System-Level Analysis of a Self-Fronthauling and Millimeter-Wave Cloud-RAN

In this work, we analytically study the performance of an in-band and self-fronthauling millimeter-wave Cloud-Radio Access Network (C-RAN). By considering a stochastic-geometry approach for the modeling of the position and number of Baseband Units (BBUs), Remote Radio Heads (RRHs), and mobile terminals (MTs), we provide the following three-fold contribution: i) We derive an analytical framework for the MT rate distribution for two types of wireless RRHs, namely half-duplex (HD) and full-duplex (FD); ii) Based on the derived framework, we prove that the maximum performance gain of the FD network over its HD counterpart is achieved for a substantially higher density of the wireless RRHs compared to the fiber-connected ones and an adequately small self-interference power level; iii) Finally, we compute an analytical expression of the total cost required to increase the density of the fiber-connected RRHs in a city that showcases the tradeoff between their density increase and the incurred cost. The aforementioned system-level trends are validated by means of Monte Carlo simulations.


I. INTRODUCTION A. Background
O VER the last years, there has been a continuous increase in the demand for higher rates owing to the proliferation of smartphone devices. According to the overwhelming figures, by 2022 global mobile data traffic is expected to reach a monthly run of around 77 exabytes per year, which corresponds to a higher than a 6-fold growth with respect to the monthly run of 2017 [1]. Obviously, such demands cannot be accommodated by the current cellular standards that rely on sub-6 GHz bands to convey information, such as the Long-Term Evolution Advanced, which can offer a peak-data rate slightly above 1 Gbps [2]. As a result, the future of the substantially congested sub-6 GHz bands that Manuscript received December 2, 2019; revised May 9, 2020 and August 20, 2020; accepted August 23, 2020. Date of publication September 4, 2020; date of current version December 16, 2020. This work was financially supported in part by the research projects AGAUR (2017-SGR-891), SPOT5G (TEC2017-87456-P) and 5G-Routes (951867). The associate editor coordinating the review of this article and approving it for publication was C. Masouros. (Corresponding author: Konstantinos Ntontin.) Konstantinos Ntontin is with the Wireless Communications Laboratory, Institute of Informatics and Telecommunications, National Centre for Scientific Research "Demokritos," 15310 Athens, Greece (e-mail: konstantinos.ntontin@iit.demokritos.gr).
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Digital Object Identifier 10.1109/TCOMM.2020.3021692 are used for communication is highly uncertain. Due to this, two important features of the forthcoming 5G technology that have been proposed to meet the ever-increasing rate demands have been [3]: i) The migration to higher than 6 GHz frequency bands due to the availability of a significantly higher bandwidth. Such an availability directly translates to higher rates according to Shannon's capacity formula; ii) Extreme small-cell densification to improve spectral efficiency.
Regarding the use of above-6 GHz bands for communication, there has been a substantial research over the recent years regarding the potential of cellular communications at the millimeter-wave (mmWave) spectrum that spans the range 30-100 GHz. As far as works that showcase such a potential are concerned, outdoor and indoor channel models have been developed that apply to carrier frequencies which exhibit a relatively small atmospheric absorption, such as the 28 and 73 GHz bands [4], [5]. According to these works, both coverage-probability and average-rate gains can be achieved compared to sub-6 GHz networks, as the density of the cells increases and for highly-directional antennas employed at both the cells and MTs. In addition, outdoor measurements in urban scenarios indicate that distances between a MT and its associated cell smaller than 200 m are needed so that outagefree communication is achieved [4]. Hence, the migration to the mmWave bands is essential to be combined with cell densification in order to leverage the substantially higher available bandwidth [6]. Regarding this, by using a stochastic geometry approach where the cells on the plane are modeled as points of a Poisson point process (PPP) 1 in [14] the authors show that although for an average cell radius of 200 m (small cell density) a network in the 2.5 GHz band outperforms a mmWave network operating at 28 and 73 GHz bands, the opposite holds for an average cell radii of 100 m and 50 m (high cell density). In addition, the significant performance enhancement achieved by mmWave networks under a high-cell densification is also demonstrated in [17] by again modeling the position and number of cells on the plane according to a PPP, as in [14].
The aforementioned works on mmWave networks that demonstrate the significant gains achieved as the cell density 1 Such a stochastic geometry approach where nodes on the plane such as base stations, small cells, relays, and MTs are modeled according to PPPs is a convenient tool for tractable system-level analysis and has been applied to different scenarios of interest, such as the modeling and analysis of downlink [7]- [9], multi-antenna [10], [11], heterogeneous [12]- [14], uplink [15], [16], mmWave [14], [17], [18] and full-duplex (FD) cellular networks [19], [20], to mention some indicative examples. 0090-6778 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
increases do not take into account the backhaul requirements. Instead, by considering only the access network implicitly suggests that there is a high-capacity wired connection, such as fiber, between every cell and the core network in which the signals of all the MTs associated with a particular cell can be multiplexed. However, fiber connecting every cell with the core network is highly unrealistic, especially for high cell densities that are envisaged in 5G networks. The reason is twofold [21]: i) High costs can be involved for installing and leasing fiber cables. In particular, many operators do not own a fiber network and, hence, they have to pay market prices for fiber leases, which can be substantial in developing countries.
In addition, as far as deployment costs are concerned, even for operators that own a fiber network fiber-connecting every small cell with the core network is not a desirable option. The reason is that although in principle in urban scenarios fiber is available near small-cell locations, to bring it to small cells mounted, for instance, on lampposts requires expensive excavation and time-permitting procedures [21]. In fact, the excavation costs involved may be multiples of the small-cell equipment cost [21,Fig. 5]; ii) The QoS requirements in a mmWave network might be achieved with a combination of fiber and wireless backhaul. Due to the aforementioned issues, operators estimate that as many as 80% of the small cells will not be fiber connected to the core network [22]. Instead, the backhaul traffic is going to reach them through the remaining fiber-connected cells via wireless links. Hence, the fiber-connected cells are going to act as relays of the traffic associated with the wireless cells. This approach is the so-called self-backhauling approach, which is instigated by wireless operators as a cost-effective small-cell backhaul solution [22]- [26] (and references therein).
Apart from the importance of the backhaul network for meeting the foreseen rates of 5G cellular networks, over the recent years the notion of fronthauling has gained equal importance. Fronthauling is inextricably linked to the Cloud Radio-Access Network (C-RAN) architecture, which is a recently proposed architecture for future 5G networks [27]. According to the C-RAN architecture, the baseband processing is detached from the already existing entities that are called base stations and allocated to particular units that are called Baseband Units (BBUs). BBUs are connected to nodes called Remote Radio Heads (RRHs) that contain the RF equipment and antennas needed for transmission and reception to/from the MTs. Hence, in such an architecture the backhaul network corresponds to the connections between the BBUs and the core network, whereas the fronthaul network to the connections between the BBUs and the RRHs. These fronthaul links should be ideally based on fiber cables for optimal performance. However, similarly to the aforementioned deployment issues that make self backhauling a more attractive option for the backhaul network, self fronthauling where a number of RRHs are fronthauled wirelessly through fiber-connected RRHs is a favorable approach for vendors [28]. To the best of our knowledge, only [29] and [30] study sub-6 GHz C-RAN architectures that consider wireless fronthauling. In particular, in [29] the authors consider a single-cell architecture where a BBU controls a number of RRHs via wireless fronthaul links. For RRHs acting as either decode-and-forward (DF) or decompress-and-forward relays, the authors consider the problem of jointly optimizing the BBU and RRH operations with the goal of maximizing the weighted sum rate subject to BBU and per-RRH power constraints. In [30], the authors consider an out-of-band multiclustering architecture, where each BBU communicates with each associated RRHs wirelessly, and jointly optimize the fronthaul and access links with the goal of maximizing the sum rate of all the MTs. Consequently, the system-level analysis of a selffronthauling mmWave C-RAN architecture is a largely unexplored area, which requires contributions due to the practical importance of including wireless fronthaul links apart from cable ones, as aforementioned.

