Ahlem Khlass
email: ahlem.khlass@orange.com

Thomas Bonald
email: thomas.bonald@telecom-paristech.fr

Salah Eddine Elayoubi
email: salaheddine.elayoubi@orange.com

Flow-level Modeling of Multi-User Beamforming in Mobile Networks

Keywords: Multi-user beamforming, LTE-Advanced, Flow Level Modeling, Queuing Theory, Simulations

Among the several features that are foreseen for increasing the capacity of cellular systems, Multi-user multipleinput multiple-output (MU-MIMO) is considered as a key enabling technology. Particularly, MU-beamforming is a powerful means of increasing the system capacity and throughput by creating several spatial signals to different users on the same time/frequency resource. In this paper, we develop an analytical model for MU-beamforming based on queuing theory combined with network simulations. The proposed framework is used for evaluating the potential gains in terms of capacity and throughput in LTE-Advanced system. Several scenarios are studied, with and without beamforming. Results show an important gain of SU-beamforming over the classical system without beamforming and a further gain of MU-beamforming, especially at high loads.

I. INTRODUCTION

Nowadays, the wireless networks industry is moving toward LTE system which is expected to improve the performance in terms of spectral efficiency and user throughput. In its release 8, it enables to achieve 300 Mb/s for the downlink and 75 Mb/s for the uplink with the utilization of OFDM and single user-MIMO (SU-MIMO) transmission. Then, in order to meet the requirements of the IMT-Advanced systems, LTE has been further enhanced to LTE-Advanced which is able to achieve a target throughput of 1 Gb/s on the downlink and 500 Mb/s on the uplink with advanced physical layer techniques [START_REF] Lim | Recent trend of multiuser MIMO in LTE-advanced[END_REF] [2] including carrier aggregation [START_REF] Lin | Modeling, analysis and design for carrier aggregation in heterogeneous cellular networks[END_REF], enhanced multi-antenna schemes and Coordinated Multi-Point transmission technique (CoMP) [START_REF]Technical specification group radio access network; coordinated multi-point operation for LTE physical layer aspects[END_REF]. Particularly, multi-user MIMO (MU-MIMO) is considered as a key enabling technology for LTE-Advanced that enables to achieve the expected performance [START_REF] Spencer | An introduction to the multi-user MIMO downlink[END_REF]. Indeed, in downlink MU-MIMO system, the Base Station (BS) creates different spatial signals to multiple Mobile Stations (MS) on the same time/frequency resource. Accordingly, the scheduling opportunities for each MS is largely improved compared to a SU-MIMO system where only a single user exploits the spatial gain offered by multi-antenna systems [START_REF] Liu | Downlink MIMO in lte-advanced: SU-MIMO vs. MU-MIMO[END_REF]. However, this operation introduces interference between co-scheduled users within the same cell in addition to the interference from adjacent cells. Therefore, advanced precoding/beamforming techniques and a well designed scheduling scheme need to be implemented in order to combat this intra-cell interference and increase the system capacity.

While a large number of papers deals with the physical layer aspects of MU-MIMO by investigating the optimal schemes with low complexity, we propose in this paper a flow level modeling of MU-MIMO in different scenarios. Indeed, existing performance evaluations of MU-MIMO are based on system-level simulations with a static number of users in different cells (e.g. [START_REF] Farajidana | 3GPP LTE downlink system performance[END_REF] [8] [START_REF] Tarighat | A multi user beamforming scheme for downlink MIMO channels based on maximizing signalto-leakage ratios[END_REF]); they do not capture the dynamics of users' behavior in the system. Moreover, they do not reflect the actual distribution of users in the cell since those at cell edge stay longer in the cell for finishing their service due to a low data rate [START_REF] Bonald | Wireless downlink data channels: user performance and cell dimensioning[END_REF]. However, in this work, we propose an analytical method based on queuing theory that captures the dynamics of arrivals and departure processes. It is practically interesting and, to the best of our knowledge, has not been proposed yet.

In this paper, we consider a special MIMO scheme which is transmit beamforming that permits to concentrate the energy towards one or more directions. Particularly, we evaluate the expected gains of MU-beamforming in terms of throughput and capacity in different scenarios. We start with SUbeamforming system, then we investigate the MU-scheduling impact under different network configurations. We propose for each scenario a flow-level model and we evaluate its performance using both Markovian analysis and network simulations in different load conditions. Results show an important gain of SU-beamforming over the classical system without beamforming and a further gain of MU-beamforming, especially at high loads.

The remainder of this paper is organized as follows. Section II presents a basic background of MIMO system and MU-MIMO framework. Section III describes the model used in this paper. We present in section IV the flow-level analysis for the SU-beamforming and the MU-beamforming in the presence of three and four serving beams. Section V gives the results using network simulations. Section VI concludes the paper.

II. BACKGROUND

A. MIMO System

One of the key technique of advanced communication systems is the MIMO transmission which enables multiple antennas at both receiver and transmitter, with additional processing, to improve the system performance in terms of coverage, capacity and robustness. There are basically three main advantages from MIMO transmission [START_REF] Sesia | LTE -The UMTS Long Term Evolution: From Theory to Practice[END_REF]:

• Diversity gain: by using the spatial diversity provided by the multiple antennas in order to improve the system robustness and reliability. • Spatial multiplexing gain: by transmitting multiple data streams to a single or multiple users on multiple spatial dimensions (i.e. layers) in order to improve the user's spectral efficiency. • Array gain: by concentrating the energy in one or more directions via precoding/beamforming functionality, thus increasing the data rates.

Various scenarios are proposed for LTE downlink; they are referred as Transmission Modes (TM) in releases' specification. The final MIMO scheme depends on the network deployment and the propagation conditions of the different users.

B. MU-MIMO Framework

The MU-MIMO framework has been introduced for LTE-Advanced standard and considered as a key enabler for achieving high spectral efficiency. It enables a BS to co-schedule a set of MSs on the same time/frequency resource. However, this operation introduces additional intra-cell interference. Therefore, advanced precoding and scheduling methods need to be implemented to get full benefit of MU-MIMO transmission.

1) MU-Precoding: The key issue with the MU-precoding is to find a compromise between performance gain, Channel State Information (CSI) requirement and design complexity. The Dirty Paper Coding (DPC) [START_REF] Peel | Linear and Dirty-Paper Techniques for the Multiuser MIMO Downlink[END_REF] enables to achieve an optimal capacity but is impractical in real systems due to its complexity and full CSI requirement. Alternatively, linear precoding methods, such as zero-forcing (ZF) [START_REF] Spencer | Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels[END_REF], appear to be more robust to erroneous CSI and with a low complexity relatively to other methods.

2) User selection/scheduling: Different factors affect the MU-scheduler performance including the wireless environment since a minimum separation between users is required. This is only possible through narrow antenna beam patterns. Also, the cell load is an important factor; indeed highly loaded cells provide more user grouping possibilities than lightly loaded cells where it is more efficient to schedule a single user. Different schedulers have been proposed in literature for MU-MIMO (e.g. [START_REF] Anton-Haro | Cross-layer scheduling for multi-user MIMO systems[END_REF] and reference therein). Since we consider a beamforming scheme, the MU scheduling can be performed using:

• Max-Sum scheduler. The aim is to find the optimal set of users covered by different beams which maximizes a total utility function. • Max-iterate scheduler. A first user is chosen according to a certain metric, then users from adjacent beams are blocked and the same process is repeated until reaching the maximum number of active beams or that there are no more users to schedule.

III. MODEL

A. Physical layer aspects

We consider a downlink multi-user environment consisting on a base station (BS) with N transmit antennas communicating with M mobile stations (MS). We focus on the beamforming system represented by the block diagram shown in figure 1 where the data information blocks are mapped into layers, then to the antenna ports by means of the precoding/beamforming functionality. We investigate two possible schemes [START_REF] Schulz | LTE transmission modes and beamforming[END_REF]: the one-layer beamforming where a single layer is assigned to one MS (i.e. SU-beamforming) and dual-layer beamforming where the two layers are assigned to two separte MSs (i.e. MU-beamforming).

