Cache-enabled Software Defined Heterogeneous ...

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Cache-enabled Software Defined Heterogeneous Networks for Green and Flexible 5G Networks Jiaxin Zhang, Xing Zhang, Senior Member, IEEE and Wenbo Wang, Senior Member, IEEE

Abstract—The network densification of small cells (SCs) is a promising way to cope with the explosive growth of future traffic demands in 5G networks. However, the overall power consumption and backhaul limitation of the network have become the key factors affecting the network performance and users’ quality-ofexperience, which have great importance in 5G wireless networks. Due to the complexity of 5G networks and the variety of user behaviors, the combination of software defined networks and content delivery strategy could be a more efficient way to manage such networks. In this paper, a cache-enabled wireless heterogeneous network with the control-plane (C-plane) and userplane (U-plane) split is proposed, where the macro cell and SCs with different cache abilities are overlaid and cooperated together in the backhaul scenario. Using an evaluation tool composed of stochastic processes and classical power consumption model, key performance indicators, e.g., the coverage probability, throughput and energy efficiency (EE), are derived as closed-form expressions or functions of the signal-to-interference-plus-noise ratio (SINR) threshold, path loss exponent, transmission power and density of macro and SCs, cache ability, file popularity and backhaul capacity. Fundamental trade-offs are illustrated between EE and transmission power, EE and SC density, as well as the throughput and density of SCs. Numerical results show that the proposed cache-enabled software defined networks have much higher throughput and improved EE than current LTE networks, which shows a promising solution for future cellular networks. Index Terms—Cache-enabled networks, software defined networks, green communications, spectral and energy efficiency, coverage probability, trade-off

I. I NTRODUCTION In recent years, the demand for mobile broadband services in cellular networks has increased rapidly, especially in video streaming and content sharing. The EU FP7 project METIS [1] has provided several key quantitative performance indicators for 5G networks, 1,000 times higher mobile data volume per area and 10 Gbps peak data rate are included. In addition, the new wireless broadband communication services, including e-banking, e-health and e-learning [2], will be integrated in future everyday life. Therefore, the future 5G network should be designed towards a highly integrated system [3], to meet the predicted data traffic growth and these various requirements. This work is supported by the National 973 Program under grant 2012CB316005, by the Fundamental Research Funds for the Central Universities 2014ZD03-01, by the National Science Foundation of China (NSFC) under grant 61372114, 61571054 and 61471062, the New Star in Science and Technology of Beijing Municipal Science & Technology Commission (Beijing Nova Program: Z151100000315077) and the China Scholarship Council. J. Zhang, X. Zhang and W. Wang are with the School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, 100876, China. X. Zhang is also with Beijing Advanced Innovation Center for Future Internet Technology, Beijing University of Technology (BJUT). Corresponding author of this paper: Xing Zhang, [email protected].

Not only traditional network optimization technologies should be utilized, such as interference management and cooperative communication, but also new up coming solutions will be of great importance, e.g., network densification, user-behaviour study[4], cognitive networks [5] [6], software-defined networking (SDN), and intelligent wireless backhauling [7]. Caching at the network edge has become an important means of offloading the traffic and tackling the backhaul bottleneck in order to reduce the latency of services and the cost of the cellular network [8]. In single-tier networks [9] [10], it has been shown that the backhaul capacity and the size of cache have a significant impact on the energy efficiency. In heterogeneous networks, much work has been done on content caching using various algorithms and schemes [11] [12] [13]. A framework to model heterogeneous cellular networks has been built with the aid of a factor graph, where distributed caching optimization algorithms are designed and compared in [11]. In [12], a coded caching scheme is proposed to enable content pre-fetching prior to knowing user demands based on the YouTube dataset. [13] proactively pushes popular content to the relays and users with caching ability via broadcasting. However, the power consumption and the backhaul limitation of the network are not negligible for future 5G green communication networks. Previous work has paid more attention to the throughput analysis in heterogeneous networks, whilst the power consumption and energy efficiency have not been well investigated, nor has the backhaul limitation and the probability of hitting the cache been taken into account. Although works in [9] [14] have nice contribution, they only focus on single-tier networks and the backhaul limitation is not studied. In [15], an energy-harvesting model with proactive content caching is proposed and energy-efficient context-aware resource allocation problem is solved in [16], but the limitation of backhaul and the software-defined feature are not utilised. In order to realize various cache management schemes, backhaul deployment approaches, cell on-off strategies in an integrated system, the concept of software defined networks can all be utilized to achieve efficiency in the U-plane transmission and to secure a lower overhead cost [17] [18] [19]. In addition, multiple papers have proposed new architectures for future 5G network in the software defined networks [20] [21] [22]. Resource allocation for energy efciency in heterogeneous Software Dened Network (SDN) with multiple network service providers (NSPs) is studied in paper [20]. Huawei proposes a two-layer network functionality separation scheme by taking UE state [21], and network functionality and signals into consideration. Similarly, with the soft-defined features, the author gives the idea of cell zooming in a hyper

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cellular network (HCN) where the size of the small cell can be adjusted according tot raffic load, user requirements, and channel conditions [22]. Under the control and user-plane (C/U-plane) split network, content delivery with a novel switch strategy and use of the concept of caching schemes has been proposed [23] [24]. However, work has so far only proposed the idea of the combination of a cache and a software defined network. The performance of the network and the impact of the cache in the backhaul limited scenario are still to be considered in heterogeneous networks. In this paper, we propose a scheme based on the idea of caching at the edge of the network and the use of a tool based on the homogeneous spatial Poisson point process (PPP). We propose a framework of cache-enabled networks with software defined features. The analysis of single-tier downlink transmission is extended to heterogeneous networks, where not only the macro cells have backhaul limitation, but the fronthaul between macro cell and SC are also limited. In addition, the power and density of macro and SCs are totally different, so that the performance of heterogeneous networks as analysed in this paper are totally different from the previous studies of a single tier network [9]. Furthermore, key performance indicators, including coverage probability, delivery throughput and energy efficiency, are studied in the proposed scenario. Relationships are derived between these key indicators and the parameters of SINR threshold, transmission power and density of macro cells and SCs, path loss exponent, cache ability, file popularity and backhaul capacity. Comparisons between the proposed network and current LTE networks are illustrated, as well as fundamental tradeoffs derived. The main contributions of the paper are summarized as follows: •

•

•

An end to end cache-enabled heterogeneous network with software defined features is proposed to provide universal high-rate services and seamless user experience when the backhaul is limited, and various cell deployment, power configurations and cache strategies are studied. The closed-form probability of hitting the content in the cache is modelled and utilized in the study of throughput and energy efficiency. The throughout is analysed under the constraint of SINR coverage, defined as the successfully delivered part of the traffic transmitted to the terminals. The performances of the heterogeneous network are analysed from the aspect of coverage, throughput and energy efficiency. Three fundamental trade-offs are derived: the throughput of SC and the density of SCs, the EE of the network and the density of SCs, and the EE of network and the transmission power of SCs. Comparisons between a cache-enabled system and current LTE networks are made to illustrate how the proposed network could become a future pathway towards green cellular networks.