B. Contribution
Motivated by the importance of C-RAN architectures for the forthcoming 5G networks and the practical need for selffronthauling in such architectures, in this work we consider the system-level analysis of a self-fronthauling in-band architecture where the same mmWave band is used for the fronthaul and access wireless links. Our contribution can be summarized as follows: • We develop a stochastic-geometry based system-level analytical framework for the distribution of the downlink MT rate, which we denote by coverage rate. The framework is flexible enough by including as parameters the densities of the wired and wireless RRHs together with the user load. Consequently, it can be used to estimate the performance for any ratio of the fiberconnected RRHs over the wireless ones. In addition, the framework incorporates two possibilities for the type of wireless RRHs, namely half-duplex (HD) and full-duplex (FD). In the HD approach, the wireless RRHs receive and transmit in different time slots, whereas in its FD counterpart simultaneous reception and transmission at those nodes occurs. Simulation results reveal that there is a close match between the simulations and the analysis, which validates the developed framework. • Apart from its close match with the simulations, the analytical framework reveals that the highest rate gain of the FD case over the HD one is achieved for a wireless-RRH density substantially higher than the one of the fiber-connected RRHs and for a substantially small self-interference power level caused by the simultaneous transmission and reception of the wireless RRHs in the FD case. However, as the power level of the selfinterference increases, these gains diminish. These trends are validated by the simulation results. • Finally, by parameterizing the possible cost per meter involved in the design and installation of fiber cables, we show that as the density of the fiber-connected RRHs increases, the involved cost substantially increases as well for indicative large cities, in terms of area, in the world. This is an important tradeoff to be taken into account by the system designer since the important rate increase achieved by increasing the ratio of the fiber-connected RRHs over the wireless ones requires notable investments regarding the fiber network. Organization: The rest of this paper is organized as follows: In Section II, we present the considered scenario together with the main assumptions. In Section III, for both the HD and FD cases we firstly present the signal model, subsequently we formulate the instantaneous signal-to-interference plus noise ratio (SINR) expressions according to our signal model and, finally, based on these expressions we formulate the MT coverage rate as the examined metric. In Section IV, we derive the analytical framework of the coverage rate, use it to extract insights regarding the comparison of the HD and FD cases, and present an expression for the total cost involved for increasing the density of the fiber-connected RRHs in a city. In Section V, the analytical model and the extracted insights are validated by means of Monte-Carlo simulations. Finally, Section VI concludes this work.

