consider the special cases depending on whether or not RRH transmit power control or RRH cooperation is active. Proposition 4.3. Under the C-RAN operating conditions where RRHs transmit with no power control (i.e., D ) and only RRH cooperation (i.e., < r < R c < ) is active, the unconditional throughput reliability ThrReliab.,, R c / is given by Pr.,, /D e % e r2 e r2 2rdr (8) r> where D.2=. 2// 2F, 2 ;2 2 ;. 2/ 2F, 2 ;2 2 ;, and % D 2TR 2 c =. 2/ 2 2F, 2 ;2 2 ; T, and D r R c.in Equation (8), the first exponential term accounts for the RRH cooperation, while the second exponential term represents the out-of-cluster interference. Proof. Setting D in the expressions for and and then substituting the results into Equation (7) gives Equation (8). Notice that the variables % and in the exponential terms are each functions of the RRH cooperation parameter R c via complicated expressions involving special mathematical functions (e.g., the Gauss-hypergeometric function); hence, at first glance, the impact of R c on ThrReliab.,, R c / is not obvious. However, an inference from Equation (8) is the following: for a fixed RRH density, an increase in the RRH cooperation parameter R c implies an increase in the number of cooperating RRHs in the cluster of interest and a decrease in the number of outof-cluster RRHs. This means an increase in the received SIR at the desired user and, consequently, an increase in the throughput reliability. Proposition 4.4. Under the C-RAN operating condition that the RRH transmit power control (i.e., < ) is active but with no RRH cooperation (i.e., < R c D r), the unconditional throughput reliability, ThrReliab.,, / is given by Pr.,,, /D e e r2 2rdr (9) r> Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd. 2829

7 Throughput reliability analysis of cloud-radio access networks F. Ghods, A. O. Fapojuwo and F. Ghannouchi where D 2R 2 cell =. 2/ 2 F,, 2 ;2 2 ; 2T and D r. /. C2 R cell Note that, unlike Equations (6), (7), and (8), the exponential term denoting the RRH cooperation no longer exists in Equation (9) because the desired user is served only by its closest RRH. The received aggregate interference by the desired user now comes from the other RRHs in the C-RAN service area, which is represented by the first exponential term in Equation (9). Proof. Please refer to Appendix B Without RRH cooperation and with distance-based power control such that the same signal power p min is received by the desired user at any location inside the coverage area of its closest RRH, the throughput reliability is influenced mainly by the received aggregate interference. Clearly, the aggregate interference is worse when the desired user is near the boundary of the coverage area of its closest RRH i.e., R cell r! resulting in lower SIR and, consequently, low throughput reliability ThrReliab.,, /. In Equation (9), is a function of the power control parameter through a complicated expression involving special functions (e.g., the Gausshypergeometric function); hence, the impact of on ThrReliab.,, / is studied via numerical calculations. Proposition 4.5. Under the C-RAN operating conditions where RRHs transmit with no power control (i.e., D ) and with no RRH cooperation (i.e., < R c D r), the unconditional throughput reliability ThrReliab./ is given by ThrReliab./D 2T. 2/ 2 F where T D e is the SIR threshold., 2 ;2 2 ; T C. () Proof. First, set D andr c D r in the expressions for and and then substitute the results into Equation (7). Next, apply a change of variables D r 2 and integrating with respect to gives Equation (). Clearly, Equation () is independent of the RRH density, consistent with published results in the literature [2]. The insight from Equation () is that, for a given environment (i.e., is fixed), ThrReliab./ decreases as the throughput threshold increases Per-user achievable average throughput result The per user achievable average throughput, EŒThr,canbe determined from Equation (2): EŒThr D EŒln. C SINR/ () ln 2 where EŒThr is in nats=sec=hz.however,eœthr can also be determined by invoking a well-known result from probability theory: for any nonnegative random variable X, the expected value of X, EŒX D R xd PrfX > xg dx [25]. Because Thr is a nonnegative random variable, the given result from probability theory is applied and EŒThr is computed by EŒThr D PrfThr >gd D ThrReliab.: : :/ d D D (2) where PrfThr >gis the unconditional throughput reliability (i.e., ThrReliab.: : :/), given by Equations (6) to (). Substituting Equations (6) to () into Equation (2) gives the expression for per user achievable average throughput for the different operating conditions of the C-RAN. Notice that, with the exception of ThrReliab.: : :/ given by Equation () (i.e., operating condition of no RRH cooperation and no power control), the calculation of EŒThr for the other C-RAN operating conditions