I Roudas

Jiang

L Miranda
email: luis.miranda@unavarra.es

Modeling long-haul optical networks with quasi-single-mode fibers

Keywords: Multipath interference (MPI), optical communications, optical fiber, quasi-single-mode (QSM) transmission

Few-mode fibers (FMFs) with weak mode coupling which are used to transmit signals predominantly in the fundamental mode are referred to as quasi-single-mode (QSM) fibers. QSM fibers can be designed to have much larger effective areas for the fundamental propagation mode than conventional single-mode fibers (SMFs). Signal transmission over the fundamental mode of QSM fibers can reduce distortion arising from the fiber Kerr nonlinearity. Random light coupling, however, among QSM fiber modes leads to multipath interference (MPI). Simultaneous reduction of nonlinear distortion and MPI can be achieved by using hybrid fiber spans, each composed of a QSM fiber segment to restrict nonlinear distortion, followed by an ultra-low-loss, large-effective-area SMF segment to suppress MPI. In this invited paper, we review modeling and simulation tools that can be used for the design and optimization of coherent optical communication systems and networks with hybrid QSM fiber/SMF spans. We show that the precise selection of the fiber splitting ratio per span is not critical for the system performance and can be calculated with sufficient accuracy using a modified version of the nonlinear Gaussian noise model for hybrid fiber spans.

Introduction

Kerr nonlinearity in single-mode fibers (SMFs) places a ceiling on the spectral efficiency of contemporary optical communication systems [START_REF] Ellis | Performance limits in optical communications due to fiber nonlinearity[END_REF]. To overcome this limitation, several techniques for nonlinear distortion mitigation and compensation in long-haul optical communications systems have been proposed over the past few years [START_REF] Dar | Nonlinear interference mitigation: Methods and potential gain[END_REF], [START_REF] Cartledge | Digital signal processing for fiber nonlinearities[END_REF].

A promising nonlinear distortion mitigation strategy uses the fundamental propagation mode of FMFs to establish single-mode links with reduced nonlinear distortion due to the Kerr effect [START_REF] Yaman | Long distance transmission in few-mode fibers[END_REF], [START_REF] Yaman | 10 × 112 Gb/s PDM-QPSK transmission over 5032 km in few-mode fibers[END_REF], [START_REF] Downie | Transmission of 112 Gb/s PM-QPSK sigover up to 635 km of multimode optical fiber[END_REF], [START_REF] Yaman | Impact of modal crosstalk and multi-path interference on few-mode fiber transmission[END_REF], [START_REF] Ryf | Mode-multiplexed transmission over conventional graded-index multimode fibers[END_REF], [START_REF] Yaman | First quasi-single-mode transmission over transoceanic distance using few-mode fibers[END_REF], [19], [START_REF] Downie | Optical transmission systems and methods using a QSM large-effective-area optical fiber[END_REF], [START_REF] Li | Quasi-singlemode optical fiber with a large effective area[END_REF]. This technique is called quasi-single-mode (QSM) transmission. By extension, FMFs with weak mode coupling which are used to transmit signals predominantly in the fundamental mode are referred to as quasi-single-mode (QSM) fibers.

Launching light in the fundamental mode of an ideal, straight, perfectlycylindrical FMF results, in principle, in pure single-mode propagation without coupling to higher-order modes. In practice, however, there always exists random coupling from the fundamental mode to higher-order modes and vice versa because of fiber irregularities. This leads to the generation and propagation of a multitude of copies of the signal waveform across the fiber link. Due to modal dispersion, these echoes propagate at various group velocities and interfere either constructively or destructively with the main signal propagating on the fundamental mode. This effect is referred to as multipath interference (MPI) [START_REF] Sui | Long-haul quasi-single-mode transmissions using few-mode fiber in presence of multi-path interference[END_REF], [START_REF] Mlejnek | Coupledmode theory of multipath interference in quasi-single mode fibers[END_REF].

A compromise between fiber nonlinearities and MPI can be achieved by resorting to a combination of a large effective mode area QSM fiber and a smaller effective mode area SMF [START_REF] Yaman | First quasi-single-mode transmission over transoceanic distance using few-mode fibers[END_REF], [19], [START_REF] Downie | Quasi-single-mode fiber transmission for optical communications[END_REF]. The QSM fiber is placed at the beginning of the span where signal power is greatest to restrict nonlinear distortion, followed by an SMF segment to suppress MPI. We can adjust the splitting ratio between QSM fiber and SMF to maximize the system performance.

Monte Carlo simulation can be commonly used to compute the optimum fiber splitting ratio. The main drawback of this approach is that it often requires excessive computational resources to evaluate the performance of a large number of candidate fiber configurations and select the best among them. This is due to the high computational complexity of the numerical solution of the Manakov equation using the split-step Fourier algorithm. A preferable alternative would be to use an approximate analytical model to either compute the optimum fiber splitting ratio directly or, at least, to limit the parameter space prior to running Monte Carlo simulations.

The nonlinear Gaussian noise model [START_REF] Poggiolini | The GN model of non-linear propagation in uncompensated coherent optical systems[END_REF], [START_REF] Poggiolini | The GNmodel of fiber non-linear propagation and its applications[END_REF] provides an analytical firstorder perturbation solution of the Manakov equation in the absence of polarization mode dispersion (PMD) and polarization-dependent loss (PDL). In this regime, signal distortion due to the Kerr nonlinearity resembles a zero-mean, complex Gaussian additive noise. The variance of the latter is calculated in closed-form from fiber and system parameters [START_REF] Poggiolini | The GN model of non-linear propagation in uncompensated coherent optical systems[END_REF], [START_REF] Poggiolini | The GNmodel of fiber non-linear propagation and its applications[END_REF].

In its original formulation [START_REF] Poggiolini | The GN model of non-linear propagation in uncompensated coherent optical systems[END_REF], [START_REF] Poggiolini | The GNmodel of fiber non-linear propagation and its applications[END_REF], the nonlinear Gaussian noise model is restricted to coherent optical communication systems using a single fiber type per span. Recently, we extended this formalism to model coherent optical communication systems with hybrid fiber spans [START_REF] Downie | Quasi-single-mode fiber transmission for optical communications[END_REF] comprising a combination of QSM fiber and SMF per span. In [START_REF] Miranda | Performance of coherent optical communication systems with hybrid fiber spans[END_REF], we used Monte Carlo simulation to validate this model. We showed that it can predict the optimum hybrid fiber configuration per span with sufficient accuracy.

The purpose of this article is to review modeling and simulation tools that can be used for the performance evaluation and optimization of coherent optical communication systems with hybrid QSM fiber/SMF spans. Using these tools, we show that the optimum fiber splitting ratio per span increases with the per-centage of MPI compensation at the coherent optical receiver. The peak system performance, however, is a slowly-varying function of the fiber splitting ratio. Therefore, the precise selection of the fiber splitting ratio per span is not critical and can be calculated with sufficient accuracy using the above-mentioned modified version of the nonlinear Gaussian noise model for hybrid fiber spans.

Theoretical model

System topology

Fig. 1 depicts the block diagram of a representative long-haul coherent optical communication system for QSM transmission with hybrid fiber spans. The transmission link of total length L is composed of a concatenation of N s identical spans. Each span has length s and comprises two fiber types. Each fiber type is characterized by its LP 01 mode effective area A eff , its nonlinear index coefficient n 2 , its group velocity dispersion (GVD) parameter β 2 or, equivalently, its chromatic dispersion parameter D, and its attenuation coefficient a. In what follows, indices 1, 2 stand for the first and second fiber segment per span, respectively. For instance, the optical fiber lengths of the two segments are s1 , s2 , and their effective mode areas are A eff1 , A eff2 , respectively. The three splices between dissimilar optical fibers denoted by ⊗ in Fig. 1 have losses χ 1 , χ 2 , and χ 3 , respectively. The optical fiber is followed by an optical amplifier of gain equal to the span loss G = χ -1 1 χ -1 2 χ -1 3 e a1 s 1 +a2 s 2 and noise figure F A . We consider wavelength division multiplexing (WDM) and polarization division multiplexing (PDM) based on ideal Nyquist channel spectra. The latter are created using square-root raised cosine filters with zero roll-off factor at the transmitter and the receiver. Furthermore, we assume that the WDM signal is a superposition of an odd number N ch wavelength channels with spacing ∆f = R s . We denote by P the total average launch power per channel (in both polarizations) and by R s the symbol rate. We want to evaluate the performance of the center WDM channel at wavelength λ.