II. SYSTEM MODEL
In this section, we first present the scenario under consideration and, subsequently, we proceed with the assumptions.

A. Scenario
We assume a C-RAN architecture where the deployed RRHs are associated with BBUs in which the baseband processing is taking place. In addition, we consider that the number and position of RRHs and BBUs are described by two uniformly distributed PPPs on R 2 , namely Φ R and Φ BBU , with intensities λ R and λ BBU , respectively. As aforementioned in Section I, due to the high deployment and leasing costs involved with fiber connections in practical cases it is expected that only a portion of the deployed RRHs are going to have fiber connection towards their associated BBUs. The rest of RRHs are going to be wirelessly connected to their associated BBUs through the fiber-connected RRHs in a twohop architecture. Based on this, we assume that the fiberconnected RRHs are described by the PPP process Φ (C) R with intensity λ (C) R and the wirelessly connected ones by the PPP process Φ R . Finally, we assume that the MTs are also described by a uniform PPP, denoted by Φ MT , with intensity λ MT . A snapshot of such a proposed architecture is depicted in Fig. 1 [32], for the blockages that may exist in the radio path (such as buildings) we consider  According to this assumption, the centers of the blockages form a homogeneous PPP Φ Blockages of intensity λ Blockages . In addition, for simplicity we assume that the radius of all the blockages is equal to R B .
By denoting by K i the number of blockages in a random link i between two RRHs or between a RRHs and a MT and by R i the length of the link, it is proved in [33] and [34] that K i is a Poisson random variable with expected value equal to βR i . Regarding β, it holds that β = −ρ ln(1−p) πA , where ρ = 2πR B and A = πR 2 B are the perimeter and area of the buildings, respectively, and p = λ Blockages πR 2 B , with 0 < p < 1, is the percentage of the area occupied by blockages. In addition, the probability that the link i does not contain any blockage, which we denote by P r {K i }, is given by Finally, for analytical tractability we assume that the number of blockages in any two links from two RRHs to a RRH or MT are independent. This means that the same blockage cannot be in the radio path of more than one link between two nodes. According to [33], such a simplification causes a minor loss in accuracy when the size of the blockages is relatively small.
2) Node Association, Path Loss, Channel Characteristics, and Access Protocol: a) RRH and MT Association: We assume that: i) Each wireless RRH is associated with the wired RRH from which it receives the strongest signal; ii) Each MT is associated with the RRH, wired or wireless, from which it receives the strongest signal; iii) Each wired RRH is associated with the closest BBU. b) Path Loss: Let us assume that the link i between two nodes in the network is denoted by R i . The resulting largescale path loss in the case of outdoor LOS or NLOS link, which we denote by l (m) si (R i ), is given by where m∈{ R (C) , R (W ) , R (W ) , R (W ) , R (C) , MT , R (W ) , MT } is the index representing the link between a fiber-connected and a wireless RRH, two wireless RRHs, a fiber-connected RRH and a MT, and, finally, a wireless RRH and a MT, respectively, s i ∈ {LOS, N LOS}, and α Rx , MT Ó denotes the path-loss exponent. 2 In addition, κ 0 = (4πf /c 0 ) 2 denotes the free-space path loss at a distance of 1 m. c) Frequency Band of Operation: We consider the 28 GHz mmWave band for operation. Such a band has been considered in several literature works on mmWave networks due to the relatively small atmospheric absorption that it exhibits [4], [6], [17]. d) Propagation Conditions: We assume that the outdoor mmWave communication can occur in line-of-sight (LOS) and non-LOS (NLOS) conditions, which is supported by reported measurements [5], [14]. e) Shadowing: For analytical tractability, we assume that the possible shadowing effects are incorporated into the blockage model, as it is assumed in [35].
f) Fast Fading: According to measurements, in mmWave bands fast fading has a less pronounced effect than the sub-6 GHz bands [36], where it is common that fast fading is modeled as a Rayleigh variable. However, due to the fact that modeling fast fading with a more flexible distribution, such as the Nakagami distribution, is not expected to provide additional insights regarding the system design, in this work we assume that the fast fading processes corresponding to the links between RRHs and MTs simply follow a Rayleigh distribution originating from a complex Gaussian process with zero mean and unit variance. On the other hand, for the connections among RRHs we logically assume that there is no fast-fading effect due to their fixed position. Finally, with h X,Y we denote the Gaussian complex envelope corresponding to the fast-fading process regarding the link between the nodes X and Y .