Let X i and W i denote the transmitted data intended to user i and its transmit beamforming vector. When one-layer beamforming is used, the received signal at M S i is given by:

Y i =H i W i X i + I i + N i ,
where H i , I i and N i denote the channel gain from the BS to the ith MS, the inter-cell interference and an Additive White Gaussian Noise (AWGN) vector at M S i , respectively. The corresponding SINR is given by:

SIN R i = ||H i W i || 2 ||I i || 2 + ||N i || 2 .
However, when dual-layer beamforming is deployed, the received signal at M S i is expressed by:

Y i =H i W i X i + H i 2 l=1 l =i W l X l + I i + N i , (1)
In Equation 1, the four terms represent the desired signal, the multi-user interference, the inter-cell interference and the noise, respectively. Hence, the SINR at user i is:

SIN R i = ||H i W i || 2 ||H i 2 l=1 l =i W l || 2 + ||I i || 2 + ||N i || 2 .
Using the Shannon's formula, we can express the transmission rate by:

R i = W log(1 + SIN R i ), (2)
where W denotes the system bandwidth. Note that, in this paper, we do not address the calculation of the optimal beamforming weights as done in several studies (e.g. [START_REF] Tarighat | A multi user beamforming scheme for downlink MIMO channels based on maximizing signalto-leakage ratios[END_REF] and references therein). We assume that the BS has an arbitrary number of transmit antennas that can provide J spaced beams per sector as shown in figure 2. The J predefined beams are considered as a fixed codebook either in SU or MU-beamforming modes. This model is used in the subsequent analysis.

B. Scheduling aspects

We consider a centralized scheduler per radio site which decides at each time slot the set of users to co-schedule on the same time/frequency resource. Different schedulers can be performed as seen in section II-B2 that aim at getting full benefit from multi-user diversity and so improving the system capacity while minimizing the intra-cell interference. In this work, we consider a Max-Iterate scheduler based on Round Robin which selects a first user at random, blocks all users in the adjacent beams and iterates until reaching the maximum number of active beams or that there are no more users to schedule. The considered MU-scheduling is described in algorithm 1.

At each timeslot

Input : Set J of active beams, M max number of beams to co-schedule, Output: Set U of MSs to schedule while

J = ∅ & size(U ) < M do pick at random a MS u, served by beam b ∈ J; J ← J \ {b, b + 1[J], b -1[J]}; U ← U ∪ {u}; end Algorithm 1: MU-Scheduling algorithm.
Although this scheduler is simple and does not take into account the radio channel conditions, it remains a good approximation of any opportunistic scheduler like proportional fair when the channel variations are limited or too fast to be exploited.

C. Traffic aspects

We assume elastic traffic. Data flows arrive according to a Poisson process of intensity λ in the reference cell. Each flow stays in the system as long as the corresponding data have not been successfully transmitted to the MS. Note that the users are assumed to be static during the whole flow duration. Flow sizes are assumed to be independent and exponentially distributed with mean σ bits. The traffic intensity A in the reference cell is the product λ × σ in bit/s.

IV. FLOW-LEVEL ANALYSIS

We start with a SU-beamforming system in the presence of J serving beams, then we investigate the impact of MUscheduling under different network configurations. We focus on a given sector. We consider a set C of classes of MSs indexed by i to reflect the different radio conditions in the reference sector. Classes are grouped into subsets C j for j ∈ J = {1, .., J} in the presence of J serving beams. Since class-i flows arrive at rate λ i , the corresponding load is:

ρ i = λ i σ R i ,
where R i is the transmission rate at class-i expressed in expression (2).

A. SU-beamforming

According to SU-beamforming system, the scheduler selects at random a user covered by a particular beam. This latter is served alone and blocks all other users in the sector. Let Z j (t) be the total number of users in beam B j at time t, for j ∈ J . Denote by Z(t) the corresponding vector. Whenever Z(t) = z, the scheduler selects a user in B j a fraction of time of [START_REF] Bonald | A queueing analysis of max-min fairness, proportional fairness and balanced fairness[END_REF]:

φ j ( z) = z j
z , where z denotes the total number of users in whole sector. The queuing system is described by the following transition rates of the Markov process Z(t) from state z to state z :

q( z, z ) =    λj for z = z + e j j ∈ J φ j ( z) Rj σ for z = z -e j , j ∈ J (3)
where e j is the unit vector on component j, for j ∈ J .

The system corresponds to a multi-class processor sharing queue with total load ρ = j∈J ρj where ρj = λj σ Rj .

The arrival rate per beam λj is given by

λj = i∈Cj λ i ,
and the mean transmission rate

Rj = i∈Cj p i i∈Cj pi Ri , with i∈C p i = i∈C λ i /λ = 1.
In order to investigate the performance of such system, we propose lemma (1).

Lemma 1. Considering a Whittle network [START_REF] Bonald | Network Performance Analysis[END_REF] of J queues of load ρ j , the stationary distribution of the process z(t) is:

π(z) = π(0)Φ(z) J j=1 ρ zj j , (4)
where Φ(z) denotes the inverse of the product of service capacities along any direct path from state z to state 0. Let

G(ρ) = z Φ(z) J j=1 ρ zj j .
For each queue j, we have:

• the mean number of users in each queue j

E(z j ) = ρ j ∂G(ρ) ∂ρ j 1 G(ρ) . (5)
• the flow-throughput

γ j =R j ∂ ∂ρ j ln(G(ρ)). (6)
Proof. Based on the normalization condition where z π(z) = 1, we have:

π(0) = 1 G(ρ) , (7)
Then, the mean number of users in each queue is given by:

E(z j ) = z z j =0 z j π(0)Φ(z) J j=1 ρ zj j =ρ j ∂G(ρ) ∂ρ j 1 G(ρ)
.

The mean sojourn time in each queue follows from Little's law [START_REF] Kleinrock | Queueing Systems[END_REF] :

τ j = E(z j ) λ j .
Hence, we obtain the flow throughput:

γ j = σ τ j =R j ρ j E(z j ) =R j ∂ ∂ρ j ln(G(ρ)).
The multi-class processor sharing queue can be viewed as a Whittle network [START_REF] Bonald | Network Performance Analysis[END_REF]. Under the stability condition ρ < 1, the stationary distribution of the system describing the number of flows in each beam of the reference cell is given by:

π( z) = π( 0) z! j z j ! j ρ zj j , (8)
Then, using lemma (1), we obtain the mean number of active users in beam-j flows:

E(z j ) = ρj 1 -ρ .
We deduce the flow throughput in beam B j

γ j = Rj (1 -ρ), (9)
The mean throughput in the cell is given by:

γ = R(1 -ρ),
where R refers to the total cell capacity defined as the maximum traffic intensity that can be handled. We note that the flow throughput decreases linearly with the load from the maximum data rate Rj when ρ = 0 to 0 when the reference cell is fully loaded (ρ = 1). However, in real cases, this is not a linear decrease since the transmission rates are not fixed and depend on the load of neighboring cells and the caused interference.

B. MU-beamforming

To gain insight into the MU gain, we consider the two-layer beamforming system in the presence of J = 3 and J = 4 serving beams per sector.

1) MU-beamforming in the presence of 3 beams: According to the MU-scheduling algorithm aforementioned, the system switches between a SU and MU-beamforming system depending on the first selected user. In fact, if a user covered by the beam B 1 is selected first, then only those covered by B 3 are eligible to be selected next. However, when a user in beam B 2 is selected first, all others covered by adjacent beams namely B 1 and B 3 are blocked. Hence, users in beams B 1 and B 3 are selected a fraction of time of:

φ 1 ( z) = φ 3 ( z) = z 1 + z 3 z ,
and those in beam B 2 a fraction of time:

φ 2 ( z) = z 2 z .
The system corresponds to a set of three coupled processorsharing queues with state-dependent service rates. The queuing system is described by the transition rates given in (3) with J = 3. This Markov process is reversible and equivalently, the queuing system corresponds to a Whittle network. The stationary distribution of the Markov process Z(t) is then given by:

π( z) = (1 -ρ1 -ρ2 )(1 -ρ3 -ρ2 ) (1 -ρ2 ) × z z 1 + z 3 ρz1 1 ρz2 2 ρz3 3 ,
under the stability condition that: We use lemma (1), we deduce from equation ( 5) the mean number of flows in each beam

ρ1 + ρ2 < 1, ρ3 + ρ2 < 1.
E(z 1 ) = ρ1 1 -ρ1 -ρ2 , E(z 2 ) = ρ2 1 -ρ2 1 + ρ1 1 -ρ1 -ρ2 + ρ3 1 -ρ3 -ρ2 . E(z 3 ) = ρ3 1 -ρ3 -ρ2 ,
and from equation ( 6) the flow throughput in each beam:

γ1 = R1 (1 -ρ1 -ρ2 ), γ3 = R3 (1 -ρ3 -ρ2 ), (10)
γ2 = R2 (1 -ρ2 ) 1 + ρ1 1 -ρ1 -ρ2 + ρ3 1 -ρ3 -ρ2 . ( 11
)
Figure 3 shows the results in terms of normalized throughput per beam and in average compared to that obtained with SU-beamforming. We see that the capacity region is improved by one half when using MU-beamforming since the system with 3 beams switches between SU and MU. In fact, depending on the first selected user, either the two beams at extremities are active or the one at the middle.