The remainder of the paper is organised as follows. Section II proposes an end to end cache-enabled heterogeneous network with software defined features, where the deployment, cache, path loss, channel, power consumption and backhaul models are introduced. In Section III, key performance indicators are defined and analysed based on the stochastic geometry.

Core network aGW

Limited Backhaul

SUE

SC MUE

Macro Cell SC SUE

...

Macro Cell

Small Cell

User

Control Link

Data Link

Limited Fronthaul

Fig. 1. An illustration of one macro cell coverage region of the cache-enabled 5G software defined networks with limited backhaul to the core network.

Numerical results are illustrated from various aspects and comparisons made between the cache-enabled system and current LTE networks in Section IV. Conclusions and future work are summarized and appendixes are given at the end. II. SYSTEM MODEL AND PROTOCOL DESCRIPTION In this work, we consider a cache-enabled network based on software defined features, in which the macro cell and SC layer are overlaid in different frequency bands. A. Software Defined Features In the proposed network with software defined features, the control and user plane are separated to improve the manageability and adaptability of the network. Key features of software defined network can be summarized here. 1) C/U Split Architecture: Traditionally, every base station has been operated in a “stand alone” configuration, which has resulted in very high overhead costs of radio resources and interference [17]. After the separation, the C-plane coverage is maintained by the macro cell, whilst a typical user equipment (UE) can benefit from higher data rates via either a macro cell UE (MUE) or SC UE (SUE), as shown in Fig. 1. In this way, the macro cell retain all the public signals and channels, and broadcast these as system information for SCs over the region. Whilst the small cells can be designed for pure data carriers [17], with most of the C-plane public signals and channels of the small cells removed. Here we only consider the scenario that the macro cell has already covered the whole C-plane for all the terminals, and the U-plane access strategy is the same as the regular cell range expansion (CRE) scheme. If the users are beyond the macro cell C-plane coverage, the SCs have to work as stand-alone cells as discussed in [17], but this is not considered in this paper. 2) Cooperation between the Macro Cell and SCs: In the software defined networks, the macro cells are configured with a Radio Resource Control (RRC) protocol to provide long-term RRC connection to users, providing “slow Radio

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Resource Management (slow-RRM)” for user radio admission control (RAC) and connection mobility control (CMC) in the C-plane. In the U-plane, the macro cells are configured with a packet data convergence protocol (PDCP) to compress the packets, attach a PDCP header, and then send the packets. The small cells have only one set of U-plane protocols from physical layer to radio link control layer, maintaining “fastRRM” for dynamic resource allocation (DRA) of UE. For a typical user in the network, it obtains access to the macro cell at first in the C-plane and then sends the service request to the macro cell. After that, the macro cell can make the major decision based on the distances from the SCs to the user, the traffic requests of SCs, the moving direction and speed of the user, as well as the on-off status of SCs. With the cooperation between the macro and SCs, the macro cell can help the user terminal to obtain access to the most suitable small cell. More on-off strategies and traffic scheduling algorithms can be applied, leading to energy-saving and high-efficiency. Furthermore, small cells connect to the core network via the S1 interface traditionally, and exchange information to perform inter-cell interference coordination through the X2 interface, as modelling in [9] [10]. As a result, huge numbers of signals through the S1 interface can be foreseen in the future, which brings a severe security problem and heavy signal load to the core network. On the contrary, with the software defined features, all the small cells are connected directly to macro cells. Besides, traffic flows are routed and despatched from one typical macro cell to SCs within the region of the macro cell coverage, via the newly defined interface Xn on the fronthaul of the small cell, as illustrated in Fig. 1. In this way, the software defined network can reduce the signals on the S1 interface, and the macro cell can also adopt intelligent backhaul allocation strategy.

B. Deployment Model and Cache Strategy Based on stochastic geometry theory, macro cells and SCs are modelled as independent homogeneous Poisson point processes (PPPs), denoted as ΦM and ΦS , with corresponding densities of λM and λS . In the cache-enabled network, the content library can be pre-loaded and cached in the storage disk of the cells, which helps to reduce the latency and the power consumption. We assume that all the macro cells are equipped with equal cache ability, as are the SCs. The cached file catalogue of macro cells and SCs are denoted as ∆M f and ∆Sf respectively and the capability of caches in both macro cell and SCs are defined as M and S respectively. The file popularity is an interesting topic as described in [25] , which has lots of challenges on how to estimate it in spatio-temporal domain and local-global level. As most of the caching works assume perfect content popularity, in this paper we also adopt the Zipf distribution to model the file popularity. Denoting the total number of files in the content library as Nf and each file of length of L, the file popularity distribution of the catalogue is

a monotonically decreasing probability distribution function (PDF). The probability of requesting file f is f −υ , PNf (f ) = PNf −υ k=1 k

(1)

where the parameter υ represents the steepness of the popularity distribution curve. As most of the users request the few most popular files, the cache strategy is also based on the popularity ranking. All macro cells are cached with the same files, ranking the top M/L in total. Similarly, all the SCs are configured to store the most popular S/L files. The probability of hitting the content is: ( PM/L M Phit = f =1 PNf (f ), if f ∈ ∆M f Phit = (2) PS/L S Phit = f =1 PNf (f ), if f ∈ ∆Sf If the requested file is cached in the local disk, the downlink rate could achieve a high link rate by the tagged cell. On the contrary, if the file requested cannot be obtained in the local disk, the requirement will be sent back to the core network via the backhaul. Then the required service will be extracted from the external disk and sent back to the previous associated cell, and the delivery rate will be limited by the backhaul or fronthaul capacity. The traffic from SCs is first gathered in a macro cell via the fronthaul and then sent back to the core network. As the backbone backhaul to the core network is limited, the overall backhaul is shared by macro cells and multiple SCs. As the macro cell is the central control function in the Master-RRM, it can make the decision of backhaul allocation based on the traffic requirement distribution and the on-off status of the small cells. Here we assume that all the macro cells and small cells occupy equal fraction of backhaul resources. So the backhaul capacity per macro cell is modeled as   C1 + C2 , (3) CM = λM + λS and the fronthaul capacity per SC is:   C1 CS = + C2 , λM + λS