g) Noise at the Receiver: We assume that the received signal is subject to additive white Gaussian noise. Its power level, denoted by σ 2 N , in dBm is equal to −174 + 10 log 10 (BW ) + F dB , where F dB is the noise figure in dB and BW is the transmission bandwidth.
h) Access Protocol: We consider a time-division multiple access (TDMA) protocol, which means that only one MT per RRH is served in each time slot to which the whole available bandwidth is given. The TDMA consideration arises from the fact that a frequency-division multiple access approach would require multiple radio-frequency chains per RRH. This can create important wide-scale deployment issues due to the high cost and power consumption associated with mixedsignal circuits at mmWave bands [37]. Due to this, the TDMA protocol that requires only one RF chain per RRH has been proposed as a more affordable approach for future mmWave networks [38], which is the reason for its adoption in this work.
Based on this, all the RRHs other than the serving RRH that concurrently transmit are interferers towards the reference MT.
3) Antenna Gains and Beamsteering: a) Antenna gains of the RRHs and MTs: We assume that antenna arrays are deployed at the RRHs and MTs in order to enable beamsteering. Their gains are given by a sectored radiation pattern as [17] 3 T x , MT , in the case of the transmit array of fiber-connected RRHs, the receive array of wireless RRHs, the transmit array of wireless RRHs, 4 and the receive array of MTs, respectively. In addition, θ ∈ [−π, π) is the angle off the antenna boresight direction, θ q is the half-power beamwidth of the main lobe, and G are the maximum and minimum antenna gains, respectively. Hence, as it is also assumed in [17], with such modeling we consider for simplicity that the array gains are constant and equal to G (max) q and G (min) q for all angles in the main lobe and side lobes, respectively. b) Beamsteering: We assume that prior to data transmission the transmit and receive nodes of interest steer the orientation of their antennas in a way that the maximum directivity gain, i.e. G Rx , MT , is achieved. This can be realized by the existence of a feedback channel and the dispatch of pilot signals from the MT/RRH to the serving RRH prior to data transmission. 5 Since the beams of the interfering links are uniformly distributed in [−π, π), there are 4 possible values of the directivity gain between a RRH interferer and the MT/RRH of interest, i.e. G with respective probabilities given in Table  I 2π are the probabilities that the nodes corresponding to q 1 and q 2 are aligned in a direction that provides antenna gains G , respectively.

4) Association Rule and Interference:
a) Association Rule: Let P R be the total transmit power budget for serving respectively. In order to ensure the total power constraint [41] as our design aim, they are defined by P R (C)(1) o = 3 Antenna arrays with important gains that are suitable for the size of MTs and are, for instance, based on both dipoles and patch antennas have been proposed in the literature [39], [40]. 4 We assume that the wireless RRHs are equipped with separate receive and transmit RF chains and antennas. 5 It is out of the scope of this work the consideration of imperfect channel knowledge at the serving RRHs that can lead to beam misalignment errors.
Similar to [8], the triplet R is identified by using the following criteria: where s i , s k , s j ∈ {LOS, N LOS} and R X,Y denotes the distance between the nodes X and Y . The association criteria in (4), (5), and (6) ensure that M T 0 receives the highest power from the available fiber-connected and wireless RRHs as well as that the serving wireless RRH, R , receives the highest power from the available RRHs.
Let the triplet of network elements R (4), (5), and (6), respectively. The typical MT, M T o , is served either via a one-or a two-hop link according to the cell-association criterion as follows [8]: where B BS is a non-negative constant, which is called bias coefficient. Depending on its value, it prioritizes either the single-hop or the two-hop transmission conditioned on the values of the path-loss exponents. In particular, the communication takes place in one hop if B BS = ∞ and in two hops if B BS = 0. b) Interfering Processes: The set of interfering fiberconnected and wireless RRHs are denoted by Φ (I) , corresponding to the interfering fiber-connected RRHs serving their associated MTs either via a one-and two-hop link, respectively. Since the cell-association rules (4)-(7) are distance-dependent, the sets Φ are not homogeneous PPPs. In addition, the number of the interfering wireless RRHs is equal to the number of the interfering fiber-connected RRHs participating in the two-hop transmissions since both convey signals using the whole available bandwidth, according to the TDMA protocol. As with Φ is not a homogeneous PPP due to the association protocol of (4)-(7).