Analytical performance evaluation

Effective optical signal-to-noise ratio (OSNR) The performance of coherent optical systems without in-line chromatic dispersion compensation is related to the effective optical signal-to-noise ratio (OSNR eff ) at the receiver input. This quantity takes into account the amplified spontaneous emission (ASE) noise, the MPI, and the nonlinear distortion. All the above effects can be modeled as independent, zero-mean, complex Gaussian noises with a good degree of accuracy. More specifically, the OSNR eff at a resolution bandwidth ∆ν res can be well described by the analytical relationship [START_REF] Mlejnek | Coupledmode theory of multipath interference in quasi-single mode fibers[END_REF]

OSNR eff = P ã + βP + γP 3 , (1)
Fig. 1: Representative long-haul coherent optical communications system with hybrid fiber spans.

where ã is the ASE noise variance, βP is the crosstalk variance due to MPI, and γP 3 is the nonlinear noise variance. The coefficients ã, β, γ depend on the fiber and system parameters.

Noise variances for systems with hybrid fiber spans Nonlinear noise accumulation for coherent optical communication systems using hybrid fiber spans can be modeled by extending the perturbation formalism of [START_REF] Poggiolini | The GN model of non-linear propagation in uncompensated coherent optical systems[END_REF], [START_REF] Poggiolini | The GNmodel of fiber non-linear propagation and its applications[END_REF].

Here, we consider ideal Nyquist PDM WDM signals with channel spacing equal to the symbol rate R s . We obtain the following expression for the nonlinear noise coefficient γ γ ∼ = 16 27

N 1+ s ∆ν res R 3 s χ 2 1 B 0 2 - B 0 2 B 0 2 - B 0 2 γ 1 1 -e -(a1+i∆β1) s 1 a 1 + i∆β 1 + χ 2 γ 2 e -(a1+i∆β1) s 1 1 -e -(a2+i∆β2) s 2 a 2 + i∆β 2 2 df 1 df 2 . (2)
In ( 2), γ m are the nonlinear coefficients, ∆β m are the propagation constant mismatches of the two fiber segments per span, m = 1, 2, and is a fitting parameter.

For modeling MPI, we assume that the QSM fibers under consideration exhibit weak coupling between the fundamental mode group LP 01 and the higherorder mode group LP 11 , i.e., the power coupling coefficient κ satisfies the relationship κ s1

1. Then, the MPI coefficient β is given by [START_REF] Mlejnek | Coupledmode theory of multipath interference in quasi-single mode fibers[END_REF] (with a sign correction)

β = N s ∆ν res R s (∆α s1 -1 + e -∆α s 1 )κ 2 ∆α 2 , ( 3
)
where ∆α is the differential mode attenuation (DMA). Finally, the ASE noise variance for arbitrary span lengths is given by [START_REF] Desurvire | Erbium-doped fiber amplifiers: principles and applications[END_REF] α = hf 0 N s (GF A -1) ∆ν res ,

where h is Planck's constant and f 0 is the center WDM channel carrier frequency.

Numerical simulations

In numerical simulations, we consider hybrid fiber spans composed of a hypothetical QSM fiber and a representative commercially-available, large-effective-area SMF. We assume an ideal Nyquist WDM signal composed of 9 wavelength channels, each carrying PDM 16-QAM. The simulation parameters are listed in Table 1. For simplicity, splice losses and splice-induced MPI are neglected. We evaluate the Q-factor vs. launch power for the central WDM channel using two different methods: (a) Monte Carlo simulation using direct error counting; and (b) The nonlinear Gaussian noise model for hybrid fiber spans described earlier.

Results and discussion

In this section, we compute the optimal fiber splitting ratio per span that maximizes system performance. In particular, we investigate how this ratio depends on the degree of MPI equalization at the coherent optical receiver.

System performance for 80 km spans At the beginning, we examine the variation of the Q-factor as a function of the launched power per WDM channel for a coherent optical system composed of 80 km spans. Fig. 2a and Fig. 2b show numerical results for two extreme MPI cases: (i) when MPI is not compensated; and (ii) when complete elimination of the MPI-induced intersymbol interference (ISI) is achieved using adaptive equalization at the coherent receiver, respectively. Different color curves correspond to different length combinations of QSM fiber and large-effective-area SMF. In Fig. 2a, the best combination of optical fibers leading to optimal system performance consists of about 40 km of QSM fiber at the beginning of each span, followed by 40 km large-effective-area SMF at the end of each span. The use of this fiber combination yields an optimal Q-factor Q 0 = 8.3 dB, which is better than that achieved with the two other displayed fiber configurations. In Fig. 2b, where we assume that there is complete equalization of MPI-induced ISI at the coherent optical receiver, the best system performance is achieved using only QSM fiber at each span. The optimal Q-factor obtained by this fiber configuration is 9.5 dB. System performance for various MPI compensation levels Fig. 3 shows plots of the optimum Q-factor Q 0 as a function of the QSM fiber length per span s1 . Curves from bottom to top correspond to progressively larger levels of MPI compensation at the coherent optical receiver. For 0% MPI compensation, about 50% of each span is QSM fiber. As MPI compensation increases, the fraction of QSM fiber per span increases. At 100% compensation, the best system performance is achieved by using exclusively QSM fiber. We observe that the proposed nonlinear Gaussian noise model given by ( 1)-( 4) describes fairly well the numerical results.

It is worth noting that Q 0 is a slowly-varying function of the QSM fiber length s1 in a wide region around the peak. For instance, in the absence of MPI compensation, the system performance changes by only 0.1 dBQ when the QSM fiber length varies in the range 22-61 km. This weak dependence of Q 0 on the QSM fiber length implies that it is not critical to determine the fiber splitting ratio per span with utmost accuracy. The nonlinear Gaussian noise model can be used to compute the fiber splitting ratio per span with sufficient accuracy even without exact knowledge of the value of the fitting parameter . For instance, in the absence of MPI compensation, using the nonlinear Gaussian noise model with = 0 yields an optimum QSM fiber length s1 = 31 km, which results in less than 0.1 dBQ decrease from the maximum performance.

These general trends persist independent of the choice of the QSM fiber LP 01 mode effective area and the fiber span length. The above results reveal that, in spite of the generation of MPI, the use of QSM fiber is beneficial.

Conclusion

The aim of this article was to review modeling and simulation tools that can be used for the performance evaluation and optimization of coherent optical communication systems with hybrid fiber spans, comprising a combination of QSM fiber and a large-effective-area SMF per span. Monte Carlo simulation was used to compute the optimum hybrid fiber configuration per span with high accuracy. We showed that the optimum fiber splitting ratio per span increases with the percentage of MPI compensation at the coherent optical receiver. For instance, for a transatlantic system with 80 km spans, in the absence of MPI compensation, it is best to use equal lengths of QSM fiber and SMF per span. In contrast, for full MPI compensation, the optimum system performance is achieved by using exclusively QSM fiber.

In addition, we analytically evaluate the performance of the aforementioned optical communication systems with hybrid QSM fiber/SMF spans. Nonlinear distortion and multipath interference are represented as additive white Gaussian noises. We extended the original nonlinear Gaussian noise formalism to model systems with hybrid fiber spans. The analytical model predictions qualitatively explain the numerical simulation results. The value of the analytical model lies in its simplicity. It helps us understand the interplay among various physical parameters. Most importantly, it can be used to compute the fiber splitting ratio per span with sufficient accuracy.

Fig. 2 :

 2 Fig. 2: Q-factor as a function of the total launch power per channel. (a) No MPI compensation; (b) 100% MPI compensation. (Symbols: Points: Monte Carlo simulations; Lines: Least squares fitting using (1) with ã, β, γ as unknown parameters.)