(4)

where C1 > 0, C2 ≥ 0 are arbitrary coefficients, so that the delivery rate from the core network via the backhaul is smaller than the downlink data rate from the local disk of cells. This assumption comes from the observation that the backhaul links might be very costly in densely deployed SBSs scenarios. C. Pathloss and Channel Model For a typical UE u, the distances to the nearest macro cell and SC are defined as rM u and rSu respectively. Assume that the transmission power of macro cells and small cells t are kept constant, denoted as PM and PSt . The standard path loss propagation model is used with path loss exponent α > 2. The independent identically distributed Rayleigh fading on all links are modelled as an exponential distribution with mean 1, shown as: hM u ∼ exp(1),

(5)

4

hSu ∼ exp(1).

(6)

General fading distribution is considered at some loss of tractability [26]. The received power from the nearest macro cell and small cell can be modelled respectively as follows: r PM =

PSr =

t M PM hu , rM u α

PSt hSu . rSu α

t M −α PM hu rM u , σ 2 + IM r

(13)

where X

IM r =

t M 0 PM hu rM 0 u −α ,

(14)

M 0 ∈ΦM /M

(8)

is the interference from the other macro cells except the connected cell M , and σ 2 is the constant additive noise power. Similarly, the downlink SINR from the nearest SC to a typical user u is: SIN RS =

As mentioned above, all of the users in the network are covered by macro cell tier in the C-plane. However, for the U-plane, the access strategy is based on the Reference Signal Receiving Power (RSRP) of macro and SCs. By keeping a dual link in control and user plane separately, users can benefit both from wide coverage, lower overhead cost, and higher throughput in this C/U split network. As there is no interference between macro and small cell layer, the CRE strategy here is used to realise cell zooming to balance the macro and small cell traffic loading under various small cell transmission configuration. The SCs are configured with cell range expansion bias η, shown as follows:  t P t E [hS ]  PM E [hM u ] > η SrSu αu , get access to macro cell rM u α (9) t t M S  PM E [hu ] < η PS E [hu ] , get access to small cell rM u α rSu α q t P Denoting θ = α η P tS , and ∆M u and ∆Su as the sets of M MUEs and SUEs, the access strategy of a typical user u can be simplified as:  u ∈ ∆M u , if rSu > θrMu , (10) u ∈ ∆Su , if rSu < θrMu , According to the property of the PPP distribution [27], the nearest distance distribution from u to macro cell is: (11)

Similarly, the PDF of the nearest distance distribution from u to SC is: (12)

III. P ERFORMANCE A NALYSIS Based on the models proposed in Section II, the SINR coverage probability, throughput, power consumption and energy efficiency are derived in this Section. According to the PPP distribution property stated in the Slivnyak’s theroem, the property of a typical point of PPP is the same as other observed by a node at origin. The downlink SINR for a typical user u,

−α PSt hSu rSu , σ 2 + ISr

(15)

PSt hSu rS0 0 u −α .

(16)

where X

ISr =

D. Access Strategy

frSu (r) = 2πλS rSu exp(−λS πrSu 2 ).

SIN RM =

(7)

As defined in 3GPP 36.932, the frequencies of macro cells and small cells are different. Small cells are deployed in hot spots with short range, so that the higher frequency for small cells is adopted as fS = 3.5 GHz , compared with the lower frequency of macro cells as fM = 2 GHz to maintain larger area coverage.

frM u (rM u ) = 2πλM rM u exp(−λM πrM u 2 ).

located at the origin of the plane and associated to the nearest macro cell M at a random distance rM u , is given by:

S 0 ∈ΦS /S

A. SINR Coverage The definition of SINR coverage is the probability of a random chosen user u being linked to a base station and the received SINR being higher than a typical threshold. It can be thought of equivalently as: a) the average fraction of users who link to the typical macro cell or SC layer at any time to achieve the SINR target; or b) the average fraction of the network area that is covered by the typical layer of macro cells or SCs. Thus the SINR coverage probability of the macro cell layer and the small cell layer are defined as follows: PcM = P (SIN RM > ΓM , u ∈ ∆M u ) = P (SIN RM > ΓM , rSu > θrM u )

(17)

PcS = P (SIN RS > ΓS , u ∈ ∆Su ) = P (SIN RS > ΓS , rM u > rSu /θ)

(18)

where ΓM and ΓS are the SINR threshold of macro cells and SCs respectively. According to Theorem 3 in [28], the probability of SINR being larger than the threshold ΓM is given as: P t hM r −α

P { σ2 + P M uP tMhuM r0 −α > ΓM |rSu , rM u } M u M0u  (19) M 0 ∈ΦM /M 2 2 = exp −rM u ΓM α σ 2 − πλM rM u 2 ΓM α Gα (ΓM − α ) R∞ 1 where Gα (y) = y α dx, y ≥ 0 : 1+x 2
 1/ sin c α2 , y− = 0    cot−1 y, α = 4, y > 0  α −1  Gα (y) = , (20) 2 2y 2 F1 1,1;2− α ;[1+y 2 ]     ,y > 0  α (α−2) 1+y 2

P∞ with 2 F1 (a, b; c; z) = 1 + k=1 Hypergeometric Function.

zk k!