whose ThrReliab.: : :/ are given by Equations (7) to (9); each requires double integrations, performed numerically. As such, the insights deduced from Equation (2) will be given after generating and plotting the numerical results in Section C-RAN ENERGY EFFICIENCY AND SPECTRAL EFFICIENCY ANALYSIS C-RAN promises to enhance both the EE and SE. In this section, we quantify both the EE and SE in a C-RAN under the operating conditions of RRH cooperation and RRH transmit power control. The results of Section 4 are leveraged in the calculation of EE and SE. 5.. C-RAN energy efficiency Energy efficiency is generally defined as the number of information bits transmitted per unit of expended energy, measured in bits per Joule. The energy consumed in a C-RAN consists of consumption for [26]: (i) data transmission and reception, transceiver circuits, alternating current to direct current (AC DC) and DC DC conversion, cooling system, and fronthaul interfacing all consumed at the RRHs; and (ii) communication protocol to support the centralized processing at the BBU pool. Recall from Section 3 that only the RAN segment of C-RAN is of interest in this paper. As such, the EE analysis presented here considers only the energy consumption of the RRHs. The components of RRH energy consumption can be divided into two parts: static and dynamic parts. The static part includes energy consumed in the transceiver circuits, AC DC and DC DC conversion, cooling system, and fronthaul interfacing, while the dynamic part is the energy consumption in the power amplifier for data transmission and energy consumption in the low noise amplifier during data reception. In what follows, we derive the result for the EE in a C-RAN under the operating conditions of RRH transmit 283 Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd.

8 F. Ghods, A. O. Fapojuwo and F. Ghannouchi Throughput reliability analysis of cloud-radio access networks power control and RRH cooperation, adopting the models described in Sections 3.4 and 3.5, respectively. For worst case analysis, it is assumed that all the RRHs are up (i.e., none in sleep mode). Also, the RRH distribution and user distribution are as described in Section 3.. The starting point in the analysis is to derive the expression for P tot,rrh, the total power transmitted by an RRH to all the users inside a cluster of K cooperating RRHs: P tot,rrh D KN u p (3) where N u is the number of users in an RRH coverage area and p is the controlled transmit power by an RRH to the desired user (the expression for p will be given later). Now, according to the linear power consumption model [27], applied to an RRH with one transceiver, the power consumed by an RRH, P in,is P in D P C P tot,rrh D P C KN u p (4) where P is the power consumed by an RRH while it is awake but not transmitting to any user (i.e., static part) and is the slope of the transmission/receptiondependent power consumption. Note that the second term of Equation (4) implies that the power transmitted by an RRH to all the users within its coverage area is exactly the same as that transmitted to all the users in the coverage areas of the other RRHs within the cluster. This implication is true because of the cooperation of all the RRHs in a cluster. Hence, the power consumed per unit area (e.g., in Watts=km 2 ) by all the RRHs in a cluster is P tot,clus D P in D.P C KN u p / (5) The network EE is defined as the ratio of the networklevel achievable throughput per unit area to the networklevel consumed power per unit area, where, without a loss in generality, the area is taken with respect to the cluster level of a C-RAN. Mathematically, EE D uthr u Thr D P tot,clus.p C KN u p / (6) Taking expectations of the random variables in both the numerator and denominator in Equation (6) gives EE D u EŒThr.P C EŒK EŒN u p / (7) where EŒK and EŒN u are the average number of RRHs in a cluster and average number of users in a cluster, respectively. Based on the assumptions regarding the RRH distribution and user distribution in Section 3., EŒK D R 2 c and EŒN u D u R 2 cell and substituting these into Equation (7) gives u EŒThr EE D P C u 2 p R 2 (8) c R2 cell where EŒThr is calculated using Equation (2). It remains to derive the expression for p the transmit power by an RRH to a desired user at any location within the RRH coverage area. From Equation (), under the assumed distance-based FPC model, the transmit power by an RRH to a user at distance r away is p min p max r. Hence, the transmit power by an RRH to a user at any location inside the RRH coverage area is given by p D Rcell p min p max r 2r R 2 cell dr D 2p min p max 2 C R cell (9) where the 2r in the integrand is the pdf of r, which R 2 cell follows from the fact that users are distributed uniformly across the RRH coverage area, assumed to be circular in shape and of radius R cell. Equation (8) offers the following insights. The expression for EE is directly proportional to EŒThr, which in turn is proportional to the RRH density. However, from Equation (8), it is seen that the C-RAN EE is also inversely proportional to the RRH density. Increasing the RRH density increases the achievable throughput but with a concomitant increase in power consumption (from Equation (5)) and, consequently, a decrease in the EE. Hence, a trade-off exists between energy consumption and throughput (or between EE and spectral efficiency). The trade-off between the energy consumption and throughput becomes more complex in a C-RAN because of the cooperation among the RRHs in a cluster and the RRH transmit power control mechanism. Moreover, Equation (8) shows that the EE is a function of the RRH cooperation parameter (R c ) and the RRH transmit power control parameter () where both parameters appear in the numerator and denominator. Hence, the impact of power control and cooperation on C-RAN EE will be demonstrated via numerical computations C-RAN spectral efficiency The SE is the rate at which the available system bandwidth is used for data transmission. Given a certain amount of bandwidth B for a C-RAN, the objective is to maximize the per user achievable throughput, EŒThr achieved via RRH cooperation. Recall that the units for EŒThr is in nats=sec=hz. Hence, EŒThr can be interpreted as the per user spectral efficiency. If the users are distributed across the C-RAN service area with density u,thense,thec- RAN area-wide spectral efficiency, expressed in units of nats=sec=hz= unit area is SE D u EŒThr (2) where EŒThr is calculated using Equation (2). From Equation (2), the SE is a scaled version of EŒThr. As such, the insights from Equation (2) will be identical to those for EŒThr. Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd. 283

9 Throughput reliability analysis of cloud-radio access networks F. Ghods, A. O. Fapojuwo and F. Ghannouchi 6. NUMERICAL AND SIMULATION RESULTS WITH DISCUSSION This Section presents and discusses the numerical results calculated using the analytical results obtained in Sections 4 and 5. In addition, we have conducted Monte Carlo simulations to validate the accuracy of the analytical results. Instead of the infinite R 2 C-RAN service area assumed in the analysis, in the simulations, we assume a finite size two-dimensional C-RAN service area. To achieve a good balance in the trade-off between solution quality (i.e., minimize the error between the finite and infinite size C-RAN service area) and solution efficiency (i.e., minimize the simulation run time), a radius of 3 m is assumed for the C-RAN service area in the simulations. An RRH density D. RRHs=m 2 is assumed, which corresponds to medium dense RRH deployment [28]. The user density u is set at.3 users=m 2. Note that u >to ensure there is at least one user in an RRH coverage area, of radius R cell D 5 m. The C-RAN is deployed in an urban environment whose propagation channel is modeled by the distance-dependent path loss (path loss exponent D 4) and small-scale Rayleigh fading (average power of unity). The RRH maximum transmit power p max is 43 dbm [27], and the receiver threshold p min issetatdbm. Note that the assumed parameter values are selected to illustrate the C- RAN performance and do not represent a specific C-RAN design. Table I summarizes the assumed parameter values, unless stated otherwise. Results are generated for six RRH operational scenarios listed as follows: () Without RRH transmit power control ( D ) and no RRH cooperation (No PC, No Coop) (Equation ()). (2) With RRH full transmit power control ( D ) and no RRH cooperation (Full PC, No Coop) (Equation (9)). (3) With RRH fractional power control ( D.5) and no RRH cooperation (FPC, No Coop) (Equation (9)). (4) With RRH full transmit power control ( D ) and RRH cooperation ( Full PC with Coop) (Equation (7)). (5) With RRH fractional power control ( D.5) and RRH cooperation ( FPC with Coop) (Equation (7)). (6) Without RRH transmit power control ( D ) and RRH cooperation (Only Coop) (Equation (8)). The appended equation number signifies the corresponding ThrReliab.:::/ expression, as provided in Section 4. Figure 2 shows the throughput reliability for the six RRH operational scenarios where, for the scenarios 4, 5, and 6, the cluster radius R c is set at 5 m. For ease of showing the results, the throughput reliability is plotted against the signal-to-interference ratio (SIR) threshold, SIR th, instead of the throughput threshold,. TheSIR threshold is defined as the minimum received SIR for acceptable communication, given by SIR th D e (Equation (A.2), Appendix A). Hence, a one-to-one relationship exists between SIR th and. For the range of values of SIR th 5to5dB considered in Figure 2, the corresponding values of vary from.43 to 3.49 nats=sec. In Figure 2, the