Fig. 3 :

 3 Fig. 3: Optimum Q-factor Q 0 as a function of the QSM fiber length s1 per span. (Symbols: Points: Monte Carlo simulations; Lines: Least squares fitting using (1)-(4) with as an unknown parameter. Here 0.2.)

Table 1 :

 1 Simulation parameters

	Parameter	Symbol	Value
	Modulation format		PDM-16QAM
	Symbol rate	Rs	32 GBd
	WDM channels	N ch	9
	WDM channel spacing	∆f	Rs
	Link length	L	6,000 km
	Span length	s	80 km
	Attenuation coefficients	α1, α2	0.155 dB/km
	QSM fiber LP01 mode effective area A eff 1	350 µm 2
	SMF LP01 mode effective area	A eff 2	150 µm 2
	Power coupling coefficient	κ	10 -3 km -1
	Differential mode attenuation (DMA) ∆α	2 dB/km
	Nonlinear refractive index	n2 2.1 × 10 -20 m 2 /W
	GVD parameter	|β2|	26.6 ps 2 /km
	EDFA noise figure	FA	5 dB

Acknowledgment

The authors would like to thank J. D. Downie, M. Mlejnek, and W. A. Wood of Corning Research and Development Corporation for fruitful discussions.


Hao Yu

Francesco Musumeci

Jiawei Zhang

Yuming Xiao
email: yumingxiao@bupt.edu.cnfrancesco.musumeci

Massimo Tornatore
email: massimo.tornatore@polimi.it

Yuefeng Ji

S W Rrh

DU/CU Placement for C-RAN over Optical Metro-Aggregation Networks

Keywords: C-RAN, functional splits, fronthaul, baseband processing deployment, wavelength division multiplexing, 5G RRH RRH RRH

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Ever-increasing mobile-traffic demand requires operators to deploy more base stations and to keep updating their radio access network (RAN). In the future, 5G RAN is set to provide an even larger variety of services with widely varying requirements on bandwidth and latency. Therefore, future RAN design is Fig. 1: Illustration of 2-layer and 3-layer C-RAN architecture expected to satisfy the very stringent constraints in terms of tolerable latency and required data rate [START_REF] Hossain | 5G cellular: key enabling technologies and research challenges[END_REF], e.g., end-to-end latency requirements below 1 ms, more than 250 Gb/s/km 2 in dense-urban areas and device density in the order of thousands per km 2 [START_REF]5G White Paper[END_REF]. Overall, a very large amount of baseband processing resources and network resources will be required to be deployed in the RAN.

In 4-th generation LTE networks, Distributed Radio Access Network (D-RAN) is the dominant RAN paradigm, where the Base Station (BS) comprises two modules: Remote Radio Head (RRH) for transmission and reception of radio signals, frequency up/down conversion and power amplification, and Baseband Unit (BBU) to perform digital processing of baseband signal. The BBU and RRH were traditionally co-located in the same housing facility, so the maintenance and investment costs of networks increase linearly with the number of BSs, which leads to a not scalable solution. An alternative RAN architecture, called Centralized Radio Access Network (C-RAN), has been proposed as a scalable solution in terms of both power and cost efficiency. In C-RAN, the BBUs are centralized into larger housing facilities, called BBU pools, which are connected with the RRHs through a high-capacity and low-latency "fronthaul" network [START_REF] Pizzinat | Things you should know about fronthaul[END_REF]. Optical metro/aggregation networks based on wavelength division multiplexing (WDM) are considered as a promising candidate for transport network of RAN. Besides performing traffic aggregation and switching (SW), the central offices (COs) at different hierarchical stages of the metro network can be also equipped with processing resources to process baseband signal. The procedure of moving BBUs from cell sites to COs is called BBU hotelling, as shown in Fig. 1

(left).

From cell site to access/main CO, to core CO, the fewer COs need to be used as BBU hotels, and the more "consolidation" is achieved through BBU hotelling. As the motivations of BBU hotelling are to allow operators to save costly installation and maintenance of processing facilities inside COs, centralizing more BBU into COs in higher stages of networks can increase these benefits.

However, due to the high fronthaul cost of C-RAN [START_REF] Zhang | Joint Wavelength, Antenna, and Radio Resource Block Allocation for Massive MIMO enabled Beamforming in a TWDM-PON based Fronthaul[END_REF], RAN architecture is further evolving towards decentralizing part of baseband processing functions at the network edge, in order to decrease the fronthaul bandwidth. BBU is now divided into two parts: Distributed Unit (DU) and Central Unit (CU). The DU contains some real-time baseband processing functions, i.e., Hybrid Automatic Repeat Request (HARQ) processing, radio coordination, while CU contains some non real-time baseband processing functions. Original RRH with part of PHYlayer functions comprises Remote Unit (RU). It follows that the RAN architecture evolves from a 2-layer (BBU-RRH) to 3-layer (CU-DU-RU) architecture. Through flexible distribution of CUs and DUs in the metro transport network, service requirements can be satisfied according to different DU/CU hotelling schemes. As shown in the right side of Fig. 1, the RU replaces the RRH at the cell sites, and DUs/CUs can be placed at any locations starting from the cell sites up to the COs at the different stages of the metro network. Compared with 2-layer RAN architecture, a new network segment is introduced, called midhaul, which connects DU and CU. In this paper, we re-consider the DU/CU placement problem in the 3-layer RAN architecture by minimizing the number of active COs for CU/DU hotelling. We also provide a mathematical model for this placement problem, and we apply this model over a limited, yet realistic network scenario. This model allows us to show the interplay between DU/CU placement and front/mid/back-haul, and to investigate the relation between the consolidation of baseband processing functions and the processing/bandwidth capacity constraints, as well as service latency. For the metro transport solutions, we consider OTN (more specifically, we assume a version of OTN optimized for mobile transport, called M3C-OTN, aiming at Mobile optimized, Multi-service and Metro Cloud OTN solution for the 5G scenario) and overlay, in line with the assumptions used in [START_REF] Musumeci | Optimal BBU Placement for 5G C-RAN Deployment Over WDM Aggregation Networks[END_REF].

The remainder of this paper is organized as follows. Section II introduces the related works. Section III introduces functional split based 3-layer RAN architecture. Section IV illustrates joint DU/CU placement problem in the metro networks. Section V shows the illustrative numerical results. Section VI concludes the work.

Related Works

The problem of baseband functions placement and traffic routing has been investigated in recent years. In traditional C-RAN architecture, authors in [START_REF] Wang | Energy-Efficient Virtual Base Station Formation in Optical-Access-Enabled Cloud-RAN[END_REF] propose the energy-efficient virtual base station (vBS) formation problem, where they combine the virtual passive optical network (vPON) with vBS to form a virtual RAN (vRAN) and minimize the number of active digital units (DUs) in the DU pool and the number of wavelengths in the PON at the same time. In [START_REF] Zhang | Energy Efficient Baseband Unit Aggregation in Cloud Radio and Optical Access Networks[END_REF], a "BBU aggregation" problem is proposed to minimize the number of the active BBUs for energy saving. BBU aggregation is modeled as an evolved 2D bin-packing problem and two heuristics to solve this problem are proposed. Authors in [START_REF] Yu | Energy-efficient dynamic lightpath adjustment in a decomposed AWGR-based passive WDM fronthaul[END_REF] motivate energy-efficient BBU aggregation problem in an AWGRbased passive WDM network. They introduce the AWGR decomposition into the BBU aggregation to help reduce the cost of the tunable transceivers and BBUs.

The problem of BBU placement over a metro/aggregation network was first proposed in [START_REF] Musumeci | Optimal BBU Placement for 5G C-RAN Deployment Over WDM Aggregation Networks[END_REF], where the relation between latency and the consolidation of BBUs is discussed under the OTN and overlay cases separately. In addition to BBU placement problem, BBU pool allocation and selection problem for C-RAN is also proposed in [START_REF] Li | Joint Optimization of BBU Pool Allocation and Selection for C-RAN Networks[END_REF], the authors investigated how to deploy BBU pool among the optical network nodes and how to choose BBU pool to host the BBU of each traffic request with the objective of maximizing traffic acceptance ratio and minimizing network resource usage.