Qk−1 l=0

(a+l)(b+l) c+l

being the

Theorem 1 (SINR Coverage Probability). For a typical user gain access to the network, the closed-form expression of network SINR coverage probability is:

5

Pc = PcM + PcS = 2 1+ΓM

+

α

1 2

2

t Gα (ΓM − α )+λS /λM (ηPSt /PM )α 1

2

2

t 1+ΓS α Gα (ΓS − α )+λM /λS (ηPSt /PM )

(21)

− 2 α

,

where the noise is ignored in the interference limited network. The SINR coverage probability can be found to be influenced by the path loss exponent, the transmission power and density of macro cell and SC, as well as the SINR threshold of macro cell and SC layer. Proof. The proof is provided in Appendix A. Corollary 1 (Optimized Density). There exists the optimized density to maximise the coverage probability in the heterogeneous network. To maximise the coverage probability, the optimum value of SC density in this heterogeneous network is √ (a−b)+2 (a−b)2 +(b2 −1)(a2 −1) (22) , λS ∗ = λM · 2 (b −1)d

2 α

where a = 1 + ΓM Gα (ΓM t 2/α ) . and d = (ηPSt /PM

2 −α

2

2

), b = 1 + ΓS α Gα (ΓS − α ),

Proof. The proof is given in AppendixB. Usually it is assumed that, the threshold of the SINR coverage of macro and SC is the same, that is ΓM = ΓS , so that a = b can be derived and leads to the following corollary. Corollary 2 (Optimized Transmission Power). There exists the optimized transmission power of small cell to maximize the coverage probability:  t ∗  − α2 PS S (23) = λλM /η, Pt M

where the SINR coverage threshold is assumed to be the same. This means that in order to maximize the coverage probability, the optimized transmission power of SCs is  − α2 ∗ λS t (24) P tS = PM /η. λM It can be deduced that the optimized transmission power does not depend on the SINR thresholds ΓM and ΓS . To optimize coverage probability, the transmission power is only related to the access bias, path loss exponent and the deployed density of macro cells and SCs. The maximized coverage probability of the network is: Pc max =

2 2 ΓM α

2 Gα (ΓM − α

)+2

.

(25)

B. Throughput In the cache-enabled software defined network, for a random selected user, the delivery throughput, denoted as τu , varies under several different conditions: • Obtaining access to the macro cell and the content required being hit within the local disk. The delivery hit throughput TM is determined by the SINR of the downlink channel. • Obtaining access to the macro cell and the content required is not hit within the local disk. The delivery

miss rate TM is limited by the backhaul capacity CM , for macro to derive data from the external network. • Obtaining access to the SC and the content required is hit within the local disk, so that the downlink throughput TShit is decided by the downlink SINR. • Obtaining access to the SC but failing to hit the content in the local disk, resulting in the throughput TSmiss being limited by the fronthaul between the SC and the macro cell. For a typical user u requesting content from the network, the delivery throughput can be summarized as follows:  hit TM , if u ∈ ∆Mu and f ∈ ∆Mf    miss TM , if u ∈ ∆Mu and f ∈ / ∆Mf τu = (26) hit T , if u ∈ ∆ and f ∈ ∆Sf  Su S   miss TS , if u ∈ ∆Su and f ∈ / ∆Sf

It is noteworthy that the throughput discussed here is the “successful delivery rate” from base station to the users, which is the upper limit on the throughput in the LTE system. Thus only the links with SINR larger than the threshold are calculated, instead of simply using the threshold to calculate the throughput, or ignoring the coverage condition of the user. This is a more accurate definition used in the green communication study. Thus, the delivery throughput in a macro cell and small cell can be expressed as: hit miss TM = TM + TM ,

(27)

TS = TShit + TSmiss .

(28)

1) Throughput of the macro cell with required content cached: If a typical user is associated with the macro cell and the content required is cached in the local disk, the delivery hit throughput TM can be written as: hit = P (f ∈ ∆M f ) TM {z } | content is hit

WM E[log2 (1 + SIN RM )|SIN RM > ΓM , u ∈ ∆M u ] | {z }

(29)

throughput of downlink channel

M = Phit WM E[log2 (1 + SIN RM )|SIN RM > ΓM , u ∈ ∆M u ]

Theorem 2. Throughput of the macro cell with required content cached: PM/L −υ hit 2 (1+ΓM )  TM = f =1 PNff −υ ·  WM ·log t /P t 2/α λS 1+ ηP k ( S M) λM PM/L k=1f −υ WM + f =1 PNf −υ · ln 2 · k=1 k R∞ 1 1 2 2 ΓM 1+ ηP t /P t 2/α λ /λ +t α Gα (t− α )−ΓM ( S M) S M

2 α

dt, 2 Gα (ΓM − α ) (1+t)

where WM is the effective bandwidth of a typical macro cell in the C/U split networks. Traditionally, the overhead in the LTE network OLT E is about 28% for the transmission of the public signals and channels [29]. However, in C/U split networks, the macro cell helps the SC to play as a data-only carrier, so that the public signals and channels of SC are broadcast via the macro cell to the terminals. So that the Overhead of the macro cell is slightly increased to OM = 28.54% [18] and the effective bandwidth to transmit the data is : WM = (1 − OM ) · W,

(31)

(30)

6

where W is the overall bandwidth of a macro cell.

4) Throughput of SC without required content cached: If one typical user is associated with a SC and the required content is not hit, the throughput of SC follows the theorem.

Proof. The proof is given in Appendix C. 2) Throughput of the macro cell without required content cached: If the required content from a typical user is not stored in the local cache, the traffic can then be delivered from the core network to the associated base station via the backhaul.

Theorem 5. Throughput of SC without required content cached: / ∆Sf ) TSmiss = P (u ∈ ∆Su ) · P (f ∈ {z } | | {z }

get access to SC content is not hit

Theorem 3. Throughput of the macro cell without required content cached:

· P (SIN RS > ΓS ) · C 0S | {z } S = (1 − Phit ) · PcS · C 0S PS/L 1− f =1

=

P (SIN RM > ΓM ) · CM · 1 − OM  |{z} | {z } Overhead delivery throughput
M = 1 − Phit · PcM · C!M · (1 − OM ) =

(32)

C1 f −υ (1−OM ) λ +λ +C2 PNf M S k−υ k=1 2 2 t 2/α 1+ΓM α Gα (ΓM − α )+λS /λM ηPSt /PM

1−



PM/L



f =1

(

)

where the definition of SINR coverage probability PcM in (17) is utilized and OM is the overhead of the macro cell in the C/U split network. In this paper, we only focus on the backhaul limited scenario, due to the fact that the backhual resources might be very costly in future ultra-dense network. Thus the delivery speed is limited from the core network to the terminals, which is modelled smaller than the downlink channel capacity from the local disk of cells. 3) Throughput of SC with required content cached: If the required content is hit in the local cache of a SC, the throughput of SC follows the following theorem. Theorem 4. Throughput of SC with required content cached: TShit = P (f ∈ ∆Sf ) | {z } content is hit

WS E [log2 (1 + SIN RS )|SIN RS > TS , u ∈ ∆Su ] {z } | =

· 0 2πλS rSu exp(−λS πrSu 2 )drSu · 2πλM rM u exp(−λM πrM u 2 )drM u · Su /θ Rr∞ P (SIN RS >max{t,TS }) P (SIN RS >TS )(1+t) dt 0

f −υ f =1 PNf k−υ k=1 − 2 t t α 1+λM /λS ηPS /PM 1 ∞ 1+t  t − 2 TS 2 2 α ηP λ S 1+ λM +t α Gα (t− α Pt S M

= R

(

PS/L

)

WS

(33)

f −υ f =1 PNf k−υ k=1

ln 2

2 Gα (TS − α

C 0S = CS − F$f 1 = λMC+λ + C2 − S

where W is the overall bandwidth of a SC. Proof: Similar to the proof of Theorem 2.