curves are the analytical results, while the markers denote the simulation results. There is a very good agreement generally between the simulation and analytical results, thus confirming the accuracy of the analytical results. The slight disparity between the analytical and simulation results for RRH operational scenarios 3, 4, 5, and 6 is due to the assumed finite size of C-RAN service area in the simulation in contrast to the infinite size of service area for the analysis. The difference becomes more pronounced for scenarios 3, 4, and 6 involving power control and cooperation, which are both sensitive to distance, the former through the adopted distance-based power control mechanism and the latter through the cluster radius. It is observed in Figure 2 that RRH cooperation provides an improvement in throughput reliability. For example, when the result of scenario 6 is compared with that of scenario, there is at least % increase in throughput reliability. At large value of SIR th, the likelihood of the received SIR exceeding the SIR th reduces, with a consequence of high number of unsuccessful transmissions, and hence a lower throughput reliability. It is also observed in Figure 2 that both FPC and full PC provide an improvement in throughput reliability, as seen from comparing the results of scenarios 3 and, and scenarios 5 and 6 (FPC), and also comparing the results of scenarios 2 and, and scenarios 4 and 6 (full PC). Clearly, both FPC and full PC reduce the level of out-of-cluster interference that leads to a high received SIR and, thus, an increase in throughput reliability. Moreover, the improvement in throughput reliability when cooperation is used with power control is higher than without cooperation, as expected. Table I. The assumed parameters values. Symbol Definition Assumed Value Density of RRHs deployed in the C-RAN. RRHs=m 2 u Density of users in the C-RAN.3 users=m 2 Path loss exponent 4 R c Radius of the cluster in the C-RAN 5 m R cell Radius of an RRH coverage area 5 m p max Maximum transmit power by an RRH 43 dbm p min Minimum received power for acceptable communication dbm 2832 Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd.

10 F. Ghods, A. O. Fapojuwo and F. Ghannouchi Throughput reliability analysis of cloud-radio access networks Figure 2. Throughput reliability for six remote radio head operational scenarios versus SIR threshold ( D 3 RRHs=m 2, R c D 5 m). Figure 3. Throughput reliability versus cluster radius ( D 3 RRHs=m 2, D 2.76 nats=sec (or SIR th D.5 db)). FPC, fractional power control. Figure 3 shows the sensitivity of the throughput reliability to the cluster radius R c, the RRH cooperation parameter. The results are generated assuming SIR th D.5 db (or D 2.76 nats=sec) for the RRH scenarios 4, 5, and 6 with and without power control, respectively. Clearly, the throughput reliability increases with R c as expected because of an increase in the average number of cooperating RRHs in a cluster as R c increases (recall that EŒK D R 2 c ). It is interesting that as R c increases, the throughput reliability tends to a limiting value. This is due to the fact that the gains in the aggregate received signal power is counter-balanced by the increase in the out-of-cluster interference causing the instantaneous per user throughput Thr to tend towards a limiting value. It is concluded from Figure 3 that, for the assumed parameter values, the throughput reliability tends to.54,.74, and.78 for RRH operation scenarios 6, 5, and 4, respectively. Figure 3 is useful to the C-RAN system designer for selecting the cluster radius value to achieve a desired throughput reliability objective and also to determine the threshold cluster radius for which further increase in cluster radius results in no further gains in throughput reliability. In Figure 4, the per user average rate (in nats=sec=hz) is plotted versus the RRH density in a C-RAN, for the six RRH operational scenarios. For scenarios 4, 5, and 6 involving RRH cooperation, the cluster radius is set at 5 m and also for scenarios 3 and 5 involving FPC, D.5. It is seen in Figure 4 that, under scenario for which there is neither RRH transmit power control nor RRH cooperation, the per user achievable average rate is invariant with the RRH density, consistent with the previous results in the literature [2]. Increasing results in an increase in the received signal power (because of the shorter distance of the desired user to its nearest RRH) and also an Figure 4. Per user average rate versus RRH Density (R c D 5 m, D.5 (FPC)). FPC, fractional power control; RRH, remote radio head. increase in the aggregate interference (because of the large increase in the number of interfering RRHs). For scenario 6 where RRH cooperation is enabled but no RRH transmit power control, it is observed that the per user achievable average rate initially increases with the RRH density and then tends to a limiting value at high RRH density. When the RRH density is increased from a low value, there is a concomitant increase in the per user average rate due to an increase in the received SIR. As the RRH density is further increased, the average rate tends to a limiting value because the gain from cooperation is approximately offset by the corresponding increase in the out-of-cluster interference. Now, for scenarios 2, 3, 4, and 5 involving distance-based power control mechanism, the per user Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd. 2833