For baseband function placement in a functional spilt RAN architecture, ref. [START_REF] Liu | Graph-based framework for flexible baseband function splitting and placement in C-RAN[END_REF] proposes a graph-based framework for flexible baseband function splitting and placement problem, and determines how to split the baseband function chain for each cell to maximize the utilization of processing resources under the constraint of latency and processing capacity using genetic algorithm. In [START_REF] Xiao | Energy efficient Placement of Baseband Functions and Mobile Edge Computing in 5G Networks[END_REF], the authors propose a fully flexible functional split RAN architecture and define a new baseband entity, called flexible unit (FU). Based on this, they motivate a minimal number of active central office problem through the energy-efficient placement of FUs.

In summary, most existing works consider baseband function placement in the 2-layer RAN, while there are no works providing the analysis of the CU and DU placement problem in 3-layer C-RAN based on the 3GPP standard functional split options and the relation between the consolidation of CU/DU and constraints of latency, network capacity, as the one provided in this paper.

Functional Split based 3-layer C-RAN Architecture

According to 3GPP [START_REF]Radio access architecture and interfaces (Release 14)[END_REF] and other standardization bodies, the 5G RAN architecture has been defined as a 3-layer architecture consisting of a CU, a DU, and a RU. Accordingly, the network between cell sites and mobile core is also divided into three segments: fronthaul, midhaul and backhaul. To address the strict bandwidth and latency requirements in 5G-RAN, 3GPP has proposed multiple functional spilt options, typically listed from option 1 to option 8, as shown in Fig. 2. In this paper we consider that the baseband processing entities (CU, DU and RU) are connected via two interfaces, F1 and Fx, as the split at Option 2 (interface F1) and Option 7 (interface Fx) have been selected by ITU [START_REF] 5gp | 5G Wireless Fronthaul Requirements in a PON Context[END_REF] as the standard split options. According to [START_REF]Functional splits and use cases for small cell virtualization[END_REF], different baseband functions have various characteristics in terms of bandwidth requirement and processing complexity. The bandwidth, processing and latency requirement of CU, DU and RU can be summarized as follows.

Transport bandwidth: In the cell level, the F1 interface scales and dynamically varies with the air interface traffic load, so midhaul bandwidth scales with traffic load as backhaul and requires only slightly more bandwidth than backhaul. The fronthaul bandwidth at Fx also varies with the air interface traffic load but requires higher rates (typically by up to an order of magnitude compared to backhaul). In the user level, the bandwidth requirement of a user is related to the resource blocks (RB) occupied by this user in the carrier spectrum. Processing complexity: The processing complexity of baseband functions can be measured in Giga Operation Per Second (GOPS) [START_REF] Debaillie | A Flexible and Future-Proof Power Model for Cellular Base Stations[END_REF]. The processing complexity of channel estimation, resource (de)mapping, FFT/IFFT is related to carrier bandwidth and number of antennas (called cell-processing functions), whereas the processing complexity of MAC/RLC/PDCP layer and the other functions in the PHY layer are related also to the traffic load besides carrier bandwidth and number of antennas (called user-processing functions). According to 3GPP [START_REF]Radio access architecture and interfaces (Release 14)[END_REF], for option 2, RRC and PDCP are in the CU, while RLC, MAC, part of physical layer are in the DU. For the option 7 OFDM and MIMO precoding reside in the DU, FFT, resource mapping and RF resides in RU. So the processing complexities of DU and CU are all user load dependent. The details for the calculation of bandwidth requirement between CU, DU, RU and processing complexity of each entity used in this paper can be found in [START_REF]Functional splits and use cases for small cell virtualization[END_REF].

Transport latency: Transport latency requirements for backhaul and midhaul links are determined by service latency requirements, i.e. around 10 msec for eMBB, about 1 msec for URLLC and ranging from 1 msec to several 10 msec for mMTC [START_REF] Nokia | White Paper 5G new radio network[END_REF]. For the fronthaul links at Option 7, the latencies are determined by the requirements of the RAN technology. To satisfy the HARQ processing latency requirement, a total round-trip latency budget of RTT BBU -RRH = 3 ms is available between a BBU and its corresponding RRH. It means that the NACK/ACK should be transported on the fronthaul link within hundreds of microseconds [15]. As we know the HARQ processing function is located in the low-MAC layer and MAC layer is in the DU, so latency requirement between DU and RU should be the same as HARQ processing latency requirement. According to [START_REF] Netmanias | Fronthaul Size: Calculation of maximum distance between RRH (at cell site) and BBU (at CO)[END_REF], the reference values of the latency in different parts of networks are given as follows:

-Signal processing latency: The BBU completes the processing and send ACK/NACK usually within 2.75 msec. In the 3-layer architecture, no matter where the DU and CU are placed, the total processing can be seen as a fixed value. or receive the data, the data must be encapsulated or de-encapsulated with CPRI protocol. This procedure will cost around 10 μsec.

Joint DU/CU Placement in Metro Networks

Problem Statement

The DU/CU placement problem over metro/aggregation networks can be stated as follows. Given network topology, number of wavelengths per link and their line-rate capacity, set of traffic requests, maximum fronthaul latency (HARQ latency) and service latency, decide the placement of DUs and CUs in different COs that maximizes the consolidation of the baseband processing functions (i.e., minimizes the number of CO housing processing) under latency and capacity constraints.

The placement of CU/DU is not only restricted by the processing capacity and network capacity, but also subjected to the RAN latency and service latency constraints. Fig. 3 shows an example of CU/DU placement with two service requests from different cell sites. For service 1, the DU and CU are placed in main COs for a higher consolidation, whereas for service 2, restricted by the bandwidth capacity, the DU of service 2 must be placed in the access CO. Next, we will show the mathematic model of the DU/CU placement problem.

Model

1) Given sets and parameters

Y s,n i = K s,i , if n= 1 1, if i = dest, n = N , ∀s ∈ S, i ∈ V, N ∈ N (2) n∈N,i∈V,w∈W X i,k,w s,n - n∈N,j∈V,w∈W X k,j,w s,n = ⎧ ⎨ ⎩ -1, if K s,k = 1 1, if k = 1 0, otherwise ∀s ∈ S, k ∈ V, l ∈ L (3)

Baseband function placement:

Y s,k r j∈V,w∈W,k l N -1 X i,j,w s,n • M r,j Y s,k i , ∀s ∈ S, k ∈ N, r ∈ V, K s,r = 1 (4) 2Y s,k r i∈V,w∈W,0 l k-1 X i,r,w s,l • M i,r + j∈V,w∈W,k h N -1 X r,j,w s,h • M r,j Y s,k r + 1, ∀s ∈ S, k ∈ N, r ∈ V, K s,r = 1 (5) D i s∈S,n∈N Y s,n i Max • D i , ∀i ∈ V (6) i∈V Y s,n i = 1, ∀s ∈ S, n ∈ N (7) H s,r n∈N Y s,n r Max • H s,r , ∀s ∈ S, r ∈ V (8) Capacity: s∈S,n∈N G n • Y s,n i C i p , ∀i ∈ V (9) s∈S,n∈N B n • X i,j,w s,n C w , ∀i, j ∈ V, i = j, w ∈ W ( 10
)

Latency:

i,j∈V,w∈W T i,j • X i,j,w s,0

T HARQ , ∀s ∈ S [START_REF] Xiao | Energy efficient Placement of Baseband Functions and Mobile Edge Computing in 5G Networks[END_REF] i,j∈V,n∈N,w∈W