5) Operational Principle of the Wireless RRHs:
We consider two types of wireless RRHs: i) HD; ii) FD. In the following, we describe their operational principle: a) HD RRHs: According to the HD principle, the wireless RRHs receive and transmit in different time slots. The end-to-end communication is realized in two phases that have a duration of one time slot each and are described as follows: 1st Phase: During the 1st phase, the fiber-connected RRHs convey their signals towards their respective wireless RRHs and MTs.
2nd Phase: During the 2nd phase, the transmissions that are allowed are the ones of the fiber-connected and wireless RRHs towards the MTs that they serve.
Hence, if an MT is served by a wireless RRH the symbol rate is equal to 0.5 symbols/time slot. b) FD RRHs: According to the FD principle, the wireless RRHs receive and transmit in the same time slot. As in the HD case, the end-to-end communication is realized in two phases that have a duration of one time slot each and are described as follows: 1st Phase: During the 1st phase, the fiber-connected RRHs convey their signals towards their respective wireless RRHs and MTs and the wireless RRHs convey their signals towards their MTs. More specifically, assuming that in time slot n is subject to self interference due to its concurrent transmission.
2nd Phase: During the 2nd phase, both fiber-connected and wireless RRHs are allowed to transmit, as in the 1st phase. More specifically, in time slot n + 1 R that reach its receive antenna. In sub-6 GHz bands, measurements have showed that the power level of the LOS component is in general much higher than the corresponding one of the NLOS component [42]. This necessitates the sophisticated design of FD nodes through analog and digital self-interference cancellation techniques so that the power level of the self-interfering signal falls below the noise floor. This poses substantial challenges regarding the design of sub-6 GHz FD nodes.
On the other hand, for mmWave bands theoretical and experimental works have shown that in the 28-GHz band it is highly probable that the NLOS component is stronger than the LOS component [43], [44]. According to these works, around 70-80 dB of self-interference mitigation can be achieved through antenna directionality and 35-50 dB of mitigation can be achieved through analog and digital techniques.
As far as the modeling of the self-interfering signal is concerned, the sub-6 GHz band related literature works mainly model it as a Rayleigh or a Rice random variable with variance that represents its residual power level after the cancellation stages [42]. To the best of our knowledge, in mmWave bands there is a lack of experimental studies regarding the statistical characteristics of such a signal. Due to this and taking into account that in this work we are primarily interested in examining the effect of the mean power level of the selfinterfering signal, in this work we model it as a fixed variable, denoted by σ 2 SI . Notation: Recurrent parameters are included in Table II.