2) MU-beamforming in the presence of 4 beams: In this case of J = 4 beams per sector, the scheduling algorithm is always able to select two users from two different beams. In fact, selecting a user from any beam leaves always the possibility to select another user from another beam (except from the adjacent ones). For instance, if a user covered by beam B 2 is selected, this blocks those covered by adjacent beams B 1 and B 3 . Then only users covered by beam B 4 are eligible to be co-scheduled jointly with the selected user from B 2 . However, when a user covered by beam B 1 is selected, this gives the possibility to users covered by both B 3 and B 4 to be scheduled. We differentiate in this case between two scheduling behaviors: a) Fixed scheduling scheme: As its name suggests, the scheduling scheme in the cell is predefined since the scheduler can either select a user covered by a beam whose index is even or odd. Indeed, if a user covered by B 1 is selected, then only a user from beam B 3 can be co-scheduled. Accordingly, at a given time slot, either beams B 1 + B 3 or B 2 + B 4 can be active at a given time slot, regardless of their corresponding loads. This can be expressed in terms of fractions of time during which the beams are active:

φ 1 ( z) = φ 3 ( z) = z 1 + z 3 z , φ 2 ( z) = φ 4 ( z) = z 2 + z 4 z .
The system corresponds in this case to a set of four coupled processor-sharing queues. The queuing system is similar to that described in (3) with J = 4. The reversibility is maintained and we deduce the stationary distribution of the Markov process Z(t):

π( z) = π( 0) × z z 1 + z 3 , z 2 + z 4 j=4 j=1 ρzj j ,
under the stability condition:

ρ1 + ρ3 < 1, ρ2 + ρ4 < 1.
For simplicity, we suppose that all beams have the same load such as ρj = ρ, ∀j ∈ J .

We use lemma (1) and we deduce from equation [START_REF] Farajidana | 3GPP LTE downlink system performance[END_REF]:

π(0) = (1 -2ρ) 3 1 -2ρ + (2ρ) 2 .
Hence, the mean number of users in each beam B j , ∀j ∈ J , follows from equation (5) so that

E(z j ) = ρ (1 -2ρ) 1 -ρ + ρ2 1 -2ρ + 2ρ 2 ,
and the corresponding flow throughput:

γj = Rj ( ρ (1 -2ρ) 1 -ρ + ρ2 1 -2ρ + 2ρ 2 ) (-1) . (12)
Note here that Rj refers to the transmission rate in B j in the presence of another active beam.

b) Flexible scheduling scheme: Under the flexible scheduling, the load in each beam is taken into account. Indeed, if a user in beam B 1 is selected, this leaves the possibility to users covered by either beam B 3 or B 4 to be co-scheduled depending on their loads. The fractions of time during which beams are active is then given by:

φ1 ( z) = z 1 + z 3 z + z 4 z z 1 z 1 + z 2 , φ2 ( z) = z 2 z + z 4 z z 2 z 1 + z 2 , φ3 ( z) = z 3 z + z 1 z z 3 z 3 + z 4 , φ4 ( z) = z 4 + z 2 z + z 1 z z 4 z 3 + z 4 .
The system corresponds to a set of four coupled processorsharing queues. The queuing system is the similar to that presented in (3) except that φ j ( z) is replaced by φj ( z) for j = 1, .., 4. This Markov process is not reversible. Therefore, the stationary distribution of the number of active flows in the system is not deduced as done previously for the fixed scheduling scheme.

The performance of the fixed and flexible scheduling schemes in a MU-beamforming system with J = 4 beams is obtained by simulation of 10 6 jumps of the Markov process and plotted in figure 4 in terms of normalized throughput per beam and in average compared to the SU-beamforming. We see that the system capacity is twice that observed with a SU-beamforming. Moreover, we see that the flexible scheme favors the beams at extremities (B 1 for instance) where users experience higher performance compared to those in other beams (e.g. B 2 ) since they have more chances to be selected at the expense of other beams. Thus, in average, the flexible MU-scheduling performs slightly better than the fixed scheme, except at high loads where the two schemes perform similarly.

In summary, we observe an important improvement of the system capacity when increasing the number of users to coschedule and the number of beams as well. For practical issues, we decide to limit the number of beams to J = 4 per sector and the number of users to co-schedule to two users, but this analysis can be further extended to any MU-beamforming scheme.

V. NUMERICAL RESULTS

While the numerical results presented in the previous section were based on normalized rates and aimed at illustrating the derived models, we present in this section a numerical analysis where the analytical models take as input realistic rates from an LTE-advanced simulator.

A. Achievable rates

We first present network simulations results that are used to calculate the achievable rates is SU and MU-beamforming in comparison to a classical system without beamforming. System level evaluation is conducted to compare the performance of a classical system without beamforming to SUbeamforming and MU-beamforming systems in LTE-advanced network settings.

Considering the system parameters summarized in table I, we illustrate in figure 5, the transmission rates at different positions of the reference site on the basis of 100 independent network states. The average values are given in table II in different scenarios. Since our purpose is to evaluate the MU gain of MU-beamforming, we do not consider advanced features of LTE-advanced networks like OFDMA for instance. We assume also that the base station transmit at full power using the whole frequency band.

We see at first that SU-beamforming enables to achieve higher transmission rates compared to a classical system without beamforming. Indeed, concentrating the transmit power on the target MS increases the received power and decreases the interference caused to other MSs. However, with MUbeamforming, the transmission rates are less important due to intra-cell interference caused by the presence of two active beams per cell.

B. Performance results

We address in this section the performance results when combining the Markovian analysis of section (IV) with the network simulations. For different traffic intensities, we plot the average throughput with MU-beamforming and SUbeamforming in comparison to the classical system without beamforming. Results are shown in figure 6. We notice an important gain of SU-beamforming over the classical system without beamforming and a further gain of MU-beamforming, especially at high loads. Indeed, the system capacity improves considerably by 30% when performing MUbeamforming with 4 beams under the fixed scheduling scheme and around 20% with 3 beams since this system switches between SU and MU-beamforming. Note that these results are valid for a constant load in neighboring cells (50%). However, in real cases, the flow throughput does not decrease linearly since the transmission rates depend on the interference caused by neighboring cells.

VI. CONCLUSION

In this paper, we proposed a flow-level modeling of MUbeamforming in cellular networks. We evaluated its performance by combining Markovian analysis with network simulations. We observed that MU-beamforming enables to improve the performance of a SU-beamforming in terms of capacity, especially at high loads. Results were given in a system providing 3 and 4 beams and a maximum of two users to co-schedule. Notice that all the Markovian analysis and the simulation results provided in this work can be easily extended to a higher number of beams and more users to co-schedule.

Although the focus of this paper was on single-cell, the framework could be extended to case of multi-cell MU-MIMO (also known as Coordinated Multipoint (CoMP) in LTE-Advanced system) and by considering opportunistic scheduling schemes. This is left as future work.

Fig. 1 .

 1 Fig. 1. Block diagram of the MU-beamforming system.

Fig. 2 .

 2 Fig. 2. System model.

Fig. 3 .

 3 Fig. 3. Normalized user throughput with MU-beamforming with 3 beams.

Fig. 4 .

 4 Fig. 4. Normalized user throughput with MU-beamforming with 4 beams.

Fig. 5 .

 5 Fig. 5. Peak transmission rates in Mbit/s.

Fig. 6 .

 6 Fig. 6. Mean user throughput vs. traffic intensity.

TABLE I

 I

	SIMULATION PARAMETERS
	Parameter	Value
	Site layout	19 sites,
		3 sectors per site
	Inter-site distance	500m
	Cell radius	350m
	System bandwidth	5MHz
	Carrier frequency band	2.6 GHz
	Antenna model	3GPP model [19]
	Propagation model	Hata model [20]
	Path loss exponent		3.5
	Load at neighboring sectors	50%
	TABLE II
	AVERAGE TRANSMISSION RATES
	System	Rate (Mbit/s)
	Without beamforming		4.66
	SU-beamforming with 3 beams		7.55
	SU-beamforming with 4 beams		8.02
	MU-beamforming with 3 beams	5.51
	MU-beamforming with 4 beams	4.95


Antonio Famulari
email: famulari@telecom-paristech.fr

Francesco Longo
email: flongo@unime.it

Giuseppe Campobello
email: gcampobello@unime.it

Thomas Bonald
email: bonald@telecom-paristech.fr

Marco Scarpa
email: mscarpa@unime.it

A simple architecture for secure and private data sharing solutions

Keywords: Storage Cloud, Security, Interoperability, Data Sharing

I. INTRODUCTION

Cloud computing is a challenging technology that promises to strongly modify the way computing and storage resources will be accessed in the near future. The traditional taxonomy about Cloud distinguishes among services at three different levels: Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS). The above reported services can be implemented in both private and public Clouds. While private Clouds have infrastructures owned and maintained by a single organization for its own use, public Clouds are made available to the general public by a service provider.