X i,j,w s,n • T i,j + r∈V H s,r • T oe T s , ∀s ∈ S ( 12
)
Additional bandwidth capacity constraint for overlay network:

s∈S,n∈N X i,j,w s,n 1, ∀i, j ∈ V, w ∈ W (13)
Eqns. ( 2), (3) enable the routing of requests over the lightpaths, the source/ destination of a request is given and the baseband functions are flexibly placed in the intermediate nodes. Eqns. ( 4) and ( 5) restricts the services starting from the source node of a request and the links between the intermediate nodes. Eqn. [START_REF] Zhang | Energy Efficient Baseband Unit Aggregation in Cloud Radio and Optical Access Networks[END_REF] indicate that if the CO i is active. Eqn. [START_REF] Yu | Energy-efficient dynamic lightpath adjustment in a decomposed AWGR-based passive WDM fronthaul[END_REF] ensures that one baseband processing entity must be located in only one CO. Eqn. [START_REF] Musumeci | Optimal BBU Placement for 5G C-RAN Deployment Over WDM Aggregation Networks[END_REF] indicates that if the service is processed in the CO r. Eqns. [START_REF] Li | Joint Optimization of BBU Pool Allocation and Selection for C-RAN Networks[END_REF][START_REF] Liu | Graph-based framework for flexible baseband function splitting and placement in C-RAN[END_REF][START_REF] Xiao | Energy efficient Placement of Baseband Functions and Mobile Edge Computing in 5G Networks[END_REF] is the capacity constraints of processing and bandwidth. Eqn. [START_REF]Radio access architecture and interfaces (Release 14)[END_REF] ensures that the placement of DU is restricted by the HARQ processing latency. Eqn. ( 13) is for the service latency. Eqn. ( 14) is the additional bandwidth constraint for the overlay solution. 5 Illustrative Numerical Results

Evaluation Settings

We consider a 15-node WDM metro/aggregation network topology as shown in Fig. 4, under three different geographical type areas (geotypes) -Dense urban, Urban, and Sub-urban -with 32 cell sites distributed in that area. The total area of cell sites for different geotypes and the total number of users in the corresponding area are shown in Table 1 [START_REF]Analysis of Transport Network Architectures for Structural Convergence, COnvergence of fixed and Mobile BrOadband access/aggregation networks-COMBO Project[END_REF]. For the cell site, we assume a radio configuration with 20 MHz, 2x2 MIMO antenna, 64QAM modulation scheme and full system load, and the reference value for processing complexity [START_REF] Debaillie | A Flexible and Future-Proof Power Model for Cellular Base Stations[END_REF] of different baseband entities and bandwidth requirements [START_REF]Functional splits and use cases for small cell virtualization[END_REF] of different network segments for the mentioned radio configuration is shown in Table 2. We assume that the resource blocks of a cell are uniformly allocated to all users, that are normally distributed in the whole area, so the processing complexity and bandwidth requirement is equally divided by all the users associated with the same cell site. For the transport network, the COs in different stages are equipped with different levels of baseband processing and switching capacity. COs are organized in a ring topology and are connected via bidirectional monofiber links, carrying W wavelengths at 10Gb/s. For the latency constraint, according to [START_REF] Netmanias | Fronthaul Size: Calculation of maximum distance between RRH (at cell site) and BBU (at CO)[END_REF], maximum HARQ latency (RU-DU) is set to be 246 μs and maximum service latency is set to be 1000 μs. When below 246 μs, the HARQ latency requirement and service latency requirement are equal, and when above 246 μs, the HARQ latency is fixed at 246 μs. We define a performance metric R, called consolidation factor, which is used to evaluate multiplexing gain of function in our simulation. R = N co /N cs , N co is the numbers of active COs and cell sites, N cs is the number of cell sites. R=1 indicates no consolidation, that is all the baseband functions are located in the cell sites, whereas 1/N cs indicates the highest consolidation degree.

Evaluation results

Fig. 4(a) shows the relationship between R and service latency requirement T s , for the 2-layer and 3-layer RAN architecture (left and right bars, respectively), when considering overlay transport technology, urban geotype case and actual processing capacity set to be 75 % of maximum processing capacity. The value of R represented as the sum of four contributions, corresponding to consolidation degree in each stage of the network. With the increase of T s , CUs and DUs can be consolidated in fewer COs to minimize the number of active COs, due to the fact that less stringent latency requirement allows the services to route along a longer path and end up in the COs of higher stages. For example, when the T s ≥ 600 μs, there is no baseband function located in the cell sites (red color). We can also find that R value of 3-layer RAN architecture is less than the one of 2-layer RAN architecture, because flexible functional split divides the traditional BBU into multiple parts which can be deployed into COs more flexibly.

Fig. 4(b) shows R as a function of Q = GOPS a /GOPS m for the different geotypes and RAN architectures when considering T s = 800 μs and overlay case. GOPS a /GOPS m is the total actual processing capacity of all the COs divided by the maximum processing capacity in the networks. We can observe that higher consolidation is obtained when Q is increasing, especially for the suburban case. Because with the increasing processing capacity of COs, the DU and CU can be finally placed in the main or core COs when the latency requirement is relatively relaxed. For example, when Q goes near to 1, the value of R reaches the lowest level among almost all the scenarios. Note also that, due to the lower number of requests in the suburban area, the DUs/CUs are more easily deployed in the COs of higher stage. From this result, we can also find that 3-layer architecture benefits more in terms of consolidation that 2-layer architecture because of the flexibility in placement.

Fig. 4(c) shows the relationship between R and network capacity in terms of number of wavelengths W . We can find that the relation between R and la-tency depends on the bandwidth constraint. When the number of wavelengths is limited, no matter how loose the maximum latency requirement is, consolidation factor R will not decrease when it arrives at a critical point. This can be explained since when if enough wavelengths are provided, the provision of baseband functions can be more flexible; whereas if the bandwidth between different COs is limited, the location of baseband functions tends to be closer to the cell sites.

Conclusion

In this work, we have modeled an optimized DU/CU placement problem for C-RAN deployment over a WDM metro/aggregation network and formalized it into an ILP model. Compared to the original 2-layer RAN architecture, we proved that the 3-layer RAN architecture has higher consolidation of baseband functions thanks to the increased placement flexibility. We also observed that: 1) looser latency constraint leads to a high degree consolidation of baseband functions; 2) the processing capacity of COs also influences the consolidation of baseband functions; 3) adopting overlay transport solution can lead to a higher baseband function consolidation. In this work, the functional split options between RU, DU and CU are fixed. In the future, we will investigate the DU/CU placement problem when the functional split options is flexible, so the relation between flexible DU/CU placement and flexible functional split option needs to be jointly evaluated. Also, the heuristics for this problem will be proposed for the realistic scenario with larger network topology. Moreover, compared to the static DU/CU placement, dynamic DU/CU allocation problem according to real-time service requests from mobile users is worthy to be investigated.

Fig. 2 :

 2 Fig. 2: Example of Function Split Options

Fig. 3 :

 3 Fig. 3: Illustration of possible baseband function placement

Fig. 4 :

 4 Fig. 4: (a) R value for increasing T s , and different RAN architectures (2-layer vs 3-layer, Q = 75%); (b) R values for increasing Q under different geotypes (overlay case; latency = 800 μs); (c) R values for the increasing W (OTN case; Q = 50%)

  : 1, if the baseband processing functions (either CU or DU) are placed in CO i, otherwise 0 H s,r : 1, if the service s is processed in the CO r

	V: set of COs
	S: set of service requests
	N: set of processing elements: RU, DU, CU, server C i p : processing capacity of COs i(GOPS)
	C w : bandwidth of wavelength (Gbps)
	G n : computing resource requirement of baseband function n
	B n : bandwidth requirement between baseband function n and n+1 T i,j : transport latency between CO i and j
	T oe : latency for switching and encapsulation
	T 3) Objective
	Minimize the number of active COs:
	min{	i∈V	D i }	(1)
	4) Constraints
	Routing:

HARQ : latency requirement for HARQ processing T s : latency reqirement for service request K s,i : service s accessed into CO i Max: a large positive value 2) Decision Variables Y s,n i : 1,if the function n of service s is located in CO i, otherwise 0 X i,j,w s,n : 1, if the function n and n+1 of service s is located in the CO i,j separately using wavelength w D i

Table 1 :

 1 No. Users of the Considered Geotypes

		Dense Urban Urban Suburban
	Total Area of 32 sites [km 2 ]	8	22	160
	Total Number of Users	2.4 × 10 4	2.2 × 10 4 8 × 10 4

Table 2 :

 2 The value of processing complexity (GOPS) and bandwidth requirement (Gbps) with radio configuration of 20 MHz, 2×2 MIMO, 64QAM (Downlink)

	Baseband entities Value Network Segment Value
	RU	48.1	fronthaul	0.97
	DU	9.1	midhaul	0.299
	RU	18.7	backhaul	0.299

Acknowledgment

This work was supported by the National Nature Science Foundation of China Projects (No. 61871051, 61771073), the Nature Science Foundation of Beijing project (No. 4192039), the fund of State Key Laboratory of Advanced Optical Communication Systems and Networks, China, No.2019GZKF5, and China Scholarship Council Foundation.