III. INSTANTANEOUS SINR EXPRESSIONS AND EXAMINED METRIC
In this section, we first present the signal model, subsequently we introduce the instantaneous SINR expressions for each of the HD and FD cases and, finally, we mathematically formulate the coverage rate as the metric of interest. , is given by where s on is the transmitted symbol in time slot n, n MTo is the noise at M T o , i R (C) (1) ,MT o is the interference process resulting from the set of fiber-connected RRHs constituting the single-hop transmissions and i R, (2) ,MT 0 and i R (W ) ,MT 0 are the interference processes resulting from the set of fiberconnected RRHs constituting the two-hop transmissions and the set of wireless RRHs, respectively. It holds that , is given by where are the interference processes resulting from the set of fiber-connected RRHs constituting the one-and two-hop transmissions, respectively. It holds that As far as the communication between R , is given by where s on is the decoded and remodulated transmitted symbol at R MTo is the noise at M T o and i  , is given by where the interference processes i R where are defined in (13) and (14), respectively, and is the interference process originating from the interfering RRHs that concurrently transmit. It holds that As far as the communication between R , is given by where    (18), (12) with (19), and (15) with (21), we conclude that: i) Both wireless RRHs and MTs are subject to higher inter-cell interference compared to the HD network due to the FD operation; ii) In contrast to the HD wireless RRHs, their FD counterparts are subject to self interference due to their concurrent transmission and reception. Due to this, an FD wireless RRH can achieve twice the rate that its HD counterpart offers only if the power level of the self-interference terms is much smaller than the noise floor. This is expected in mmWave TDMA networks that we consider in this work due to: i) The large available bandwidth per transmission due to the TDMA protocol; ii) The high directionality needed regarding the transmissions from RRHs so that the additional path loss at mmWave bands compared to the sub-6 GHz ones is substantially mitigated. Such a high directionality is feasible even for the compact sizes that RRHs are expected to have due to the fact that the shorter wavelengths of mmWave bands allow the placement of a notably higher number of antennas at the same physical space compared to the currently used sub-6 GHz bands. 6 Apart form path-loss compensation, a notable directionality can also substantially mitigate both the intercell and self interference. Especially, in the later case theoretical and experimental results have showed that in the 28-GHz band an FD node is expected to require between 35-50 dB self-interference mitigation so that the power level of the self-interference components falls below the noise floor [43], [44]. Such a required cancellation level is much smaller than the one that would be needed at sub-6 GHz and likely to be feasible with proper analog and digital cancellation components as it is concluded in [44]; iii) The dense-blockage conditions likely to occur in urban scenarios. This increases the probability of these networks being noise limited even for dense RRH setups [34]. , is given by where I R where As far as the communication between R , is given by where I , is given by

b) Two-Hop Communication: For the communication between R
where , is given by where I R (C) (2) o ,MTo and I , respectively.

C. Coverage-Rate Formulation
The coverage rate, which is denoted by R (HD) cov cov (R t ) in the HD and FD cases, respectively, is defined as the probability that the instantaneous rate is larger than a threshold R t . It is given by the sum of the following terms: i) The coverage rate in the case of 1-hop communication, which is equal to the average value with respect to where l ∈ {HD, F D} and with N MT is the number of MTs served (either directly or through wireless RRHs) by the fiber-connected RRH that is associated with the reference MT and ξ (HD) = 1 2 , ξ (F D) = 1.

IV. PERFORMANCE ANALYSIS AND INSIGHTS
The aim of this section is: i) To present an analytical approximate expression of the coverage rate for each of the HD and FD cases; ii) To extract important trends regarding the performance comparison of these two cases for different regions regarding the ratio of the density of the wireless RRHs over the one of the fiber-connected ones; iii) To present an analytical estimation regarding the expected cost for increasing the density of the fiber-connected RRHs in a city.
Towards these, we first present the considered noise-limited and LOS ball approximations that enable us to derive an analytical expression of the coverage rate.

A. Noise-Limited Approximation
As we have mentioned in Remark 1, it is expected that the the considered network is noise limited even for dense RRH topologies. This is due to the considered TDMA protocol and the resulting large bandwidth per transmission, the high directionality that is possible in the considered band of 28 GHz, and the high density in blockages that exists in urban scenarios. Due to this, for the extraction of an analytical expression for R (l) cov (R t ), l ∈ {HD, F D} we consider the noiselimited approximation regarding the intercell interference. Hence, the resulting approximate SINR expressions, which we denote by SIN R , are given by where l ∈ {HD, F D} and ζ (HD) = 0, ζ (F D) = σ 2 SI .

B. LOS Ball Approximation
Due to the complicated forms of the probability density function of a MT or RRH to its nearest LOS or NLOS RRH [17,Eq. (6)], [17, Eq. (7)], we consider the LOS approximation that is commonly used in analyzing mmWave cellular networks [17], [36]. According to it, up to a certain distance the probability that the link is LOS is 1 and 0 above it. Hence, we distinguish 3 breaking distances for the