· C 0S ,

$ Ff

(36)

,

where $ is the typical size of signal measurement reports transmitted between macro and SC via Xn interface, and Ff if the average period of the transmission of measurement reports. Thus the delivery throughput of the macro cell is hit miss TM = TM + TM

f −υ PNf k−υ k=1  t 2/α λS ηPSt /PM λM

WM ·log2 (1+ΓM )

= ·

R∞

PM/L

WM

f =1

 1+(

PM/L f =1

+

)

f −υ PNf k−υ k=1

ln 2

1  t 2/α (1+t) dt+ 2 2 ηP λS −2 −2 S α α α α )−ΓM Gα (ΓM ) 1+ λM +t Gα (t Pt M ! PM/L −υ (1−OM ) 1− f =1 PNf   f k−υ C1 k=1 + C 2 2 2/α −2 λ +λ t t M S α )+λ /λ ηP /P 1+Γ α G (Γ 1

ΓM

α

M

S

M

(

S

·

f −υ f =1 PNf k−υ k=1 − 2 t t α 1+λM /λS ηPS /PM

WS ·log2 (1+Ts )

= R∞ ΓS

M

(37)

)

)

WS

f −υ f =1 PNf k−υ k=1

PS/L

+

ln 2

1

λ 1+ λM S

) 2

(34)

PS/L

(

1−

where WS is the effective bandwidth of the SC in the C/U split networks. According to [18], with the assistance of the macro cell, the downlink public channels, for example, PDCCH and PBCH, and downlink cell-level reference signals of SCs are removed. Thus the effective bandwidth of the SC is: WS ≈ W,

− 2 α

where C 0S is the effective fronthaul capacity from a typical SC to a macro cell. The exchanging of the measurement reports and signals also occupy a certain amount of capacity of the fronthaul, to achieve time synchronising of the macro and SCs and realising master-slave RRM management. The effective fronthaul capacity C 0S is derived as:

dt, 2 )+TS α

2

2

TS = TShit + TSmiss

PS/L

+

!

and the delivery throughput of the SC is

R∞

WS ·log2 (1+Ts )

f −υ PNf k−υ k=1

t 1+ΓS α Gα (ΓS − α )+λM /λS (ηPSt /PM )

M

throughput of downlink channel

S WS ·Phit R ∞ln 2

(35)

successful delivery throughput

miss / ∆M f ) · TM = P (u ∈ ∆M u ) · P (f ∈ {z } | | {z } get access to macro  content is not hit



ηP t S Pt M

−

2 α

2 +t α

2 Gα (t− α

f −υ f =1 PNf k−υ k=1

2 )+ΓS α

2 Gα (ΓS − α

1 1+t dt+ )

!

PS/L

2

1+ΓS α Gα (ΓS − α )+

λM λS



ηP t S Pt M

−

2 α

·



C1 λM +λS

+ C2 −

$ Ff



The average rate in a reference area TA is defined as the average downlink throughput of a random selected area. In this paper, the reference area is define as the area of one typical macro cell coverage area, in which several SCs are deployed. So that the overall average rate in this reference area is the sum of the throughput from all the cells in the area: TA = TM +

λs TS λM

(39)

(38)

7

TABLE I S IMULATION PARAMETERS .

0.7 0.74

Value 2 GHz 4 28.54% −10, 0, 10dB 24 bits 43 dBm 4.7 130 W 0 Mbps 300 Mbps 240 Mbits 5000L

Parameter fS η v W Ff PSt αS PS0 WBH WCA Nf S

Value 3.5 GHz 0 (default), −10, 10 dB 0.8 (default), 0.6 10MHz 5 ms 21 (pico), 38 (micro) dBm 4.0 (pico), 2.8 (micro) 6.8 (pico), 56 (micro)W 5 × 10−7 W/bps 6.25 × 10−12 W/bit 10000 500L ,1000L, 2000L

Under this proposed architecture, the power consumption can be divided into three parts: • Transmission and Circuit Power Consumption The basic power consumption of the base station is based on the outputs from the EARTH Project [30], where The basic power model of the macro cell and SC are modelled as follows:  0 t , if u ∈ ∆Mu + PM PtM = αM PM (40) 0 t PtS = αS PS + PS , if u ∈ ∆Su

•

, where αM and αS are the increased power coefficients 0 and PS0 is the static of macro and small base station, PM power consumption of the macro cell and SC. Caching Power Consumption If the required content is stored in the SC or macro cell, the base station will need to retrieve the data from the local hard disk. This part of the power consumption is related to the downlink delivery throughput. According to [31], the caching power consumption is related to the number of bits cached in each macro and small cell, which can be expressed as follows: PCM = wCA · M,

(41)

PCS = wCA · S,

(42)

where wCA is the power efficiency of caching hardware in watt per bit of high-speed solid state disk. Backhaul Power Consumption The backhaul power consumption is modelled as the microwave link power consumption defined in [32]: miss PBM = wBH · TM ,

(43)

PBS = wBH · TSmiss ,

(44)

where wBH is the power consumption per backhaul capacity. For a typical macro cell in a cache-enabled soft-defined network, the overall power consumption is P owM = PtM + PCM + PBM ,

0.68 0.7 0.68 0.66 0.66

0.64 0.64 0.62

0.6 0.62 0.58

-10

-8

0.6 -6

-4

-2

0

2

4

Access Bias  (dB)

6

8

10

0

10

20

30

40

50

60

70

80

90

100

0.58

SC Density per Macro Cell (S / M)

Fig. 2. U-plane coverage probability, with SINR threshold ΓM = ΓS = t = 46dBm, 0dB, path loss exponent α = 4, and transmission power PM PSt = 21dBm.