Hilary Frank
email: hilary.frank@bristol.ac.uk

Rodrigo S Tessinari

Yuqing Zhang

Zhengguang Gao

Carlos Colman Meixner

Shuangyi Yan

Dimitra Simeonidou

Resource Analysis and Cost Modeling for End-to-End 5G Mobile Networks

Keywords: 5G, Capex, Opex, TCO, End-to-End, Fiber, Microwave, CRAN, Backhaul, and Core Network

5G network demands massive infrastructure deployment to meet its requirements. The most cost-effective deployment solution is now a challenge. This paper identifies a cost implementation strategy for 5G by reformulating existing cost models. It analyses three geo-type scenarios and calculates the total cost of ownership (TCO) after estimating the Capex and Opex. The calculations are narrowed to specific cities for clearer understanding instead of the usual generic estimates. An end-to-end 5G network resource analysis is performed. Our result shows that by the end of first year Capex constitutes over 90% of TCO for urban scenarios. Also uniform capacity deployment across geo-types impose severe investment challenges.

Introduction

The growth of mobile communications since inception in the 1980s indicates that capacity is increasing along with rising demands for higher data rates. This trend has now witnessed four generations of mobile networks. Current research anticipates the next generation of mobile networks (NGMN) around 2020 [START_REF] Frank | Mobile Networks Beyond 4G[END_REF]. The rate of revenue growth from wireless networks has not been proportional to the exponential increase in the networks over the years. Telecommunication companies in the UK suffered revenue fall in 2017 [2] despite raising demand. The impact of continuous traffic upsurge on network infrastructure has been a challenge for Mobile Network Operators (MNOs) [START_REF]5G Infrastructure Requirements in the UK[END_REF]. Balancing the capacity needs of the networks with profitability is now a growing source of concern for MNOs.

MNOs must devise innovative ways to bring down cost while providing enhanced services to customers [START_REF] Checko | Cloud RAN for mobile networks -A technology overview[END_REF]. The crucial challenge of realizing 5G is becoming more economic than technological [START_REF] Charni | Total cost of ownership and risk analysis of collaborative implementation models for integrated fiber-wireless smart grid communications infrastructures[END_REF].

It is important that suitable cost models are devised and applied to ensure an efficient use of resources to optimize Capital expenditure (Capex) and Operational expenditure (Opex). A detailed discussion on the TCO model for backhaul deployment was done by [START_REF] Mahloo | Cost modeling of backhaul for mobile networks[END_REF]. The study identified critical cost factors in order to achieve a cost-efficient strategy after considering two technology options: fiber and microwave. Our study shares some similarities with this work as it relates to cost models for wireless network. We extended the analysis to cover an endto-end of the network and narrowed our discussion to three geo-type scenarios.

The idea of Centralized or Cloud Radio Access Network (CRAN) has been proposed by many studies. [START_REF] Andrade | Cost models for baseband unit (bbu) hotelling: From local to cloud[END_REF] shows that centralized Baseband Unit (BBU) is a viable option to save cost. Their considerations comprise cost comparisons in relation to baseband pooling and virtualization gains. This method is important for cost reduction towards TCO. But our analysis extend beyond the CRAN to encompass the entire mobile network end-to-end. We explored the deployment of 5G network by analyzing the key performance indicators. The number of small cells and macro cells were calculated for our case study cities -Lucca, Bristols and London.

Our paper reformulated earlier models to estimate the Capex, Opex, and TCO for the different geo-type scenarios. Some assumptions were considered in applying our model. Based on the results we recommend a 5G deployment strategy that would improve network cost efficiency.

The rest of the paper is structured as follows. Section 2 describes 5G Networks in detail. In Section 3, we present our cost model with analysis on the different aspects of the formulations. In Section 4 our case study is discussed with results while Section 5 concludes the paper and presents our future work. To achieve the target of 1000x capacity, 5G networks will adopt ultra-dense small cell, millimeter wave (mm-wave), and massive MIMO [START_REF] Frank | Interference mitigation for femto deployment in next generation mobile networks[END_REF]. The NGMN would converge diverse technology types to deliver the key performance indicators (KPIs) as shown in Table 1. It describes 5G disruptive potentials and the superior KPIs.

Wireless Access Networks in 5G

5G will consist of 3 spectrum layers namely -Lower, Middle and Upper frequency bands, corresponding to 700MHz, 3.5GHz and 26GHz respectively. The use of higher frequency for future mobile networks has become imperative for small cells. The mm-wave spectrum range of 30GHz to 300GHz is attractive for 5G cost reduction strategy because it opens more room for spectrum and permits higher data rates [START_REF] Siddique | Wireless backhauling of 5G small cells: challenges and solution approaches[END_REF]. However, mm-wave suffers increased path loss beyond 200m [START_REF]5G Infrastructure Requirements in the UK[END_REF].

Experimental results show that the compression of higher order antenna elements against the shorter wavelength of the mm-wave bands compensates for the path loss. Massive antenna elements are projected to be as much as 10x the number of streams in service to all terminals, compared to present MIMO [START_REF] Frank | Interference mitigation for femto deployment in next generation mobile networks[END_REF].

Cloud Radio Access Networks

The concept of Cloud or Virtualized RAN is one that basically divides the functions of the gNodeB (gNB) and centrally positions it at greater distance (up to kilometers) from the Remote Radio Head (RRH), to a shared pool of virtualized BBU [START_REF] Checko | Cloud RAN for mobile networks -A technology overview[END_REF]. This increases spectral efficiency, throughput and reduces equipment and power cost at cell sites. In 5G New Radio (NR) transport architecture, BBU is split into RRH, Distributed Unit (DU) and Central Unit (CU). CRAN is viewed as an enabler for 5G dense networks. It benefits the ultra-dense cell structure by the avoidance of inter-cell interference through centralized management and distribution of intelligent resource [START_REF] Taufique | Planning wireless cellular networks of future: Outlook, challenges and opportunities[END_REF]. 5G Fronthaul and Midhaul have evolved with the concept of CRAN. The portion of wireless architecture referred to as fronthaul is the link between DU or radio controller and the RRHs. The DU interfaces with the RRH through an optical fiber connection called enhanced Common Public Radio Interface (eCPRI). The eCPRI link forms the fronthaul of the Network as Fig. 1 shows. This imposes strict latency and synchronization requirements [START_REF] Jaber | 5G backhaul challenges and emerging research directions: A survey[END_REF] [START_REF] Lisi | Cost-effective migration towards C-RAN with optimal fronthaul design[END_REF]. Different options of functional splits are now being proposed [START_REF] Pelekanou | Provisioning of 5G services employing machine learning techniques[END_REF].

According to [START_REF] Checko | Cloud RAN for mobile networks -A technology overview[END_REF], BBU centralization can provide as much savings as 50% Opex and 15% Capex. Also, MNOs expend as much as 80% Capex on RAN. This implies that gNB infrastructure constitute significant cost component for RAN [START_REF]5G Infrastructure Requirements in the UK[END_REF], which could reduce considerably with the use of CRAN and substantially decrease TCO.

Multi-access Edge Computing

Multi-access Edge Computing (MEC) is an innovative concept that converges telecom and information technology applications by orchestrating cloud-based services at the edge of computing networks [START_REF] Taleb | On multiaccess edge computing: A survey of the emerging 5G network edge cloud architecture and orchestration[END_REF]. MEC run applications nearer the edge of the network. It brings the system closer to the end users and hence reduces latency, network congestion and creates an efficient backhaul and core networks. 5G latency dependent applications and services would benefit from this strategy, when distributed around the network edge. MEC is a promising innovation for 5G success and would reduce the cost of its implementation.