11 Throughput reliability analysis of cloud-radio access networks F. Ghods, A. O. Fapojuwo and F. Ghannouchi Figure 5. Energy efficiency versus RRH density (R c D 5 m, D.5 (FPC)). FPC, fractional power control; RRH, remote radio head. Figure 6. Spectrum efficiency versus RRH density (R c D 5 m, D.5 (FPC)). FPC, fractional power control; RRH, remote radio head. average rate decreases with RRH density whether or not RRH cooperation is enabled. The decrease in the data rate is due to the complex interaction between the power control and cooperation mechanisms. Regardless of whether or not cooperation exists, the per user average rate achieved with full power control is generally higher than that of fractional power control. Note also that the per user average rates for scenarios 2, 3, 4, and 5 are generally better than those for scenarios and 6, further demonstrating the benefit of cooperation and power control. Figure 5 presents the network EE performance for the six RRH operational scenarios. There are four main findings from Figure 5. First, the C-RAN EE decreases with increasing RRH density. From Equation (8), the increase in RRH density raises the network power consumption to a value much higher than the corresponding increase in the network throughput, thus resulting in the decrease in C-RAN EE. Second, for the scenarios involving no RRH transmit power control, it is interesting to find that RRH cooperation is not beneficial to C-RAN EE. In fact, from Figure 5, the C-RAN EE with RRH cooperation is less than that without cooperation by 56%. The explanation is as follows: at a given cluster radius, not only the improvement in the received aggregate signal power from all the K cooperating RRHs in the cluster is nearly cancelled out by the increased out-of-cluster interference but also the cooperation increases the network power consumption by a factor of K, thus resulting in less network EE compared with that without cooperation when K D. The third major finding from Figure 5 is that the distance-based power control mechanism significantly enhances the C-RAN EE than without, where with full power control providing the highest gain. From Figure 5, full power control and fractional power control at D.5 provide 278% (approximately threefold improvement) and 89% improvement in EE, respectively, over that of the corresponding scenario without power control. Controlling the RRH transmit power at a given RRH density results in reduced network power consumption and, consequently, an increase in the network energy efficiency. The fourth finding from Figure 5 is that with power control, the benefit of RRH cooperation is marginal, where the explanation is similar to that provided previously for the second finding. Finally, Figure 6 presents the C-RAN SE plotted against the RRH density. As seen in Equation (2), the C-RAN SE is a scaled version of Figure 4, depicting the per user average rate, where the scaling factor is the user density. As such, the explanation provided on Figure 4 also applies to the C-RAN SE behavior shown in Figure 6. From Figure 6, full power control and fractional power control at D.5 provide 8% (approximately onefold improvement) and 85% improvement in SE, respectively, as compared with the No PC, No Coop scenario. 7. CONCLUSION Spectral efficient and energy efficient transmissions are of considerable interest in C-RANs. In this work, mathematical analysis based on stochastic geometry is performed to investigate the impact of power control and cooperation on the throughput reliability, per user achievable average rate, EE, and SE performance of C-RANs. On one hand, the use of a distanced-based power control for tuning the RRH transmit power results in reduced network power consumption and thus improves the network EE. On the other hand, cooperation provides a boost in the aggregate received signal power leading to an increase in the per user achievable average rate and, hence, SE improvement. Thus, it is concluded that cooperation along with power control helps to enhance both the SE and EE performance of C-RANs. As revealed from the numerical results, it is feasible to realize close to threefold increase in the EE along with 8% 2834 Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd.