C. Performance Analysis
Before proceeding with the analytical expression of R (l) cov , l ∈ {HD, F D}, we first present Lemma 1.
Lemma 1: The probability that N MT is equal to n, where n = 1, 2, 3, . . ., which is denoted by P r {N MT = n}, is given by Proof : (37) originates from the typical Poisson-Voronoi tesselation [36, Section III-C]. Although the distribution of the association areas of the fiber-connected RRHs would be different due to the LOS and NLOS conditions originating from blockages together with the presence of wireless RRHs, the mean area that they cover is the same as the mean area of the typical Poisson-Voronoi tesselation [36, Section III-C].
where ψ ∈ {ψ 1o , ψ 2o , ψ 3o } and p (ψ) (x) = βf for ψ = {ψ 1o , ψ 2o , ψ 3o }, respectively. In addition, where ζ (HD) = 0 and ζ (F D) = σ 2 SI . R (1,hop) cov (R t ) and R (2,hop)(l) cov (R t ) are the coverage rates in the case that the communication is realized in 1 or 2 hops, respectively. They are given by the probability of having 1-or 2-hop communication multiplied by the probability that the instantaneous rate in each case is larger than a threshold R t , taking into account all the possible combinations of the involved links R In addition, N trunc is introduced so that the series in (39) and (40) are not infinite. A rule of thumb for the choice of N trunc is that it should be a multiple of λMT λ R (C) [36]. Proof : See APPENDIX A. Remark 2: The computational complexity of (38) can be substantially reduced at the cost of accuracy by removing the summation over the possible number of MTs per fiber-connected cell and replacing n in R with the average number of MTs per fiber-connected cellN MT , which is given by [36] (54)

D. Insights Regarding the Comparison of R
Proposition 2: In the unbiased case, i.e. B BS = 1, R Proof: For tractability regarding the proof of Proposition 2 and without loss of generality, let us assume that: i) The probability that the links R where In such a case, from (57) we understand that R  7 Considering the value 2, i.e. free-space path-loss, for the path-loss exponent in the case of LOS mmWave propagation is a common assumption in literature works [17], [35]. tend to 0 and 1, respectively. Hence, the maximum gain of R (2,hop) (R t ) as the results of Section V reveal..

E. Average Cost for Fiber-Cable Deployment in an Area
Let us assume that within a land area denoted by S area an operator has some already deployed fiber-connected RRHs with density λ (initial) R (C) . In addition, the operator would like to densify the network by deploying additional fiber-connected RRHs with density λ (added) R (C) . The average number of fibercable connections per BBU, denoted byN λBBU . Furthermore, considering the fact that according to our system model the fiber-connected RRHs are associated with their closest BBU, the pdf of the distance R R (C) ,BBU between a fiber-connected RRH and a BBU, which we denote by f R R (C) ,BBU (x), is given by Consequently, the average distance value of R R (C) ,BBU , denoted byR R (C) ,BBU , is given bȳ Based on the above, if the installation cost per meter of a fiber cable (including design and excavation costs) is equal to c fiber , the total average cost for the fiber connections required between the added fiber-connected RRHs and their associated BBUs in S area , which we denote byC (added) cable , is given bȳ The aim of this section is twofold: i) To validate, by means of Monte-Carlo simulations, Propositions 1 and 2; ii) To substantiate the tradeoff between the induced cost and performance enhancement achieved by densifying the network with fiber-connected RRHs. Towards this, we use the parameters of Table III. Such a value of p corresponds to a scenario dense in blockages, such as the one encountered in big cities like Chicago and Manhattan [34]. As far as the simulation setup is concerned, we consider a circular simulation area of radius 2 km and as far as the buildings that act as blockages are concerned, we generate circles of radius R B with centers following a PPP of intensity λ Blockages . Regarding the fiberconnected and wireless RRHs, if an RRH is generated inside the area occupied by a building we consider that the link between that RRH and any other node is a NLOS link. This is consistent with the simulation-setup considerations in the literature [34].

A. Validation of Propositions 1 and 2
In Fig. 2, we present the R (HD) cov cov (R t ) vs. R t plots for a high and a small ratio of the density of the wireless RRHs over the total density of the RRHs in the network and for a low, moderate, and high value of σ 2 SI . From Fig. 2, we observe that: i) There is a close match of the analytical model with the simulations for both ratios and for all the R t regimes. This validates the extracted analytical model, according to Proposition 1 and the noise-limited nature of the network (assumption which the extraction of the analytical model was based on) even for such a high value of λ R (network dense in RRHs) that we consider in this work. Hence, the system designer can readily use this framework to estimate the performance achieved for any ratio of the wireless over the total number of RRHs in the network; ii) The highest difference between R (F D) cov (R t ) and R (HD) cov (R t ) is achieved for the 70% ratio of the density of the wireless over the total RRH density and adequately high cancellation level of the self interference.In fact, we see that the the σ 2 SI = 0.01σ 2 N and σ 2 SI = σ 2 N achieve almost the same performance, which means that the need for very high cancellation levels of the self interference can be alleviated. Such trends validate Proposition 2. Such a trend is attributed to the fact that when λ the communication in the vast majority of cases takes place in 2 hops and, hence, the advantage of FD RRHs becomes more pronounced when σ 2 SI is substantially low. On the other hand, if the latter does not hold, a network with HD RRHs will provide better performance than its FD counterpart, as we can see from Fig. 2-(a). Hence, if the density of the wireless RRHs is not much higher than the corresponding one of the fiber-connected RRHs or the selfinterference cancellation level cannot be adequately high, for the system designer it might not worth the burden to deploy FD wireless RRHs for achieving a relatively small gain over the HD case. This is due to the fact that the FD functionality requires a careful design regarding the selfinterference cancellation part, which is expected to consume additional power regarding the electronic components of the FD nodes.
To further substantiate how the gap of the achieved performance of the FD-based network with respect to its HD counterpart is reduced as the ratio  is depicted in Fig. 3-(b), which indicates that this ratio monotonically reduces as