Backhaul for 5G Network

Backhaul or transport network, is the connection that transports data between the CU and 5G Core based on the N2 and N3 interfaces. The backhaul link is dimensioned to meet the required peak data rates and high-speed applications. This connection can be either wired or wireless. Different backhaul solutions include microwave, fiber optics, meshed wireless, copper cable and Free Space Optical communication (FSO). Contemporary 4G networks mostly use either fiber or Line of Sight (LOS) solutions.

The topology of fiber backhaul deployment has a structure of either in a tree or point-to-point (PtP) topology. In PtP the central office (CO) connects one optical line terminal (OLT) through a devoted fiber to an optical network unit (ONU) in the user/client premises. These devices perform signal conversions from electrical to optical and vice versa.

In a tree-based approach, such as Passive Optical Network (PON) or Active Optical Network (AON), one OLT is linked to multiple ONUs through splitting and switching devices located in street cabinets [START_REF] Mahloo | Cost modeling of backhaul for mobile networks[END_REF]. Fiber optics are transmitted across long distances starting from the transponder and existing the node at designated port. Amplifiers are installed about every 80 km to amplify fiber links that suffers attenuation over those distances.

The expected huge data traffic from 5G ultra-dense small cells that would be connected via the backhaul to the core network imposes extreme requirements in terms of capacity, energy, latency, and cost [START_REF] Jaber | 5G backhaul challenges and emerging research directions: A survey[END_REF]. It becomes important to devise innovative backhaul provisioning to cater for these extreme requirements.

Core Network

The Core Network is the control hub of a telecom network infrastructure. Mainly it performs aggregation, authentication, charging, service invocation and gateway functions. This involves the control plane such as the Access and Mobility Management Function (AMF), Session Management Function (SMF) or Authentication Server Function (AUSF) and the data plane involving User Plane Function (UPF).

Two key innovations are being proposed that are timely for 5G network architecture. These are software defined networking (SDN) and network function virtualization (NFV) [START_REF]5G Infrastructure Requirements in the UK[END_REF]. SDN basically separates the forwarding of data function from the control using software. This makes a dynamic architecture that is much easier to adapt, manage and cost-effective to implement [START_REF] Jaber | 5G backhaul challenges and emerging research directions: A survey[END_REF]. New developments are likely to come about due to SDN capabilities, one of which is the possibility of a reduced core network infrastructure [START_REF]5G Infrastructure Requirements in the UK[END_REF].

NFV technology enables key network functions to be executed in software environment by enabling scalability and flexibility in programmable network slices. NFV creates the possibility of shorter deployment time and the use of commercial off the shelf (COTS) based solutions instead of proprietary hardware that are usually vendor specific [START_REF]5G Infrastructure Requirements in the UK[END_REF]. The availability of COTS solutions will lead to reduce deployment cost.

5G Use Cases

The NGMN will witness much higher bandwidth with lower latency and massive interconnection of devices. The use cases can be classified into three main categoriesmassive Machine Type Communication (mMTC), enhance Mobile Broadband (eMBB) and Ultra-Low Latency Communications (URLLC). Most of these 5G use cases depend on computing intelligence requiring sensor networks and driven by virtual reality and tactile internet. The capabilities of these uses cases are described in Table 1. Their implementation would pave the way for diverse business concepts at various levels of connectivity [START_REF] Agyapong | Design considerations for a 5G network architecture[END_REF]. This will enrich the prospects of commercial involvement in the deployment of the NGMN.

Cost Model

The 5G objective calls for considerable planning. The usual resource over-provisioning strategy often result in network resource under utilization and high energy consumption [START_REF] Charni | Total cost of ownership and risk analysis of collaborative implementation models for integrated fiber-wireless smart grid communications infrastructures[END_REF]. We devised our model based on the following assumptions:

Capacity Planning Estimation

The network coverage and capacity analysis will include the following, type of information, coverage area available spectrum, subscriber forecast and traffic density. The demographics for the three cities in our case study from where other calculations such as cell range, number of cells, users per cell arise are presented in Table 2.

Coverage, Cell Site and Traffic Capacity (TC) Calculation

Area of the hexagonal shape is given by the following equation:

3 √ 3 /2 .d 2 (1)
TC = Pop. density x 10% subscription x 5% usage x data rate Hence number of small and macro cells for coverage, traffic capacity and mean traffic capacity are shown in Table 2.

The mean traffic capacity per user (MTC) equals to the cell capacity divided by the number of users. MTC is approximately 500 Mbps.

Total Cost of Ownership

Our research calculates the total cost of 5G deployment to equal the summation of the total cost of Capex and Opex. A cost model summary of non-sharing infrastructure is presented

TCO 5G = N c i=1 Capex 5G + N o i=1 Opex 5G [/yr /i n f l] N yr s
(2) The Total Cost of Ownership for 5G network consist of Capex and Opex for the end-to-end stretch of wireless network. Reflecting the network portions in the TCO is given as follows

TCO 5G =
TCO = Capex [Acc+BH+C N ] + Opex [Acc+BH+C N ] (3)
Where Acc, BH and CN denotes the Access, Backhaul and Core portions in the wireless network. Our model performs joint calculations for the Access and Backhaul segments of the network, particularly for some Opex cost factors such as energy consumption, maintenance and reparation cost. This is an error avoidance strategy. At points of convergence, such as cabinets, the distinction between Access and Backhaul for the purpose of Opex calculation diminishes greatly. In calculating the cost of Core network upgrade, we followed [START_REF]5G Infrastructure Requirements in the UK[END_REF], which assumes 10% of RAN deployment cost as the cost of Core network upgrade.

Capex calculations

Capex is the capital expenditure which refers to a one-off-investment cost used to acquire or upgrade physical assets or infrastructure. Our formulation comprises the summation of equipment, infrastructure and installation cost plus spectrum licence fee.

Capex = N E q i=1 Cost Eq + N I n f r a i=1 Cost I n f r a + N I nst a i=1 Cost I nst a + N L i=1 Cost L f ee (4)
Equipment cost This refers to all cost connected to the acquisition of equipment both for fiber and microwave cost components. Fiber and microwave equipment cost are modelled as follows

Cost F Eq = N O LT i=1 Cost OLT + N O N T i=1 Cost O NT + N s i=1 Cost s ( 5
)
Cost M w Eq = 2N M wlink .Pr ant + N sw .Pr sw [START_REF] Mahloo | Cost modeling of backhaul for mobile networks[END_REF] Equation 4 follows that of [START_REF] Mahloo | Cost modeling of backhaul for mobile networks[END_REF]. Where Cost OLT , Cost O NT and Cost s denotes cost of OLTs, ONTs and Splitters. Also, N M wlink , Pr ant , N sw and Pr sw represents the number of links used for microwave, antenna price, number of switches and unit price of switches.

Infrastructure cost This refers to the total cost needed to deploy or lease communication infrastructure. We have associated fiber cost to the infrastructure component because the fiber length determines the duct and trenching length. It works better when these components are factored in common. On the part of microwave, the infrastructure cost include cost associated with microwave hubs, masts and antennas.

Cost F I n f r a = L. (Cost F + Cost CW ) (7)
Where L denotes length of trenches, whereas Cost F and Cost CW represents cost of fiber and civil works. The formulation for microwave is as follows

Cost M w I n f r a = N hu b i=1 (N M whub .Pr hub ) (8)
Where N M whub denotes number of microwave hubs and Pr hub its unit price.

Installation cost

The installation component captures man-hours required to perform the necessary installations, wiring, preparation of sites, technician salary and travel time to and from site locations. The formulation is given by [START_REF] Charni | Total cost of ownership and risk analysis of collaborative implementation models for integrated fiber-wireless smart grid communications infrastructures[END_REF].

Cost I nst a = N l i nk i=1 (IT i + 2T i ) .T S NT i (9)
Where IT i and T i , denotes installation and travel time, TS and NT i represents technician salary and number of technicians respectively.