12 F. Ghods, A. O. Fapojuwo and F. Ghannouchi Throughput reliability analysis of cloud-radio access networks improvement in the SE of C-RANs. Moreover, this paper shows that high interference makes power control inappropriate for super dense networks and cooperation gain remains significant against only up to a certain number of cooperating RRHs. However, cooperation worsens EE by up to 56%, which is overcome by using PC while improving SE up to 8%. The significance of these findings is that it is imperative to utilize an optimal RRH density where each RRH in the cooperating cluster is configured with a certain power control setting not only for maximizing EE and SE but also for minimizing the network s capital and operational expenditure. As a future direction, use of partially overlapped channels, instead of orthogonal channels, with the C-RAN architecture will be studied to utilize the spectrum more efficiently. Moreover, a sleeping strategy can be considered in further study with a view to reducing network power consumption and interference by dynamically turning off the RRHs when users become inactive in their coverage areas. APPENDIX A: PROOF OF PROPOSITION 4. Appendix A derives the result for the conditional throughput reliability, defined as the probability that the achievable throughput exceeds a certain threshold, given the desired user is at a distance r from its closest RRH, denoted Pr.Thr >jr/. Starting from Equation (2) in the text, discounting the (= ln 2) factor and making SINR explicitly a function of distance r, wehave Pr.Thr >jr/.a/ D PrŒ ln. C SINR.r// > (A.) interference and aggregate received signal power from the cooperating RRHs, respectively. Now, 2 3 L I.s/.e/ D E s X p j h j R A5 j (A.4) 2 j2nfa,:::,a K g.f/ D E 4 Y i E hj hexp sp j h j R j (A.5) j2nfa,:::,a K g 2 3.g/ Y D E 4 C sp j R 5 j2nfa,:::,a K g j (A.6).h/ D exp! 2 R c C Tr p p RdR jr (A.7).i/ D 2 RdRC R = A c r C R r C2 R cell 2T (A.8).j/ 2T =! 2 Dexp@ r R du A cell C 2 udˇ (A.9).k/ D exp 2R2 c. 2/ 2 F, 2 ;2 2! ; (A.) ".b/ p h r C P # K D Pr id2 p i h i ri Pj2nfA,:::,A K g p jh j R j C N >.e / 2.c/ D Pr 4h > e p r p j h j R j C N e j2nfa,:::,a K g KX id2 p i h i r i 3 A5 (A.2) where r is the distance between the desired user and its nearest RRH. The label (a) follows from the Shannon capacity law, where ln. C SINR.r// is the achieved data rate in nats=sec=hz by the desired user. Label (b) substitutes SINR.r/ definition under the general case of having both RRH power control and RRH cooperation, and (c) rearranges Equation (A.2). For notational simplicity, set s D p r, T D e, I D T Pj2nfA,:::,A K g p jh j R j, w D P K id2 p i h i ri. Recall from Section 3.2 of text that h exp./. The conditional throughput reliability is then expressed as Pr.Thr >jr/.d/ D e sn L I.s/L w. s=t/ (A.3) where (d) follows from the fact that h exp./,andl I.s/ and L w. s=t/ denote the LT of aggregate inter-cluster where (e) follows from the definition of the LT, (f) uses the fact e c.acb/ D e ca e cb, (g) follows from the independence of the h j s and LT of the exponential function. (h) follows from the probability generating functional for PPP [29] and replacing p j by p j as the RRH j transmit power to its own user where the user is located anywhere inside the RRH j s coverage area. The label (i) substitutes distance-based FPC scheme p D p pmin r max p max and p j D R R cell xd p jf xj.x/ dx D 2p pmin R cell max p max C2 by considering probability density function of x j as f xj.x/ D 2x, R 2 cell assuming uniformly distributed users in light of the fact that PPP distribution becomes uniform distribution when the area is bounded [9]. The label (j) employs a change Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd. 2835

13 Throughput reliability analysis of cloud-radio access networks F. Ghods, A. O. Fapojuwo and F. Ghannouchi of variable u D 2 Rc r C2 r 2T R cell R r C2 = 2 r R cell 2T and sets ˇ D = 2, (k) applies some simplifica- tions by using Mathematica where D C2 2T rr cell r R c. Next, the LT of the aggregate received signal from the cooperating RRHs is determined as follows: L w. s=t/.l/ D E w Œe ws=t D E K "exp ".m/ Y K D E K E hi hexp id2 " K #.n/ Y D E K s id2 T p iri.o/ D exp 2 rc wdr s T KX s T p ih i r i id2 i # p r p i p i h i r i!# w wdw! (A.).p/ Rc D 2 wdr wdwc = A C w r C2 r R cell 2 (A.2).q/ 2 =! 2 Vul D exp@ r R dv A cell C2 VDV ll C V =2 (A.3).r/ D exp 2r2 # 2F, 2. 2/ ;2 2 ; #!. 