C. Power Consumption

•

Coverage Probability

Parameter fM α OM ΓM , ΓS $ t PM αM 0 PM C2 C1 L M

0.72

(45)

which is the sum of the transmission and static power, caching power consumption and backhaul power cost.

The power consumption of a typical SC in cache-enabled soft-defined network is P owS = PtS + PCS + PBS .

(46)

For a typical one macro cell covered area, the overall power consumption is the consumed power cost by the macro cell and the small cells: λs P owS . (47) P ow = P owM + λM

D. Energy Efficiency The most commonly used metric for the energy efficiency of a communication link is defined as the ratio of the total network throughput to the energy consumption, with units of bits/Joule. So the average energy efficiency of the network can be expressed as: TA , (48) P ow which is the overall average data rate transmitted per watt. EE =

IV. N UMERICAL R ESULTS AND D ISCUSSION In this section, we evaluate the impact of deploying caches in the heterogeneous network, and discuss the main relationship between the performance metrics and key parameters. Simulation parameters are listed in Table I utilising the simulator of MATLAB. The value of overhead signal costs are taken from [29] [18]. The typical size and frequency of exchanging reports between macro and SCs are taken from [17]. The power consumption related parameters are from the Earth Project [30] [32], and the cache related parameters are from [31]. A. Factors Affecting SINR Coverage As introduced in SectionII, the C-plane coverage is maintained by the macro cell, and the U-plane service is supported by both the macro cell and the SC layer. In Fig. 2, the Uplane coverage probability is illustrated with the density of SCs and the access bias. As defined in Section III-A, the coverage probability of a random selected user is equivalent to

8

0.75  M   S  10dB

0.8 0.6

 M   S  0 dB

0.4

 M   S  10dB

0.2 0

10

20

30

Coverage Probability

Coverage Probability

1

40

50

60

  10 dB

0.7

  0 dB

0.65 0.6 0.55 0

SC Density per Macro Cell (S / M)

5

10

15

  10 dB 20 25

30

35

Transmission Power of SC (dBm)

Fig. 3. Network coverage probability, with path loss exponent α = 4, λS /λM = 50: (a) Network coverage probability vs. SC density per macro cell, with t = 46dBm, P t = 21dBm; (b) Network coverage probability vs. Transmission power of SC, with SINR access bias η = 0dB, transmission Power PM S threshold ΓM = ΓS = 0dB.

the average coverage probability of the whole network. With the increase of density of SCs per macro cell, the average distance from the user to the nearest small cell reduces, so that there is a higher probability for a random selected user to gain access to the SC layer. As a result, the coverage probability of the macro cell decreases with λS /λM , while the coverage of SCs simultaneously increases. In general, the overall network coverage probability peaks at first and then decreases gradually with the increase of SCs, under the combined effects of macro and small cell layer as shown in Fig. 2. In Fig. 2, it can be found that the U-plane coverage is a combined result of macro cell and SC layers. When the density of SC is low, the increasing of bias takes the advantage of the SC layer and increases the coverage. But when the density of SC is large enough, lager bias results in poor performance without macro cell instead. Thus, the optimal bias factor is related to the density of SC in practical scenario. Fig. 3 (a) illustrates the impact of threshold on the network coverage probability. As the SINR threshold increases, the network coverage probability gradually reduces. As expected, the optimum values of the SC density to maximise the coverage are the same under various thresholds, as derived in Corollary 2. In Fig. 3 (b), the influence of SC transmission power on the network coverage performance are shown. When the access bias of the network is low, e. g., η = −10dB, the network coverage probability initially increases and then decreases with the transmission power of the SCs. This is the combined result of macro cell and SC layers. As the access bias increases, more users are associated to SCs, so that the optimum transmission power reduces. The optimum value of transmission power decreases with η, while the maximum values of network coverage under various η remains the same, because the optimized coverage performance is determined by the SINR threshold and path loss exponent, which matches the conclusions of Corollary 2. Fundamental conclusions on the SINR coverage can be summarized as follows: • The network SINR coverage probability initially increases and then decreases with the growth of SC density per macro cell λS /λM ;

•

•

Lower SINR thresholds TM and TS lead to higher SINR coverage probability, whilst the value of threshold does not affect the optimum density λS /λM to maximize the coverage probability; The optimum value of transmission power decreases with η, whilst the maximum values of network coverage are the same under different access bias η. The optimized coverage probability is determined by the SINR threshold and path loss exponent.

B. Impact of SC Density on Throughput In Fig. 4, the throughputs of macro cell and SC layer are shown and compared with the current LTE network. With the increase of density of SCs per macro cell, the throughput of macro cells shows a downward trend, shown in Fig. 4 (a), and the proposed C/U split network with cache ability achieves much higher throughput than the LTE network. As the SC cache strategy has no impact on the cell association strategy of users, the macro cell layer throughput remains the same under various cache capabilities of the SCs. In contrast, the higher the cache capability per SC, the higher the throughput of the SC layer, as shown in Fig. 4 (b). In LTE systems, the largest throughput of LTE networks is determined by the backhaul and fronthaul capacity. Thus, as the number of SCs increases, the fronthaul capacity of each SC reduces, so that the delivery throughput of the SC in the LTE network decreases with λS . However, in the cache-enabled C/U split network, the cache deployment strategy plays a critical role. When the cache capability of the SC is high, e.g., 1000 files cached (equal size of L), the probability of hit in the small cell is quite high, so that the distance from the UE to the associated SC decreases and improves the SINR. However, when the cache capability of the SC is small, e.g., 500 files cached amongst 10000 total files, the key factor becomes the limitation of the fronthaul shared by increasing number of SCs. Thus there exists a trade-off between the increase of λS and the throughput of SC. This means that the densification of SCs does not always increase the throughput of the SC in the backhaul limited scenario.