Recently Storage as a service (STaaS) Cloud gained popularity both among private users and enterprises [START_REF] Kolodner | A cloud environment for data-intensive storage services[END_REF]. STaaS is a Cloud business model in which a service provider rents space in its storage infrastructure to individuals or companies. In this context, some of the main challenges, both from an industry and an academy point of view, are related to security (particularly associated to the personal sphere of users, compliance with legislation, and problems of trust) and interoperability.

Security problems [START_REF] Wang | Toward secure and dependable storage services in cloud computing[END_REF] are connected to the value and sensitivity of the data stored in the Cloud. On the one hand, big industrial groups might hesitate to put their sensitive data in the Cloud, under the control of other organizations, if any guarantee of privacy, integrity, and availability of data is not provided. Besides data themselves, privacy of related metadata and interactions is also important. In fact, such information is usually fully accessible to the Cloud operator. On the other hand, common users do not usually care about privacy and security of their data. Not subjected to strong regulation as industrial groups or unaware of risks and implications for their privacy, they tend to accept terms of use and conditions imposed by the different Cloud operators.Nevertheless, problems for user privacy are still an actual menace.

Besides privacy and security concerns, with respect to big industrial groups, common users are more concerned with the other challenge of Cloud computing, that is interoperability [START_REF] Dowell | Cloud to cloud interoperability[END_REF]. In fact, several Cloud services cannot interoperate among each other due to the absence of standard mechanisms. As a consequence, in order to fully profit of interaction facilities, two generic users usually need to rely on the same STaaS provider. This also makes difficult to migrate data from one platform to another without relying on local equipment.

Several works in literature deal with security [START_REF] Wong | Secure group communications using key graphs[END_REF] [5] [START_REF] Li | A novel framework for outsourcing and sharing searchable encrypted data on hybrid cloud[END_REF] and interoperability [3] [7] [8] issues focusing on standardization of Cloud services. Our goal is not to provide a new standard but to propose an approach that is transparent for both users and providers. In particular, we present a solution that is able to allow integration among different STaaSs without asking for changes in their internal policies or implementations. As a consequence, service providers can be unaware of the solution. Note that our work is not focused in presenting new encryption mechanisms or techniques. In fact, our solution is more targeted on privacy preservation and with this aim it is able to directly exploit a variety of encryption algorithms already present in literature with minor changes in the design and implementation. Our proposal relies on: i) a user client containing all the added complexity, ii) out of band (OOB) communication mechanisms (e.g., email or XMPP services) used for signaling purposes, and iii) potentially any existing STaaS with minimum sharing requirements for user data storing.

II. MOTIVATIONS AND REQUIREMENTS

Two kind of requirements have been identified: privacyrelated requirements and functional requirements.

A. Privacy-related requirements

In the context of the present work, privacy is intended as the effectiveness for a user to be able to restrict the access to data he/she is responsible for (e.g., as a producer of the content) or related to (e.g., details about his/her interactions). We thus differentiate among privacy of data and privacy of metadata. Such an effectiveness can be affected by technical and/or social (e.g., social engineering) interferences [START_REF] Zhou | Security and privacy in cloud computing: A survey[END_REF]. Privacy of data. Privacy of data is satisfied if a user, as producer or owner of a given piece of content, is able to define who can access it and he/she is not obliged, by construction of the platform, to make it accessible to any other party, included any service provider or any other entity running the service. We believe that not only the user should have an exact perception of who can access his/her data, but that it should be possible to assure that nobody but intended parties may access shared content.

Privacy of metadata. Metadata attached to user data may sometimes reveal more information than the data itself. As an example, let us consider metadata of a photograph: it may contain several sensible information such as GPS position, date and time of the photograph, device that has been used, and so on. We believe that medatada should be protected neither more nor less than data, and it should be exclusively accessible to intended parties [START_REF] Snively | An application of security access and control to semantic metadata management[END_REF]. Moreover, nobody but interacting parties should be aware of any social interaction/relationship.

B. Functional requirements

In the present work, we focus on functional requirements from two main point of views. On the one hand, we put our attention to the flexibility in the choice of the external resources and services that user can exploit. On the other hand, the granularity of the access control mechanisms is taken into consideration.

Flexible choice of external resources. One of the main functionalities that users ask for when using STaaS platforms is the possibility to share content with other people. However, for several reasons (e.g., cost, trust toward the provider), users often rely on different storage services [START_REF] Li | A novel framework for outsourcing and sharing searchable encrypted data on hybrid cloud[END_REF]. In this case, the interaction capabilities are rather limited to the simple link sharing, and rely OOB (with respect to the exploited platforms) mechanisms such as e-mail or instantaneous messages (IM). Also, to the best of our knowledge, data migration from one platform to another is not supported by any standard mechanism. We believe that an effective sharing mechanism should guarantee full interoperability among different STaaS platforms, allowing users to interact also with principals using different services, to easily define sharing groups, and to migrate from one service to another in a simple way without relying on local equipment.

Access control. Typical access control mechanisms are much harder to be implemented in a decentralized platform with respect to centralized counterparts. However we believe that also in a decentralized sharing platform, a user should be able to define, in a simple way, with whom to share a piece of content and to easily assign and revoke such privileges.

III. ARCHITECTURE OVERVIEW AND FUNCTIONALITIES

In this section, we provide an overview of the proposed architecture and we describe the main functionalities.

A. Architecture entities

The architecture we propose in the present work is composed of three main classes of entities: (i) one or more STaaS spaces which support easy sharing mechanisms, such as HTTP or WEBDAV, used for storing data, metadata, and any information about user interactions; (ii) one or more communication services, such as e-mail or IM services, used for the signaling mechanism; (iii) one local client on each device of each user.

STaaS spaces. Our architecture is designed in order to work with several heterogeneous STaaS spaces. The configuration process consists of setting a vector <URL, credentials> for each of the STaaS spaces that the user is willing to use to store his/her data. The credentials will be provided to the client so that it will be able to login and access the storage spaces. Each user will only write on his/her storage space, which we will refer at as personal space.

Communication services. Any e-mail or IM service can be used for the signaling mechanism. In general, users should reserve one or more accounts for the platform, so that signaling messages related to our sharing mechanism do not interfere with common messages.

User client. The local client is the core of the system and provides a set of primitives/functionalities that can be used to implement a rich interaction model relying on the STaaS spaces for storing data, metadata, and information about interactions and on the communication services for the signaling and interactions. The interaction model, in terms of functionalities is independent from the used STaaS and may also be exploited by third party applications which can be implemented on the top of our client.

B. Configuration

The user needs to install the client on each local equipment that he/she wants to use and configure one or more storage spaces. Also, he has to configure one or more e-mail or IM accounts, which should be reserved for the platform usage. Then, he/she has the possibility to add a certain number of colleagues. Each colleague is identified by an identifier (e.g., name, nickname, email address). To such identifier the following items will be linked: (i) one or more URLs of the personal space of the colleague which will point to a file, called activity stream where the colleague will report his activities, and to an entry point to the colleague's data; (ii) a security association between the user and the colleague, e.g., a key or a set of keys, so that the user and the colleague may communicate and share content in a secure way; (iii) optionally, an e-mail or IM contact reserved to such usage that will be used for signalling purposes.

C. Working principle

The proposed solution implements primitives for storing content and sharing with other colleagues. Store a content. Each user authenticates and stores data only on his/her own personal spaces, hosted by a STaaS on his choice. STaaS authentication vectors will never been shared with other users. Data are always stored in an encrypted form, using encryption and key handling mechanisms embedded in the client. Contents that are not intended to be shared are stored in an encrypted way with keys that are known only by the owner of the content. Share a content. Stored content can thus be shared via public sharing links, so that anybody can download it. However, in order to access a content a user has to own the decryption keys. The application will handle encryption/decryption operations as well as assignment and revocation of privileges (in the form of keys for accessing content) and notification.