B. Tradeoff Between Performance and Cost as λ R (C) Increases
Let us assume that λ (initial) R (C) = 22/km 2 . In Fig. 4, we present the performance/cost tradeoff as λ (C) R increases through the increase of the number of fiber-connected RRHs, λ (added) R (C) , that are added in the network. In Fig. 4-(a), as λ increases we observe the performance enhancement vs. λ (added) R (C) /λ R , which is the ratio of the density of the added fiber-connected RRHs over the total RRH density. The performance evaluation is in terms of the median-rate gain over the median rate that corresponds to λ (initial) R (C) . As we observe from Fig. 4-(a), moving to around 50% of RRHs being fiber connected increases the median rate about 10 times compared to the one corresponding to the λ case. This is due to the fact that as the density of the fiberconnected RRHs increases, the number of served MTs per fiber-connected RRH decreases. However, the cost to achieve such an enhancement might be substantial, as we observe in Fig. 4-( /λ R for major cities in the world. 8 The system designer can use such curves to extract the best tradeoff between performance enhancement and cost in scenarios of interest. 8 Data for Sarea of the presented cities were obtained from [45].

C. Suitability of the RRH PPP Modeling
Let us now discuss the suitability of modeling the RRHs as points of a uniformly distributed PPP. Based on such an assumption, at any given realization there is a non-zero probability that 2 generated RRHs are located arbitrarily close to each other. However, in real-world conditions there is a minimum distance of separation between any given pair of RRHs, which originates from their deployment onto structures, such as lampposts. Hence, a more realistic approach would be to model the RRHs as points of a Matérn hardcore point process (MHCPP) of type II with parameter d rep , which is called repulsion and denotes the minimum allowed distance between any RRH pair [46]. Based on this, the question that arises is whether such a consideration would change the key outcomes corresponding to the comparison of the FD with the HD-based network. To answer this, in λR , we see that as d rep increases it slightly reduces, which reveals that increasing the repulsion among RRHs has a minor effect on the ratio of the wireless-RRH number over the total RRH number in the network.  λ R remains almost constant as d rep increases. Hence, as an outcome, repulsion reduces the achievable performance of the HD-and FD-based networks, but the relative gain that the latter network achieves over its former counterpart remains almost constant as the repulsion increases. Consequently, such a gain can be extracted by the considered PPP modeling for the RRHs, which simplifies the analytical derivations.

VI. CONCLUSION
Motivated by the importance of self-fronthauling in future 5G networks, in this work we have provided an analytical study for a C-RAN self-fronthauling architecture where the wireless RRHs are fronthauled through the fiber-connected RRHs. By focusing on the in-band case where the fronthaul and access networks use the same mmWave frequency band and by considering a stochastic-geometry approach for the modeling of the position and number of fiber-connected RRHs, wireless RRHs, and MTs, we have derived an analytical framework for the coverage rate in the downlink. The derived framework incorporates the two possible types of wireless RRHs, namely HD and FD and, according to the results, it exhibits a good match with the Monte-Carlo simulations. In addition, we have analytically proved and validated against the simulations that the maximum rate gain of the FD over the HD case is exhibited if the density of the wireless RRHs is substantially higher than the one of the fiber-connected ones and for an adequately small selfinterference power level. On the other hand, if the density of the fiber-connected cells is notably higher than the one of their wireless counterparts, the HD and FD cases asymptotically overlap.
Finally, the tradeoff between performance enhancement and cost as the density of the fiber-connected RRHs increases was examined. Towards this, an analytical estimation of the induced cost was provided that incorporates the area of cities as a parameter. The results show that although the median rate can substantially increase when the network is densified in fiber-connected RRHs, the induced deployment cost of fiber substantially increases for large cities, such as New York and Chicago. These are issues that the system designer, based on our framework, can take into account when deciding about the particular ratio of the wireless-RRH density over the total RRH density that is going to be realized in the network.
the noise-limited approximation of SIN R , it holds that There are 4 possible cases of the links R