9

S  500 L

12

Proposed

10

12

Throughput of SC (Mbps)

Throughput of Macro Cell (Mbps)

14

S =1000 L

LTE 8 6

LTE

4 2

10

Proposed

S  500 L

8

S  1000 L 6

LTE

4

LTE

2 0 10

20

30

40

50

60

70

80

90

100

10

20

30

40

50

60

70

80

90

100

SC Density per Macro Cell (S / M)

SC Density per Macro Cell (S / M)

Fig. 4. The impact of density of SCs per macro cell on throughput, with SINR threshold ΓM = ΓS = 0dB, access bias η = 0dB, transmission Power t = 46dBm, P t = 21dBm, path loss exponent α = 4, number of files cached in Macro cell M = 5000L, P: Proposed system. (a) Throughput of PM S macro cell layer; (b) Throughput of SC layer. 1200

S  500 L

Area Average Ergodic Rate (Mbps)

1000

Proposed

S  1000 L 800

LTE

600

LTE

400

200

0 10

20

30

40

50

60

70

80

90

100

SC Density per Macro Cell ( S / M)

Fig. 5. The impact of density of cells on the area average ergodic rate, with SINR threshold ΓM = ΓS = 0dB, access bias η = 0dB, transmission t = 46dBm, P t = 21dBm, path loss exponent α = 4, number Power PM S of files cached in Macro cell M = 5000L.

In Fig. 5, the area average ergodic rate is illustrated under different densities of SCs λS . Although for each SC, the throughput is related to the cache ability, shown in Fig 4. (b), the overall average ergodic rate in one area increases with λS , as a result of the deification of small cells. As shown in Fig. 5, the proposed network achieves a much higher data rate than for LTE networks. Fundamental conclusions on the impact of SC density on throughput can be summarized as follows: • The proposed cache-enabled network with software defined features has much higher macro cell throughput, SC throughput, and area average ergodic rate than in current LTE networks; • macro cell throughput decreases with SC density per macro cell λS /λM , whilst a trade-off exists between SC throughput and λS /λM , the optimum SC density is determined by the cache ability in the SC. The area ergodic rate increases linearly with λS /λM . C. Impact of SC Density on Energy Efficiency In Fig. 6, network energy efficiency is compared between the proposed network and the current LTE system. With the increase of λS , the EE in the LTE network increases initially

benefiting from the shorter distance between the UE and the associated cell, and then decreases because of the backhaul limitation and the increase of power consumption. In Fig. 6 (a), the transmission power of SCs is relatively low, e.g., PSt = 21dBm as pico, so that the throughput grows faster than the energy cost via the increase in SCs in our proposed system. In comparison, when the transmission power of SCs is relatively high, e.g., PSt = 36dBm as micro cell, there exists an obvious trade-off between EE and SC density per macro cell λS /λM , so that higher density of SCs per macro cell region λS /λM , does not always result in higher energy efficiency. If the small cells are equipped with large cache size, more SCs per macro cell also leads to higher EE, similar to the conclusion when the transmission power is low. On the contrary, when the cache ability of SCs is poor, which is equivalent to lower probability of hitting the content, the fronthaul limitation plays the main role and the power consumption increases much faster than the throughput. So that the energy efficiency decreases with λS /λM when the transmission power is higher. In LTE networks, the EE also reduces under the combined effect of the throughput and energy consumption. Because of higher overhead cost and backhaul limitation of the network, the EE of the LTE network is smaller than in the proposed network. Fundamental conclusions regarding the impact of SC density on EE can be summarized as follows: • •

The EE of the proposed network is much higher than in LTE networks; Higher SC density does not always improve the EE of network: 1. When the SC transmission power is relatively small, e.g., 21dBm, the network EE increases with SC density; 2. When the SC transmission power is relatively high, e.g., 36dBm, there exists a tradeoff between EE and SC density. If the SC cache size is large, the EE also increases with SC density. If the SC cache size is small, the EE will decrease with SC density, due to the fact that the throughput is limited by the capacity of the fronthaul and the power consumption increases faster than the throughput.

10

1100

Network Energy Efficiency (Mbps/kW)

900 800 700 600

S  500 L S  1000 L S  2000 L LTE

LTE

500 400 300

180

Network Energy Efficiency (Mbps/kW)

Proposed

1000

160 140

100

S  500 L S  1000 L S  2000 L LTE

80

LTE

60 40

200 100 10

Proposed

120

20

20

30

40

50

60

70

SC Density per Macro Cell (S

80

90

/ M )

100

10

20

30

40

50

60

70

80

SC Density per Macro Cell ( S

/ M )

90

100

t = 46dBm, path loss Fig. 6. Impact of SC density per macro cell on the network energy efficiency, with access bias η = 0dB, transmission power PM exponent α = 4, number of files cached in macro cell M = 5000L, SINR threshold ΓM = ΓS = 0dB: (a) EE v.s. λS /λM when PSt = 21dBm; (b) EE v.s. λS /λM when PSt = 36dBm.

     

1200 1100 1000 900

250

 0.8  0.8  0.8  0.6  0.6  0.6

S / M =50

Network Energy Efficiency (Mbps/kW)

Network Energy Efficiency (Mbps/kW)

1300

800 700 600

N f  1000,5000,10000

500 400 300 0

500

1000

1500

2000

2500

3000

3500

4000

4500

Number of Files Cached in SC

P：S  500 L P : S  2000 L

150

S / M =10

P : S  500 L

100

LTE:S / M =50 LTE:S / M =10

50

0 10

5000

P：S  2000 L

200

LTE 15

20

25

30

35

40

45

50

Transmission Power of SC (dBm)

Fig. 7. Network energy efficiency, with SINR threshold ΓM = ΓS = 0dB, access bias η = 0dB, path loss exponent α = 4, number of files cache in macro N t = 46dBm, P t = 21dBm: (a) Impact of the number of files cached in SC, with various number of total cell M = 2f L, with transmission Power PM S number of files Nf and Zipf distribution parameter ν; (b) Impact of transmission power on Energy Efficiency under multiple cache ability of SC, with total number of files Nf = 10000.