In particular, when a user shares a piece of content with a colleague, the content is encrypted with a fresh symmetric key, which in turn is shared with the recipient of the content in a secure way by mean of asymmetric public-key cryptography. Similarly, when a colleague shares a piece of content with groups of users, the piece of content is encrypted with a fresh symmetric key and only one copy of the encrypted content is produced. The symmetric encryption key is thus encrypted for the group using a group key, which is owned by all the members of a group, and shared among recipients. This assures that only intended parties may access the content. The recipient is then notified via mechanisms described below.

D. Notification mechanisms

The notification mechanisms are one of the most important aspects of the proposed architecture. They must be able to provide easy inter-Cloud sharing, meaning that they do not have to rely on sharing facilities provided by specific storage providers. In fact, thanks to our architecture two generic users do not need to rely on the same providers for interaction. The architecture supports a proactive and a reactive notification mechanism.

Proactive notification. The first mechanism relies on email or IM services to send notification messages to the colleague (or list of colleagues) to be notified. When a user chooses to share an information with someone else, a message is sent by either e-mail or IM mechanism with the link to that information into the STaaS provider infrastructure. Please note that the link to the content itself, embedded into the message, gives no access to the content, since the latter is stored in an encrypted form. The advantage of the proactive method is that thanks to "push" techniques, supported by IM and most e-mail services, an asynchronous notification is built.

Reactive notification. The second mechanism is based on a regular verification, performed by each user, of a stream file (namely Activity Stream) which is accessible on the public space of each colleague. According to such a mechanism, in order to notify a colleague of a new sharing, a user has to report such interaction in his/her activity stream. At the time of execution and regularly at predefined intervals, each client downloads and verifies the content of the activity streams of each or part of his contacts.

Note that the activity stream only contains entries addressed to specific contacts or groups of contacts. Specific entries are cryptographically protected for the user or the group of user, based on discussed security associations.

IV. IMPLEMENTATION DETAILS

A. User Client implementation

Figure 1 shows a graphical representation of the client layered architecture and its interactions with external STaaS spaces and communication services. Five modules are present in the User Client: User Interface/API, Social Engine, Encryption Module, Read/Write Module, and Signaling Module. The User Interface allows the user to interact with the system. The same layer also provides APIs to possible third party applications which can implement complex interactions based on basic functionalities provided by the system. The Social Engine handles the system life cycle implementing the orchestration of the main functionalities. The Encryption Module allows to encrypt/decrypt pieces of content through the considered encryption method. The R/W Module behaves as an abstraction layer for the different STaaS spaces that the system can deal with. Such module will be able to write only on the user personal space and read from any storage. Finally, the Signaling Module implements the communication layer by abstracting the different communication service providers.

Two main high-level functionalities are present in our prototype (refer to Figure 2 for the steps described below). On one hand, the user is allowed to share a piece of data with other users by selecting it from the local file system. First of all, the user can indicate the identity of the users or groups of users with which he/she wants to share the data (1). Then, the encryption module is instructed for encrypting the piece of content accordingly [START_REF] Wang | Toward secure and dependable storage services in cloud computing[END_REF]. Afterwards, the encrypted piece of content is uploaded to the selected Storage Cloud through the Storage Module [START_REF] Dowell | Cloud to cloud interoperability[END_REF][START_REF] Wong | Secure group communications using key graphs[END_REF]. Finally, the corresponding notification is sent to such users through the selected signaling method by mean of the Signaling Module [START_REF] Yu | Achieving secure, scalable, and fine-grained data access control in cloud computing[END_REF][START_REF] Li | A novel framework for outsourcing and sharing searchable encrypted data on hybrid cloud[END_REF].

On the other hand, the recipient client can receive signals about content that has been shared with him/her [START_REF]Association and the Open Grid Forum[END_REF][START_REF] Zhou | Security and privacy in cloud computing: A survey[END_REF]. When a notification is received through the Notification Module, the Social Engine retrieves the content on the remote Storage Cloud on which it is stored through the Storage Module [START_REF] Snively | An application of security access and control to semantic metadata management[END_REF][START_REF]The activity streams format6[END_REF]. Then, the piece of data is decrypted by mean of the Encryption Module [START_REF]Cloud data management interface (CDMI)[END_REF] and it is made available to the user through the User Interface (13).

B. Adopted standards and technologies

We implemented a prototype of the proposed architecture on an Android Samsung Galaxy Note device. Dropbox and Google Drive have been selected as STaaS spaces while Gmail as been taken into consideration as communication service. Particularly interesting are the technologies adopted in order to implement reactive notification mechanisms and group encryption mechanisms. Group keying mechanisms. So as to support easy sharing with locally defined groups of users, each principal may locally define groups of users such as friends, family, co-workers. Our proposal relies on Group Encryption with hierarchy of keys [START_REF] Wong | Secure group communications using key graphs[END_REF], which allows to define by construction of the group several subgroups. Such approach allows the issuer of the group to address content to the whole group as well as to one or more subgroups. It also allows for easy revoking privileges to one user, i.e. removing one user from a group, reducing the number and the complexity of the operations for re-keying remaining users.

C. Reactive notification module

We a JSON format for the activity streams. More in particular, a customization of the approach proposed by [START_REF]The activity streams format6[END_REF] has been implemented. In Figure 3, the structure of the Main Activity Stream is shown. Field "url" contains the URL of the user personal space, which is the entry point to his/her data while "totalitems" is the maximum number of objects that the stream may contain. This has been set up to 45 in order to maintain the activity streams small. As soon as the number of elements exceeds such limit, a new Activity Stream is generated, which links to the previous one via field "prev". Each Activity Stream also links to the following one via field "next". The current Activity Stream is always available at the same URL in order to facilitate the retrieval while previous Activity Streams are moved at different URLs as specified by fields "prev" and "next". Field "first" links to the first Activity Stream so that it is possible to go through the whole list of streams starting from the beginning. Field "main activity array" lists all the activities reported in the Fig. 3. Structure of the Main Activity Stream current stream. As discussed above, each activity reported in the Main Activity Stream is referred to a list of users and thus described in the related List Activity Stream, linked through field "url" of "main activity array".

List Activity Streams have a very similar structure with the exception that several objects link at the content rather than at other streams as in the case of Main Activity Streams. In Figure 4, the structure of object "image" in a List Activity Stream is depicted. Field "title" is a human readable message that is displayed to the user. Field "url" contains the URL of the personal space of the user while "id" is composed of the list-id joined with a sequential number for the list. Main Activity Streams are downloaded in parallel and the analysis of each of them starts as soon as the download is completed. Based on the content of the latter, List Activity Streams are possibly downloaded and analyzed.

D. Proactive notification module

We relied on email as messaging system. Messages follow JSON format very similar to the one adopted for Streams. The adopted email address is exclusively used for the system. As soon as a new activity is performed by the user, the latter can choose one or more recipients. Thus, the system automatically generates email messages addressed to the recipients with a description of the new activity. At the reception of the email, the client automatically reacts decrypting and analyzing the message and displaying the notification on the terminal.

E. Internal database

The internal status of the application is maintained within an internal database which has been implemented in SQLite. Such database is stored in an encrypted form on the personal space of the user and contains basic information about the user (his email, personal information and keys), his contacts (e.g. associations between users and related keys, lists of friends and related keys) and his activities within the platform (for example, each sharing activity is reported). Such database is upgraded on the personal space of the user each time the latter launches the application, performs a significant action (e.g. adds a new contact, shares a new piece of content) and allows the user to accesses the platform from different devices. Based on our experience, the size of the SQLite database is few KB, and grows very slowly as the number of contacts or activities increases.

V. EVALUATION

In this section we provide both qualitative and quantitative evaluation.

A. Qualitative Evaluation

The system we propose implements a simple co-working environment, allowing sharing of contents and providing a framework that can be exploited for building complex interactions, relying on several STaaS which are in general unable to interact.

More in details, qualitative advantages of our system are the following.

• It add new mechanisms for inter-Cloud data sharing among different STaaS without the necessity for them to change anything in their way of working, while previous works mostly focuses on standardization of Cloud to Cloud interfaces [START_REF]Cloud data management interface (CDMI)[END_REF], [START_REF] Luo | Experiment design for cloud storage application based on cdmi[END_REF]. Complex functionalities can be implemented as plugins on the top of the system, which provides primitives for interactions.

• It only relies on basic services of the Internet for sharing content (e.g., HTTP, WebDAV) and communication (e.g., e-mail, IM). Relying on these services ensures durability, robustness, and compatibility of the service in the current Internet.