Opex calculations

Opex translates to operational expenditure, which means the recurring cost needed to continuously operate the business daily. One of the key cost components for network operators is power consumption. We have formulated our Opex cost by remodelling that given by [START_REF] Chiaraviglio | Bringing 5g into rural and low-income areas: Is it feasible?[END_REF]. The major Opex cost components are energy consumption, maintenance and fault management or reparation cost. Our model for the Opex calculation is given as follows

Opex = 365 N i=1 (24P h .C E ) .N C + N m i=1 C M .C F c (10)
Energy consumption Electricity consumption is an important Opex cost driver. Between 70% -80% of energy requirement of the network is projected to be consumed by the access network [START_REF] Agyapong | Design considerations for a 5G network architecture[END_REF]. In view of the expected ultra-dense network, innovative energy management schemes are needed to cut operating cost of 5G network. We have derived the energy cost by adding the consumption cost of every electrical equipment in the different locations within the network such as those in the central office, cell sites and street cabinets.

Cost E n = 365 N i=1 24P h .C E .N C (11)
Where P h , C E and N C represents electric power needed per hour, cost of one kWh of energy and number of cabinets, which in this case could mean, Central Office, cell sites or street cabinet.

Maintenance expenses are regularly incurred to keep the network running at optimal performance. This may consist of routine system upgrade, equipment testing, and software licence renewal among others. Our maintenance cost model is given by [START_REF] Mahloo | Cost modeling of backhaul for mobile networks[END_REF].

Maintenance cost

Cost M = N i=1 (Co m + Cab m + M M w + Sw lic ) (12)
Where Co m , Cab m and M M w denotes the cost incurred from maintaining central offices, street cabinets and microwave links. Sw lic reflects licence fee for periodic software upgrade. Details of this formulation can be obtained in [START_REF] Mahloo | Cost modeling of backhaul for mobile networks[END_REF].

Fault management/reparation cost Reparation of system failures such as fiber cut, and other natural or man-made faults incur cost. We have remodelled this cost component to reflect the probability of failure employing the Weibull distribution which is mainly applied in reliability engineering from [START_REF] Charni | Total cost of ownership and risk analysis of collaborative implementation models for integrated fiber-wireless smart grid communications infrastructures[END_REF].

Cost F m = N i=1 (F R + Pen) P f (13)
Where FR and Pen denotes failure reparation and penalty cost respectively. P f represents probability of failure following Weibull's distribution.

F R =       N f i=1 MTT R f + 2T i .T S       NT R f (14)
Where MTT R f reflects mean time to repair failure and NT R f denotes number of people to repair failure. Further details can be obtained in [START_REF] Charni | Total cost of ownership and risk analysis of collaborative implementation models for integrated fiber-wireless smart grid communications infrastructures[END_REF].

Case Study

Table 3 presents cost values used.

Our result in Fig. 2 (a) shows that fiber is consistently the most capital intensive cost factor in all scenarios. The result reveals significant cost difference between fiber and microwave for Lucca than Bristol and London. Whereas the later two cities have 16% and 21% difference respectively, Lucca has as much as 56%. It is relatively more expensive to deploy fiber in Lucca than in the other two cities. This identifies the most cost-effective backhaul deployment for the NGMN.

The cost breakdown in Fig. 2 (b) presents infrastructure as the most dominant cost component constituting at least 30% of TCO in all scenarios.

The TCO as in Fig. 2 (c) shows that London has the highest deployment cost and Lucca the lowest. Bristol has the lowest cost per user, which validates the result that Lucca is relatively more expensive in comparison. Also Lucca with approximately 1% of London's population requires as much as 12% of London's TCO. This is due to the role of area and population density in the economies of scale.

Fig. 2 (d) shows the result of three comparisons. The ten years Opex has been calculated with compounding inflation rate. It shows that capital expenditure constitutes over 90% of TCO for Bristol and London by the end of first year, while Lucca's operational expenditure was as much as 15% for the same period. But after ten years, while Opex was still below Capex by 12% for Bristol and 10% for London, Lucca's Opex exceeds Capex by 50%. This trend depicts increasing operational expenditure cost as population density of the scenario decreases.

Conclusion and Future Work

We conducted an end-to-end analysis of 5G architecture. Given the 5G KPI's, we also calculated capacity requirements for three selected cities, including the number of small cells, macro cells and traffic capacities. We reformulated exiting cost models to estimate the total cost of ownership by calculating Capex and Opex for the different segments of the wireless network.

Based on the results, we conclude that investment consideration should be a function of the geo-type scenarios. As a result, 5G system capacity should be adjusted in less densely populated areas to allow for profitable deployment. In such areas wireless backhaul option becomes a compelling economic choice. Consideration should be given to a capacity trade-off in favour of coverage. However, the benefits accruable to a network when ubiquitous services are rendered should not be overlooked.

As future work, we intend to investigate the impact of infrastructure sharing in under neutral host concept. We also aim at revenue estimation for a projected number of years and make similar comparisons between the different scenarios. Finally, we aim to investigate the effects of application related cost on cost savings and revenue forecast for the NGMN.

Fig. 1 .

 1 Fig. 1. End-to-End 5G Mobile Network Architecture

  Total cost of 5G network deployment Capex 5G = Sum of capital expenditures Opex 5G = Sum of operational expenditures plus inflation N yr s = Number of years used for Opex calculation

Fig. 2 .

 2 Fig. 2. (a) Capex comparison for fiber and microwave. (b) TCO breakdown across all scenarios. (c) TCO and cost per population density comparison showing Bristol with a higher TCO but much lower cost per population density than Lucca. (d) Capex, 1st year Opex, and 10 years cumulative Opex comparison.

Table 1 .

 1 5G Disruptive Capabilities[START_REF]5G Infrastructure Requirements in the UK[END_REF][START_REF] Agyapong | Design considerations for a 5G network architecture[END_REF]

	KPI	Requirement	Description
	Peak data rate	≥ 10 Gbps	Low mobility
	Peak data rate	≥ 1 Gbps	High mobility
	Availability	99.999%	Reliability
	Data traffic density ≥ 10 Tbps/km 2 Network throughput per km 2
	Device density	≥ 1 Million/km 2 Connected devices per km 2
	Energy consumption ≤ 10% of 4G	Total energy consumption
	Latency	<1ms	10x reduction in 4G latency
	Mobility	Up to 500 km/h Speed between Rx and Tx
	Network Opex	≤ 20% of 4G	Total network management
			Opex

Table 2 .

 2 Demographic, cell site and traffic capacity calculations

		Lucca Bristol London
	Population	92,155 452,790 8,850,000
	Area (km 2 )	185.5 110.0 1,572.0
	Population Density (per km 2 )	496	4116	5629
	User Density (per km 2 )	50	412	563
	Traffic Capacity (Gbps per km 2 ) 25	206	282
	Mean Traffic Capacity (Mbps) 510	500	501
	Number of Users per Cell	4.9	41.2	56.3
	Small Cell (SC)	1850 1100	15720
	Macro Cell (MC)	71	42	605

-5% of subscribers simultaneous usage of network; -50:50 wired to wireless backhaul deployment ratio; -2.5% annual inflation rate; -Fiber deployment option: cascaded splitter; -Cost of Core network upgrade is 10% of RAN deployment cost

[START_REF]5G Infrastructure Requirements in the UK[END_REF]

; -Small and Macro cell radius 200 m and 2 km.

Table 3 .

 3 Values used for cost calculations

	Components / parameters	Price (Euros) Source
	OLT core shell	5000	[17]
	OLT cross connect	8000	[17]
	OLT service shell	5000	[17]
	ONT	150	[17]
	Technician salary (hour)	52	[6]
	Small / large microwave antenna 200 / 2000	[6]
	Power splitter (1:16 / 1:32)	170 / 340	[6]
	Fiber (km)	80	[6]
	Trenching (km)	45000	[6]
	Microwave link	400	[13]
	Yearly cell site rent	8000	[13]
	Microwave hub	800	[13]
	Electricity cost	0.2 per kWh [16]
	Energy consumption per hour	1.4 kW	[16]

Acknowledgments

We thank TETFUND, Ken Saro-Wiwa Polytechnic, Nigeria, EU H2020 Metro-Haul and 5GCity grant agreement No. 761727 and No. 761508 for their support.