D. Impact of File Numbers and Transmission Power on Energy Efficiency The impact of the cache related parameters on the network EE is illustrated in Fig. 7 (a). It can be concluded that larger SC cache ability not always leads to higher network energy efficiency, because when caching power increases faster than the backhaul power reduction when the SC is caching quite large number of files. Furthermore, as the content required from the users are more concentrated to the few most popular files, represented by higher ν, the EE can also be improved. Similarly, when ν is constant but the total number of files is smaller, the EE of the network increases. In Fig. 7 (b), The impact of transmission power on network EE is shown, compared with LTE networks. In the proposed network, it clearly shows that there exists a trade-off between EE and transmission power of SC PSt , because the throughput and power consumption increase at the same time. The EE initially increases with PSt and then decreases gradually. The optimum value of transmission power decreases with the increase of SC density, while it is independent of the cache size in each SC. The same conclusion can be drawn for LTE networks. Fundamental conclusions about the impact of file numbers and transmission power of SC on the network EE are:

•

• •

Larger cache size not always leads to higher network energy efficiency and larger value of parameter ν of Zipf distribution can improve the network energy efficiency; There exists a tradeoff between EE and SC transmission power; The optimum transmission power decreases with the growth of SC density in both the proposed and the LTE networks.

V. C ONCLUSION AND FUTURE WORK In this paper, a cache-enabled 5G network with software defined features is proposed, with the control and user plane separated. The probability of content demanded by a connected user is modelled and utilized in the study of throughput and energy efficiency, and the coverage probability is considered in the calculation of the “successful delivery rate” in the network with limited backhaul capacity. The performances are derived from the aspects of coverage, throughput and energy efficiency, as a function of key parameters of coverage threshold, transmission power, density of cells, cache size, file popularity and backahul limitation. Comparisons of throughput and energy efficiency are made with an LTE network. Numerical results are presented to validate the analysis and the impacts of the key parameters on the performance. Based on the latter, it was found that the proposed network has much higher throughput

11

and energy efficiency than current LTE networks. Fundamental trade-offs exist between the throughput and the density of SCs, network EE and the transmission power of SCs, as well as the network EE and density of SCs. Based on these results, the proposed cache-based network with software defined features proves to be a promising solution as compared with the LTE network under backhaul limitation, towards future green communication networks. In future, different access strategies based on various cache schemes will be studied based on the group user behaviour in mobile social networks. More energy harvesting and cell dynamic management methods can be also be encouraged into the models. A PPENDIX A P ROOF OF T HEOREM 1

where in (a) frSu (rSu ) and frM u (rM u ) are given in (11) and (12) respectively . As the interference from other macro cells is much stronger than the background noise, ignoring the noise σ 2 and using the substitution x = λM πrM u 2 and y = λS πrSu 2 , the coverage probability of macro cell layer can be obtained:   R∞ 2 2 PcM = 0 exp(−x 1 + ΓM α Gα (ΓM − α ) )dx R∞ λS t t 2/α exp(−y)dy (50) λM x(ηPS /PM ) 1 = , 2 2 t 2/α 1+ΓM α Gα (ΓM − α )+λS /λM (ηPSt /PM ) Similarly, the coverage probability of SC layer is shown as follows: 1 PcS = (51) 2 . 2 2 − t )− α 1 + ΓS α Gα (ΓS α ) + λM /λS (ηPSt /PM For a random chosen user, the coverage probability is the sum of both layer: (52)

Theorem 1 is derived and the proof is finished. A PPENDIX B P ROOF OF C OLLORAY 1 For the coverage probability of the network, shown in (21), it could be optimized by adjusting the fraction of density of macro cell and SCs, defined as x = λS /λM . 2 2 For simplicity, we denote that a = 1 + ΓM α Gα (ΓM − α ), 2 2 t 2/α b = 1 + ΓS α Gα (ΓS − α ), and d = (ηPSt /PM ) , the coverage probability in Theorem 1 can be written as follows: Pc = f (x) 1 = a+xd +

1 1 b+ xd

,

df (x) d −d dx = (a+dx)2 + (bdx+1)2 2 2 2 x +2(b−a)dx+1−a2 = d (b −1)d (a+dx)2 (bdx+1)2

(53)

(54)

= 0.

Thus the optimum value to maximize the coverage probability is the solution of the following equation, (b2 − 1)d2 x2 + 2(b − a)dx + 1 − a2 = 0, as b2 − 1 > 0, the solution of the optimum of x∗ is √ (a−b)+2 (a−b)2 +(b2 −1)(a2 −1) ∗ x = , (b2 −1)d 2

For a typical user, the probability to gain access to the macro cell and achieve the target SINR threshold is R∞ R∞ PcM = 0 frM u (rM u )drM u θrM u frSu (rSu )drSu P (SIN RM (rSu , rM u ) > ΓM ) (a) R ∞ 2 (49) R=∞ 0 2πλM rM u exp(−λM πr2M u )drM u 2πλ r exp(−λ πr )dr S Su S Su Su θrM u   2 2 · exp −rM u ΓM α σ 2 − πλM rM u 2 ΓM α Gα (ΓM − α )

Pc = PcM + PcS .

where a > 1, b > 1 and d > 0. It is easy to find f (x) is a convex function, and to optimize the coverage ∗probability is (x ) the same to find the optimum x∗ to realize dfdx = 0: ∗

2

2

(55)

(56) 2

where a = 1 + ΓM α Gα (ΓM − α ), b = 1 + ΓS α Gα (ΓS − α ), t 2/α and d = (ηPSt /PM ) . Corollary 1 is derived and the proof is finished. A PPENDIX C P ROOF OF T HEOREM 2 Denote the SINR received from the attached macro cell SIN RM by x, and denote the coverage event SIN RM > ΓM by ΦX (x). E[log R ∞2 (1 + SIN RM )|SIN R ∞ RM > ΓM , rSu > θrM u ] = 0 frM u (rM u )drM u θrM u frSu (rSu )drSu R∞ log (1 + x)f (x|ΦX (x))dx 0 R ∞2 R∞ = ln12 0 frM u (rM u )drM u θrM u frSu (rSu )drSu R∞R∞ 1 1+t dt R0∞ t f (x|ΦX (x))dx R∞ = 0 frM u (rM u )drM u θrM u frSu (rSu )drSu ln12 R ∞ P (SIN RM )>max{t,ΓM }) P (SIN RM >ΓM )(1+t) dt 0

(57)

For a typical user associated to macro cell, with the required data stored in the local disk, the downlink data rate is M hit = Phit WM TM E[log2 (1 + SIN RM )|SIN RM > ΓM , rSu > θrM u ] R∞ R∞ M =nPhit WM ln12 0 frM u (rM u )drM u θrM u frSu (rSu )droSu (58) RΓ R∞ P (SIN RM (rSu ,rM u )>t) 1 dt + ΓM P (SIN · 0 M (1+t) RM (rSu ,rM u )>ΓM )(1+t) dt

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