• It assures good levels of protection for the personal sphere of users: all data stay under the control of the owners and remain inaccessible to any unauthorized party, included the storage service. Besides, access to data is as anonymous as possible, since the access control relies on encryption and users never have to authenticate in order to access a piece of content. The Cloud provider can only track accesses based on the IP addresses, but this kind of tracking has always been there since the born of Internet. Also, several project aiming at providing anonymity at IP level already exist, such as the TOR project, which allow to avoid IP-based tracking.

• It abstracts from the exploited storage service: each user may rely on the service of his choice, provided it allows to share a piece of content via a sharing link. Each user will always write on his/her own space. Each sharing, modification, comment to a content can only be done by uploading content on the own storage space and relying on the interaction mechanism for notification.

B. Quantitative Evaluation

We consider the dependency on the signalling module, which for some interactions is based on the publish/subscribe approach, as critical with respect to system performance. In fact, in order to display the list of activities of a user contacts it is necessary to download, decrypt, and analyze several activity streams.

With the aim of evaluating the efficiency of such approach, we tested our prototype in the more demanding case of social network interaction dynamics, since inter-cloud sharing and social network platforms are collapsing in one unique interaction model. Also, although inter-cloud sharing systems are mostly intended for usage from a PC, we also considered usage from smart phones. We thus tested the publish/subscribe approach on both a mobile device (Android Samsung Galaxy Note) and a PC (Pentium 4, 2GHz, 1GB RAM) and observed a very weak dependence on the local hardware with respect to other parameters. More in particular, performance depends on several variables: (i) Internet connection used for downloading user activity streams; (ii) performance of the different services users leverage for storing their own data; (iii) number of contacts of which it is necessary to download, decrypt, and analyze the related activity streams; (iv) number of activities of such contacts in the context of the social network; (v) employed device.

For what concerns the Internet connection, we tested the mechanism in the case of both the Ethernet-based Internet connection of our University Department and a 3G Internet connection (usually used on smart phones). As storage services we relied on Dropbox. Concerning the number of user contacts, we identified 3 different scenarios which are typical of social network platforms [START_REF] Ugander | The anatomy of the facebook social graph[END_REF]: users with a small number of contacts (25 contacts), users with average number of contacts (100) and users with a huge number of contacts (500). However, the majority of social network users tend to be interested at and to interact with a much smaller number of contacts [START_REF]Maintained relationships on facebook[END_REF], that is usually about 20% and however never more than 50 contacts; that is interactions with 5, 20 and 50 contacts in the three discussed cases. That means a social system can give higher priority to such subsets of contacts for providing a first activity stream of most important contacts, then download in the background data for all the remaining contacts. Note that this approach is somewhat similar, in terms of user experience, as what common social networks provide by allowing users to favorite some contacts for filtering out most interesting entries in the activity stream. For what concerns the activity of contacts, we considered average levels of activity for all contacts, that is about five activities per day [START_REF]Typical daily facebook activities[END_REF]. However, among all the activities a user can perform, only a subset of them are notified via the publish/subscribe mechanism, that is notification to a wide range of contacts; while others, for example direct one-to-one interactions, are notified via direct messages (e.g., IM, email). Such distinction is not foregone, and depends on design choices. With respect to the list of typical activities the ones notified via the publish/subscribe model are: (i) new friendship/contact: since in general new relationships are notified to all contacts; (ii) posted a status update, a new picture, or a wall post etc.: since that concerns several contacts of a user; (iii) liked a friend's content: so as to implement a basic recommendation system. Such subset of activities represents about 47% of all typical day's activities [START_REF]Typical daily facebook activities[END_REF]. Results of the simulations for the three cases are summarized in Table 1. We report in parentheses the results obtained by considering the subset of maintained relationships only, as discussed above. The bottleneck seems to reside in the download of the several activity streams, while decryption and analysis operations seem to have a smaller impact on overall performance of the system. That means the system remains usable in the case of University Internet connection in all the cases except the most demanding one (a user with 500 contacts who is interested at the activities of all his contacts, which in general is not the case). On the other hand, that is with a 3G Internet connection, the system seems to be usable only in the case where one is interested at a very small subset of contacts. However, in the case of inter-cloud sharing users tend to maintain a very small number of contacts.

VI. CONCLUSIONS AND FUTURE WORK

In this work, we proposed a new approach for inter-Cloud data sharing. We first identified the main requirements and then provided both high-level and implementation-level details of our approach. Relying on open standards, such as HTTP, WebDAV, e-mail, and IM, our approach ensures durability, robustness, and compatibility of the approach in the current Internet by providing security and interoperability. In the future, we aim at implementing a more complete prototype of our architecture and quantitatively investigating functional and non-functional requirements. Moreover, we plan of building on top of our architecture by implementing a distributed, shared, and secure file-system exploiting STaaS spaces available online.

Fig. 1 .

 1 Fig. 1. Graphical representation of the proposed architecture.

Fig. 2 .

 2 Fig. 2. Interactions between two clients.

Fig. 4 .

 4 Fig. 4. Structure of object "image" in a List Activity Stream

TABLE I

 I

		.	PERFORMANCE OF THE SYSTEM
	Connection	25 (5) contacts	100 (20) contacts	500 (50) contacts
	University	4.6 (1.6) sec.	5.6 (4.6) sec.	15.5 (5.2) sec.
	3G	10.9 (3.8) sec.	34.5 (13.5) sec.	48.5 (13.5) sec.

ACKNOWLEDGMENT

The research leading to these results has received funding from the Italian National project "Integrated Cloud-Sensor System for Advanced Multirisk Management" under grant agreement PON01 00683.


T Bonald

S E Elayoubi

A El Falou

J B Landre

Radio capacity improvement with HSPA+ dual-cell

This paper studies the radio capacity improvement provided by an HSPA+ key feature, dual-cell, combined with MIMO. The proposed method combines drive test measurements, link-level simulations, and a queuing theorybased statistical capacity model, thereby providing a reliable estimate of the network radio capacity. Simulation results show that dual cell combined with MIMO and non-linear receivers using Successive Interference Cancellation (SIC) significantly increases network radio capacity. These results confirm that HSPA networks evolutions are promising.

I.

INTRODUCTION

3G wireless technology has kept improving since the first releases of the 3G standards. Each new release of 3GPP specification comes with new features that bring progress both to consumers and network operators. 3GPP Release 7 specifies HSPA+, which introduces several significant improvements over HSDPA Release 5 [1], such as Continuous Packet Connectivity (CPC), 64QAM modulation and MIMO [START_REF]Physical layer procedures (FDD)[END_REF]. In Release 8, HSPA dual-cell aggregates two adjacent carriers, thanks to a joint scheduling scheme. In Release 9, dual-cell and MIMO can be combined [3]. The advantage of dual-cell is that it improves the user throughput for a given load, for any location in the cell, even at cell edge. Moreover, it is expected to bring high radio capacity gains. This feature is therefore held as the most important feature of HSPA+ so far. The reason is that operators are facing an important increase of data traffic, which they may not be able to cope with in the medium term. They obviously pay a high attention to HSPA features that improve spectral efficiency since this can delay the need for new spectrum, and also delay the rollout of new LTE networks that have better spectrum efficiency. The purpose of this paper is to assess the capacity gain provided by HSPA dual-cell feature, first for Release 8 compliant networks (i.e. without MIMO), and second for Release 9 compliant devices (i.e. when dual-cell and MIMO are combined). In [START_REF] Saadani | Realistic Performance of HSDPA Evolution 64-QAM in Macro-Cell Environment[END_REF], we proposed a throughput prediction method that combines drive test measurements made with a scanner equipment, and link-level simulations results. This method is able to give accurate HSPA throughput predictions for any HSPA device. We show in this paper how to combine these realistic throughput predictions with queuing theory methods in order to derive the capacity gains for streaming and data services. In particular, we extend the theory developed in [START_REF] Bonald | Wireless downlink data channels: User performance and cell dimensioning[END_REF] for single carrier systems to the dual-cell case; the main difficulty comes from the mix between legacy, single-carrier devices and HSPA+ dual cell ones.

The capacity gain from dual-cell is known to come from frequency diversity, higher multi-user diversity, and trunking effect due to statistical multiplexing. A few previous works have started the evaluation. In [6], the gains from frequency diversity and higher multi-user diversity have been evaluated; these gains are used as inputs for our capacity model. Simulation results are provided in [7] and [START_REF] Seidel | Dual cell HSDPA and its future evolution[END_REF] for full-buffer traffic. However, the trunking gain cannot be observed for full buffer traffic, as explained in [6], and has not yet been evaluated. This paper gives for the first time an evaluation of the trunking gain for elastic data traffic and streaming traffic, and brings a complete model for the HSPA+ dual-cell feature. This paper is organized as follows. Section II presents the link level modeling and throughput predictions. We discuss in section III the methodology to estimate cell radio capacity. The obtained results are shown and discussed in section IV.