2/ 2F, ;2 ; # 2 2 (A.4) where (l), (m), (n), (o), and (p) use the same reasoning as (e), (f), (g), (h), and (i), respectively. The label (q) employs a change of variable V D w r C2 = 2 r R cell 2 where V ul D R c r C2 = 2 r R cell 2 and V ll D r C2 = 2 R cell 2. The label (r) applies some simplifications by using Mathematica, recalling the fact that R b xda f.x/ dx D R xda f.x/ dx R xdb f.x/ dx where D r R c, # D 2R. C2/r cell. Finally, p TNr max sn.u/ B p min C e D A D e Nı p max (A.5) where (u) simplifies e sn in Eq. (A.3) by substituting sd p T r and p and setting ı D Tr. / p max p =pmax min. Next, substituting Equations (A.), (A.4) and (A.5) into (A.3), the conditional throughput reliability is determined as follows: ThrReliab.,, R c, jr/ D e Nı e e r2 (A.6) where D.2R 2 c =. 2// 2F, 2 ;2 2 ;, D r R c, # D 2R. C2/r cell, T D e, D.2#=. 2// 2F, 2 ;2 2 ; #. 2/ 2F, 2 # ;2 2 ; p, ı D Tr max p =pmax min, D C2 2T rr cell r R c, and 2 F.a, b; c; d/ is the Gauss-hypergeometric function. Clearly, Equation (A.6) is the same as Equation (5) in Section 4 of the paper, thus completing the Proof. APPENDIX B: PROOF OF PROPOSITION 4.4 Appendix B derives the result for the unconditional throughput reliability under interference limited (i.e., N D ) condition and C-RAN operational scenario of RRH transmit power control but no cooperation. Setting N D and R c D r in Equation (6) gives ThrReliab.,, / " #.a/ p h r D Pr r> Pj2nfA g p jh j R >.e / e r2 2rdr j (B.) ThrReliab.,, /.b/ D e r2 L I.s/2rdr (B.2) r> where (a) substitutes SIR definition for the case of having power control with no cooperation and (b) follows the same analysis as Equation (A.3) by setting I D Pj2nfA g p jh j R j, r D r, T D e, s D r T, p D p,andh exp./. 2 L I.s/.c/ D E 4 Y j2nfa g.d/ D 2 C Tr p j R j R cell C Rpr T Kp j 3 5 RdRA (B.3).e/ D 2 R RdRC = A cell R C r C2 r R cell 2T (B.4).f/ D exp 2R2 cell. 2/ 2 F, 2 ;2 2! ; (B.5) 2836 Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd.

14 F. Ghods, A. O. Fapojuwo and F. Ghannouchi Throughput reliability analysis of cloud-radio access networks where (c) arises from the similar reasoning as in Equations (A.4), (A.5), and (A.6), and (d), (e), and (f) use the same analysis as Equations (A.8), (A.9), and (A.) where D C2 2T r. /. R cell Substituting Equation (B.5) into (B.2), Equation (9) gets deduced. REFERENCES. Qualcomm Incorporated (23 June). The x data challenge. Available from: com/x/ [accessed on August 25]. 2. Jorguseski L, Litjens R, Oostveen J, hang H. Energy Saving in Wireless Access Networks. River Publishers: Aalborg, 2, Bangerter B, Talwar S, Arefi R, Stewart K. Networks and devices for the 5G era. IEEE Communications Magazine 24; 52(2): L IC, Rowell C, Han S, Xu, Li G, Pan. Toward green and soft: a 5G perspective. IEEE Communications Magazine 24; 52(2): Ha VN, Le LB, Dao ND. Cooperative transmission in c-ran considering frounthaul capacity and cloud processing constraints. In IEEE Wireless Communications and Networking Conference (WCNC), Istanbul, 24; Checko A, et al. Cloud RAN for mobile networks a technology overview. IEEE Communications Surveys & Tutorials 25; 7(): China Mobile. C-RAN: The road towards green RAN, Guan H, Kolding T, Merz P. Discovery of cloud- RAN. Technical Report, 2. Nokia Siemens Netw., oetermeer, The Netherlands. 9. Suryaprakash V, Rost P, Fettweis G. Are heterogeneous cloud-based radio access networks cost effective? IEEE Journal on Selected Areas in Communications 25; 33(): Shao S, Han L, Shen Y, Tang Y. Energy efficient radio remote units placement for single user uplink in c-ran. Concurrency and Computation: Practice and Experience 22; 25(9): Huang K, Andrews JG. A stochastic-geometry approach to coverage in cellular networks with multicell cooperation. In Global Telecommunications Conference (GLOBECOM). IEEE, Houston, TX, USA, 2; Tanbourgi R, Singh S, Andrews JG, Jondral FK. A tractable model for non-coherent joint-transmission base station cooperation. IEEE Transactions on Wireless Communications 24; 3(9): An L, Lau VKN. Joint power and antenna selection optimization for energy-efficient large distributed MIMO networks. In IEEE International Conference on Communication Systems (ICCS), Singapore, 22; Liu, hu, Deng H, hou S. A power allocation algorithm maximizing system capacity in radio access networks. In Ninth International Conference on Natural Computation (ICNC), Shenyang, 23; Liu L, Bi S, hang R. Joint power control and fronthaul rate allocation for throughput maximization in OFDMA-based cloud radio access network. IEEE Transactions on Communications 25; 63(): Brown TX. Cellular performance bounds via shotgun cellular systems. IEEE Journal on Selected Areas in Communications 2; 8(): Baccelli F, Klein M, Lebourges M, uyev S. Stochastic geometry