II. USER THROUGHPUT EVALUATION METHODOLOGY

A. Link level modelling and outputs

The link-layer modeling methodology is detailed in [START_REF] Saadani | Realistic Performance of HSDPA Evolution 64-QAM in Macro-Cell Environment[END_REF]. It consists of four steps: a. Estimate of SINR at the receiver's output. b. Selection of the modulation and coding scheme (MCS) combination that maximizes the throughput. c. Packet viability assessment according to FER lookup table. d. HARQ retransmission in case of packet error. Chase combining with a maximum of four retransmissions is modeled.

Each device category is simulated with the most probable receiver based on a market survey: Rake receivers are used for 1.4Mbps-capable devices. Linear minimum mean squared error (LMMSE) receivers, combined with receive diversity are used from 3.6 to 21 Mbps-capable devices, as well as for dualcell devices [6]. LMMSE, combined with successive interference cancellation (SIC) receiver, is used for MIMO devices [START_REF] Landre | HSDPA radio capacity improvement with advanced devices[END_REF] [START_REF] Ghauri | Receiver designs for MIMO HSDPA[END_REF].

B. Single-user throughput evaluation

Single-user throughput is calculated with the method defined in [START_REF] Saadani | Realistic Performance of HSDPA Evolution 64-QAM in Macro-Cell Environment[END_REF]. This method combines the accuracy of field measurements on a live network with an estimate of the performance of all HSDPA devices. There are two steps in the calculations. First, an estimate of the average HS-DSCH Signal to Noise Ratio (SNR) is calculated using CPICH Ec/I0 and CPICH RSCP figures measured by a scanner equipment during drive tests. Second, HSDPA throughput for this average SNR is obtained from lookup tables that contain the results of the link-level simulations. A "simulated" HSDPA drive test is obtained at the end, with an estimate of the throughput that would have been experienced by an HSDPA device for each measurement sample. As the scrambling code of the serving cell is available for each sample, the measurements relative to each of the cells can then be extracted, and calculations can be made cell by cell. This method can be applied for all HSDPA device categories, for all the receivers' type (rake, LMMSE, SIC-LMMSE …), on the same drive test. This comes with a huge improvement over classical system simulations that are based on hexagonal cells modeling, and statistical propagation models such as Cost-Hata [START_REF]Digital cellular telecommunications system (Phase 2+); Radio network planning aspects[END_REF], which is quite far from reallife conditions. Measured Ec/I0 and RSCP figures are much more accurate than predicted values.

III. RADIO CAPACITY

HSDPA radio capacity calculation is not as straightforward as one might expect. The common method consists in defining the cell capacity as the served throughput for a given number of users in the cell, using a static simulator ([8] [START_REF] Holma | HSDPA/HSUPA for UMTS: High speed radio access for mobile communications[END_REF]). There are however one key drawback in this method: it does not consider the statistical behavior of the traffic demand. Indeed, in a real network, the number of users in the cell keeps changing, and the activity of each user is not constant over time. We usually refer to these models as "Erlang-like", since they model the statistical behavior of the traffic, in a similar way as the Erlang B law does.

A. Elastic traffic 1) Single Carrier

We start with the simplest case, where only legacy terminals are served by the cell. In the absence of load balancing mechanisms, the traffic demand, denoted by A, can be considered as equally split between the two operating carriers. The capacity of a single HSDPA carrier has been addressed in [START_REF] Bonald | Wireless downlink data channels: User performance and cell dimensioning[END_REF] for a circular cell case. In this paper, we show how to apply this model on drive test predictions. Let C be the harmonic average of the single-user throughput, obtained from the drive test simulations:

(1) where S is the set of points considered in the studied cell and |S| its cardinality.

is the throughput predicted by the drive test simulations in position u.

To calculate user throughput, we use a Processor Sharing (PS) queue that gives the distribution of users in the cell. Defining the carrier load , the probability that the number of users in the cell is equal to m, is:

(

Based on this probability distribution and on the single-user throughput over the cell, we can characterize the user perceived QoS, in terms of average throughput and throughput percentiles.

First, the probability that a HSDPA user, located at position u in the cell, has an average flow throughput equal to , knowing that there are m active users in the cell, is given by:

(3) where is the average number of users in the cell. Thus, the average user flow throughput over the cell is:

(4)
If a target throughput T min is fixed for HSDPA users, the probability of achieving this target is equal to:

(5)

2) Dual Carrier New HSDPA UE categories (21-24) have been introduced to support the DC HSDPA feature. They can simultaneously use the two available carriers in the cell, as described in Figure 1. This doubles the stand-alone throughput at each point of the cell and its harmonic average throughput. Thus, the cell load becomes:

. This leads to the same probability distribution function and a doubling in the average flow throughput of equation ( 4). However, the percentiles of the throughput are not doubled, as the probability of achieving a throughput target can be calculated, as above, by: ( 6)

3) Mix of single and dual carrier users Even if all new UE categories are DC-compliant, they will coexist with legacy SC users. Therefore, the available MHz carriers are used to serve both SC and DC users simultaneously. The cell can then be modelled as three queues: two queues of capacity C each receiving the single carrier traffic, and one queue of capacity 2C receiving all the traffic (see Figure 2). We denote by class 1 the legacy traffic carried by one carrier; by class 2 the legacy traffic carried by the other carrier and by class 3 the dual carrier traffic. The network state is defined by the vector where is the number of classc users in progress. According to [START_REF] Bonald | Computational aspects of balanced fairness[END_REF], the steady-state probabilities describing the evolution of the number of calls of each class, are calculated by: (7) where is the offered load of class c flow ( and ) and .

The function describes the balanced allocation between carriers and can be calculated recursively by: [START_REF] Seidel | Dual cell HSDPA and its future evolution[END_REF] where is a ( ) vector with 1 in component c and 0

elsewhere. The resources allocated to the different classes is: The average flow throughput of a class-c user at position u is: [START_REF] Landre | HSDPA radio capacity improvement with advanced devices[END_REF] And the probability of attaining the target throughput T min for class-c calls is equal to:

(9)
(11)

B. Streaming traffic

Unlike elastic traffic whose QoS is expressed by a throughput performance, streaming calls require a guaranteed throughput over time; their QoS is thus expressed by a blocking rate.

1) Single Carrier

Let m u be the number of streaming users in position u of the cell. The Call Admission Control (CAC) condition ensuring that the required throughput is guaranteed for all users is: [START_REF]Digital cellular telecommunications system (Phase 2+); Radio network planning aspects[END_REF] Indeed, a call with a stand-alone throughput equal to occupies all the carrier resources for a time proportion equal to . The capacity of the system can then be analysed using a classical multi-Erlang approach, where the state of the system is defined by the vector describing the number of calls of different radio conditions and the CAC condition becomes , where is the vector of required throughputs.

The steady-state probabilities are then calculated by: (

) 13
where E is the traffic in Erlang. The blocking probability is:

However, as there are many measurement positions in the cell, the calculation of blocking probabilities becomes infeasible. We thus use the well known Kauffman-Roberts recursive formula [START_REF] Roberts | A service system with heterogeneous user requirements[END_REF] that calculates rapidly the blocking rates.

2) Dual Carrier For a cell containing only DC users, the stand-alone throughput is doubled and the cell is viewed a one queue carrying all the traffic. The CAC condition is thus given by and the steady state probabilities become:

The blocking rates can thus be easily solved using the Kaufman-Roberts formula.

3) Mix of single and dual carrier users When a mix of single carrier and dual carrier users coexist in the cell, the system is again modeled as a network of queues as in Figure 2. This network of queues is now governed by a system of three simultaneous CAC conditions corresponding to the three queues: The blocking probability for each queue is then calculated by:

(18)

where is a vector having 1 in the component corresponding to position u of queue c and 0 elsewhere. Unfortunately, the Kaufman-Roberts formula cannot be used in this case. A conservative bound for the blocking rates is obtained by taking independently each queue c with its own CAC condition and calculating its blocking rate using Kaufman-Roberts formula. The blocking rates are thus approximated by: (19)

4) Mix of streaming and elastic flows

We finally consider the most general case, where single carrier and dual carrier, streaming and elastic flows share the capacity. streaming traffic is served first in order to obtain its guaranteed QoS, we use the quasi-stationary assumption and consider that elastic flows receive the average remaining resources, as illustrated in Figure 3. The average amount of time resources consumed by streaming traffic in both carriers is calculated by: Elastic flows thus benefit from a single-user equal to on each carrier. Their performance can thus be assessed as explained before.