and architecture of communication networks. Journal Telecommunication Systems 997; 7(): Haenggi M, Andrews JG, Baccelli F, Dousse O, Franceschetti M. Stochastic geometry and random graphs for the analysis and design of wireless networks. IEEE Journal on Selected Areas in Communications 29; 27(7): Wang CC, Quek TQS, Kountouris M. Throughput optimization, spectrum allocation, and access control in two-tier femtocell networks. IEEE Journal on Selected Areas in Communications 22; 3(3): Andrews JG, Baccelli F, Ganti RK. A tractable approach to coverage and rate in cellular networks. IEEE Transactions on Communications 2; 59(): Novlan TD, Dhillon HS, Andrews JG. Analytical modeling of uplink cellular networks. IEEE Transactions on Wireless Communications 23; 2(6): Jindal N, Weber S, Andrews JG. Fractional power control for decentralized wireless networks. IEEE Transactions on Wireless Communications 28; 7(2): Rao J, Fapojuwo AO. Analysis of load dependent energy efficiency of two-tier heterogeneous cellular networks. In IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), London, 23; Lee J, et al. Coordinated multipoint transmission and reception in LTE-advanced systems. IEEE Communication Magazine 22; 5(): Ross SM. Stochastic Processes. Wiley: New York, Alhumaima RS, Al-Raweshidy HS. Evaluating the energy efficiency of software defined-based cloud radio access networks. IET Communications 26; (8): Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd. 2837

15 Throughput reliability analysis of cloud-radio access networks F. Ghods, A. O. Fapojuwo and F. Ghannouchi 27. Auer G, et al. How much energy is needed to run a wireless network? IEEE Wireless Communications 2; 8(5): Di Renzo M, Guidotti A, Corazza GE. Average rate of downlink heterogeneous cellular networks over generalized fading channels: a stochastic geometry approach. IEEE Transactions on Communications 23; 6(7): Stoyan D, Kendall W, Mecke J. Stochastic Geometry and its Applications (2nd edn). John Wiley and Sons: Chichester, 996. AUTHORS BIOGRAPHIES Fatemeh Ghods is currently a Ph.D. Candidate in Electrical and Computer Engineering at the University of Calgary, Calgary, AB, Canada. She received the M.Sc. in Computer Engineering from the Sharif University of Technology in Tehran, Iran in 22. Her current research interests include performance evaluation and interference management of cloud-radio access network. Abraham O. Fapojuwo received the B.Eng. degree (first class honors) from the University of Nigeria, Nsukka, in 98 and the M.Sc. and Ph.D. degrees in Electrical Engineering from the University of Calgary, Calgary, AB, Canada, in 986 and 989, respectively. From 99 to 992, he was a Research Engineer with NovAtel Communications Ltd., where he performed numerous exploratory studies on the architectural definition and performance modeling of digital cellular systems and personal communications systems. From 992 to 2, he was with Nortel Networks, where he conducted, led, and directed system-level performance modeling and analysis of wireless communication networks and systems. In January 22, he joined the Department of Electrical and Computer Engineering, University of Calgary, where he is currently a full Professor and Associate Head, Graduate Studies. His current research focus is on energy efficient radio resource management, quality of experience, and security and performance analysis of 5G (fifth generation) mobile cellular networks and wireless sensor networks. Dr. Fapojuwo is a recipient of the Best Paper Award at the 24 IEEE Wireless Communications and Networking Conference and co-author of the Best Student Paper Award at the 2th IEEE Personal, Indoor and Mobile Radio Communications Symposium 29. He also received the 28 IET Ambition and Achievement Awards Communications Premium. Dr. Fapojuwo is a registered Professional Engineer in the Province of Alberta, Canada. Fadhel Ghannouchi is currently a professor, Alberta Innovates/Canada Research Chair, and Director of the iradio Laboratory ( ucalgary.ca) in the Department of Electrical and Computer Engineering at the University of Calgary, Alberta. His research interests are in the areas of RF and wireless communications, nonlinear modeling of microwave devices and communications systems, design of power-efficient and spectrum-efficient microwave amplification systems and design of SDR systems for wireless and satellite communications applications. His research has led to over 7 refereed publications and 2 US patents (5 pending), 4 books and 3 spun-off companies Wirel. Commun. Mob. Comput. 26; 6: John Wiley & Sons, Ltd.