IV. SIMULATION SCENARIOS AND RESULT

A. Scenarios and drive test measurements

The measurement campaign has been run in the centre of a major European town. Measurements are available for hundreds of cells, and one cell is selected for the capacity calculations (measurement samples are filtered with the scrambling code of the selected cell). This cell is composed of several (non contiguous) parts, which is common in live networks, especially in urban areas, because of irregular propagation from both the serving cell and the many interfering cells around, and because of the irregular cell planning. 1000 measurement samples are available for this cell. The average CPICH Ec/I0 on the cell is -7db, and the average CPICH RSCP is -65dBm. The map of the drive test is shown in Figure 4. For the sake of simplicity, the main capacity results we present assume that all the devices belong to the same category. Mixes of devices of different categories are then only considered to show the impact of dual-cell devices penetration on the gain. Calculations have been run for streaming traffic, elastic data traffic and a mix of them.

B. Simulation results and discussion

Single-user throughputs are calculated for all the locations in the cell, for each HSDPA device category. Figure 5 Capacity results are given in Figure 6, 7 and 8. It turns out that higher HSDPA mobile categories bring significant capacity improvement over basic ones: from 1.8 Mbps devices to single-cell 42.2 Mbps ones, a increase of the cell radio capacity is achieved. The capacity gain from dual-cell (Cat 24) is 38% for streaming services (Figure 6) and 60% for elastic data traffic (Figure 7), which is huge.

Figure 7 shows the impact of a progressive introduction of dual cell devices (Cat 24) in the market, while other legacy devices are supposed from category 14. The capacity, calculated using the model of section III.A.3, increases rapidly until reaching the maximal gain (60%) when dual cell devices become very popular. As of Figure 8, it illustrates the capacity of a cell carrying both streaming and elastic users, all equipped with category 24 devices. As streaming calls have priority over elastic ones, the capacity left for data calls reduces when the streaming traffic increases, until reaching almost zero when the streaming traffic attains the cell capacity of 21 Erlangs. Note that, from Figure 6, it is obvious that, among the HSPA technology evolutions, those that enhance performance at cell edge also improve significantly the radio capacity. This is true for receive diversity (Cat 6 vs. Cat 12) and MIMO (Cat 16 vs. Cat 10). This is also the case for the dual-cell feature, which provides a twofold improvement of the throughput at cell edge (Cat 24 vs. Cat 14 and Cat 28 vs. Cat 20). The reason is that users at cell edge require an important amount of the shared resources (streaming calls) or stay for a long time in the cell until transferring their files (elastic calls). This is also the reason why 64 QAM does not bring a large capacity gain as it is achieved for a small proportion of users at cell center.

When we compare MIMO with dual cell, the former brings a 95% capacity gain while the latter brings a 45% gain (Figure 6). However, dual-cell has an important advantage over MIMO: it comes only with a software network upgrade, while expensive hardware upgrades are required for MIMO (a new transceiver must be added for each sector). This makes dualcell more interesting for network operators than MIMO in Release 8, where both features cannot be combined. However,

C. Comparison with other statistical capacity models

In this section, we compare the capacity results obtained with our model with some common models of the literature.

1) Streaming

The classical method for the streaming capacity is to calculate the average throughput over all points of cell (

) and to use the Erlang-B formula based on the modified admission condition from Eqn. ( 12):

, m being the number of users in the cell and G div the diversity gain.

2) Elastic data traffic

The classical measure of network capacity when data calls are considered is the average (arithmetic) cell throughput when several users are served ( [7][START_REF] Seidel | Dual cell HSDPA and its future evolution[END_REF]). However, we have shown in [START_REF] Bonald | Wireless downlink data channels: User performance and cell dimensioning[END_REF][10] that the "harmonic mean" of the achievable throughputs gives the maximum traffic the cell can sustain while being stable, but without any QoS guarantee. Indeed, the harmonic mean takes into the fact that users with bad conditions stay longer in the cell and contribute more to the cell load. Figure 9 compares five capacity measures: the arithmetic and harmonic averages of the throughput (after adding the diversity gain), and the statistical cell capacity when the target throughput is equal to 250, 384 and 500 Kbps. First, we observe that the arithmetic mean over-estimates the capacity. Second, the higher is the target QoS, the lower is the cell capacity. Indeed, all the results from the statistical model are lower than the harmonic mean (that can be considered as the capacity with a target throughput of 0); when target QoS decreases, the capacity thus closer to the harmonic mean.

As of the dual cell gain, the inverse tendency is observed. Indeed, if we focus on dual cell Cat 24 devices and compare them to single carrier ones (Cat 14), the capacity gain is 60%, 46%, and 33% for a target QoS of 500 Kbps, 384 Kbps and 250 Kbps, respectively. The only gain for the harmonic mean is that due to increased diversity gain (10%). This is not surprising since the trunking capacity gain is known to increase when the relative QoS (target QoS divided by the absolute capacity) increases.

V. CONCLUSION

This paper develops a complete HSPA+ radio capacity model that starts from link level simulations, combines them with drive test measurements, and uses the obtained data rates as an input for a queuing theory model. The results show that the HSPA+ dual cell feature improves the cell capacity significantly (around 40% of additional streaming capacity). This capacity gain increases up to 150% if dual cell is combined with MIMO, using non-linear SIC receivers (both are Release 9 features). Thanks to HSPA+ technology evolution, HSPA networks shall thus be able to successfully face the traffic increase in the upcoming years.

As of future work, our aim is to study the joint scheduling over 4 carriers, proposed in 3GPP Rel. 10. The capacity model proposed in this paper can also be reused for the LTE-Advanced carrier-aggregation feature, also planned in Rel. 10.

Figure 1 .

 1 Figure 1. From single-cell scheduling to dual-cell in 3GPP R8

Figure 2 .

 2 Figure 2. Both SC and DC users coexist in the cell.

  n in queue c and is the overall system state. We denote by the set of admissible states verifying the three CAC conditions defined above; the steady state probabilities are thus calculated by: (17)

Figure 3 .

 3 Figure 3. Mix of streaming and elastic traffic.In order to assess the capacity improvement of HSPA+ dual-cell over the previous HSPA devices, HSPA Release 5 devices have been simulated (categories 12, 6, 8, 9 and 10) as well as HSDPA Release 7 devices (categories 14 and 16) and HSDPA Release 8 (category 20) devices. Simulation parameters are given in Table1. The symmetrical mode of dual-cell, in which common channels are set on the secondary carrier, is modeled.

  shows the single-user throughput distribution for 21.1 Mbps-capable (category 14) devices. The throughputs are lower than the peak Multithe tricky radio propagation conditions, and because of the high inter-cell interference conditions.

Figure 4 .Figure 5 .

 45 Figure 4. Map of the drive test for the measured cell

Figure 6 .

 6 Figure 6. Streaming all HSDPA device categories (on 10 MHZ)

Figure 7 .Figure 8 .

 78 Figure 7. Elastic traffic capacity for different dual-cell devices penetration

  although MIMO and dual-cell are "competing" features in release 8, they can be combined in Release 9, bringing a combined gain of 150% (Cat 28 vs. Cat 14).

Figure 9 .

 9 Figure 9. Cell elastic traffic capacity for several QoS targets

Table 1 .

 1 The symmetrical mode of dual-cell, in which common channels are set on the secondary carrier, is modeled.

	PARAMETER	SETTING
	Multipath channel	Pedestrian A 3km/h
	Orthogonality factor	0,25 for RAKE 0,15 for LMMSE
	Downlink interference rise	6 dB
	Indoor penetration factor	8 dB
	Diversity gain from proportional fair	10%
	scheduling (PFS)
	Diversity gain from PFS in the	20%
	presence of dual-cell [6]

Table 1 :

 1 Radio parameters used in the calculationsAll the other network settings, that are usually set in simulators as parameters (inter-site distance, antenna gain, path loss model, etc.) do not need to be set in our calculations since they come from the live network.

	PARAMETER	SETTING
	User throughput target for	500 kbps
	elastic data services	achieved with a 90%probability
	Streaming service throughput	250 kbps (5% blocking rate)

Table 2 :

 2 Parameters used in the capacity calculations

Table 3 :

 3 Table 3 compares the capacity results for both models. It can be seen that the Erlang B method is optimistic as it does not quantify the impact of cell edge users on capacity. Model comparison with Erlang B results. The average throughput over the cell for Cat 24 devices is equal to 7.76 Mbps.

	METHOD	CAPACITY
	Erlang B law	25.7 Erlangs for 5% blocking
	Model described in III	21.3 Erlangs for 5% blocking