Computer Networks 94 (2016) 164–175

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An efficient location aware distributed physical resource block assignment for dense closed access femtocell networks Sudeepta Mishra∗, C. Siva Ram Murthy Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai 600036, India

a r t i c l e

i n f o

Article history: Received 11 June 2015 Revised 8 October 2015 Accepted 10 November 2015 Available online 22 November 2015 Keywords: Macro–Femto cellular network Resource allocation Power control Energy efficiency

a b s t r a c t The demand for higher data-rate in the indoor environment is unrelenting, and has triggered a huge deployment of Femto Base Stations (FBSs) in such environments. A large portion of these FBSs are privately owned and operate in closed access mode. However, due to aggressive spectrum reuse among these FBSs, co-tier interference is very high. Techniques relying on Fractional Frequency Reuse (FFR) will not scale in these dense FBS networks as the effective available spectrum per FBSs will be a little to support any meaningful data-rate at any FBS. Moreover, the techniques that use both power control and sub-channel allocation usually operate in a centralized fashion. Hence, these are a huge burden to the entire system. To handle this additional interference without significantly affecting spectrum efficiency, efficient location aware Physical Resource Block (PRB) assignment among interfering FBSs is necessary. In this paper, we formulate the PRB assignment problem as a Mixed Integer Non-Linear Program (MINLP) that exploits User Equipment (UE) location with respect to its interfering FBSs. Since the optimization problem is NP-hard, we propose a twofold solution which can efficiently reuse the PRBs while maintaining the interference below a threshold. First, an iterative elimination algorithm for PRB allocation and second, an adaptive PRB power control to find the required transmission power which minimizes interference. The proposed technique operates in a distributed manner and improves per FBS PRB reuse, energy efficiency, system blocking. Obtained results are verified using extensive simulations. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Higher capacity and better coverage are two of the most important requirements of a User Equipment (UE) and goal of a cellular network. High powered outdoor Macro Base Stations (MBSs) can provide better coverage and capacity to highly mobile outdoor UEs. But when it comes to the indoor environment such as homes, offices, and shopping malls, they fall short to provide acceptable signal quality [1], which results in low capacity and intermittent coverage. In order to improve the system performance, a large number

∗

Corresponding author. Tel.: +91 7200670654. E-mail addresses: [email protected], [email protected] (S. Mishra), [email protected] (C.S.R. Murthy). http://dx.doi.org/10.1016/j.comnet.2015.11.013 1389-1286/© 2015 Elsevier B.V. All rights reserved.

of MBSs can be deployed but it will result in very high capital and operational expenditure. Moreover, recent studies show that 50% of voice and 70% of mobile data originate from indoors [2] which cannot be efficiently served by such traditional outdoor MBSs. Hence, the use of small and low powered Femto Base Stations (FBSs) has been suggested to improve indoor coverage and capacity. FBSs do so by decreasing the distance between the transmitter and the receiver [3] and increasing the spectrum reuse. Moreover, FBSs are connected to the cellular backbone over an Internet based back haul through Femto Management Gateway (FMG) using either DSL or ADSL. This feature allows ad-hoc deployment of FBSs by users. An FBS can support a few UEs and hence, it should be clear as to which UE can get service from a specific FBS. Currently there are three different access modes defined for an FBS viz.,

S. Mishra, C.S.R. Murthy / Computer Networks 94 (2016) 164–175

(i) Open Access mode: any UE can access an FBS and benefit from its services, (ii) Closed Access mode: only a specific set of UEs belonging to a Closed Subscriber Group (CSG) of UEs can get service from an FBS, (iii) Hybrid Access mode: an FBS has different set of service rules for UEs in CSG and non-CSG. It has been predicted that, by 2016, more than half of all cellular traffic each month from mobile-connected devices (almost 14 exabytes) will be offloaded to the FBSs [4]. Hence, the number of FBS will increase exponentially which will result in a large number of dense FBS networks [5]. These dense uncoordinated deployment of FBSs will result in increased co-tier interference to neighboring FBS UEs. Specifically, in the case of closed accessed FBSs this interference is going to aggravate further [6]. In order to harvest meaningful capacity from such dense FBS networks, the interference should be handled carefully. For this, numerous interference management schemes [7,8] based on frequency reuse and/or power control techniques are available in the literature. The next section briefly reviews these schemes and also presents our contribution in this respect. 2. Related work Fractional Frequency Reuse (FFR) is a type of frequency reuse technique that allocates orthogonal PRBs among neighboring FBSs to minimize the co-tier interference. Several algorithms and approaches viz., clustering, graph coloring and Integer Linear Programming (ILP) have been used for PRB assignment using FFR in dense FBS networks. In this direction, authors in [9,10] allocate a fixed number of PRBs to each FBS depending on traffic conditions and channel characteristics. If some PRBs are not utilized in an FBS, then they are not used by any other FBS and are wasted. The authors in [11] propose a distributed graph based clustering technique to find different non interfering FBS clusters in which the complete set of PRBs can be allocated. However, the proposed technique assumes at most one active UE per FBS. Moreover, the scalability of this algorithm for more than one user is difficult and complex. The authors in [12] suggest a clustering based approach in which FBSs are divided into non interfering clusters, and an FBS is selected as a cluster head which takes care of the PRB allocation in its cluster. Further a feedback mechanism is used to remove the interfering PRBs shared by clusters. They extended their work further to take care of PRB allocation among high priority and best-effort UEs. Graph theory and ILP have been extensively used to model the PRB assignment problem in a network consisting of FBSs and UEs. The authors in [13] formulate an ILP problem to achieve FFR of PRBs among neighboring FBSs. Subsequently, they undertake a three step approach to solve their ILP problem viz., FBS PRB requirement estimation, interference graph computation, and graph coloring. The authors in [14] suggest an interference aware graph coloring technique for PRB assignment. First they color the nodes with highest interference, then they color the remaining nodes in such a way that previously colored nodes experience least interference. In this technique, a node is assigned only one color corresponding to its weight. Additionally, all the nodes need to be colored. This technique cannot handle dynamically varying FBS demands. The solution in [15] also suggests a graph based technique that selects a set of non interfering FBSs

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using Maximum Weighted Independent Set (MWIS) and then allocates the PRBs among these FBSs. This solves the problem of assigning multiple PRBs to an FBS. But the MWIS technique used in the above paper has a very high computational overhead. The authors in [16] present a decentralized algorithm using message passing to decide the assignment of PRBs to FBSs. Compared to this, [17] proposes a self selection technique to find the set of non interfering PRBs that are not used by its neighboring FBSs. FFR is simple and effective in minimizing the interference from neighboring FBSs but it reduces the PRBs available at individual FBSs. Hence, the need for higher PRB reuse is necessary. Full Reuse (FR) is an extreme approach which can attain highest PRB reuse but it results in very high interference among neighboring FBSs. In this approach every FBS shares the same set of PRBs available to the FBS tier. However, to manage the high co-tier interference, power control based PRB assignments are required. The authors in [18] investigate the co-tier (FBS-to-FBS) and cross-tier (MBS-to-FBS) interference mitigation problem using power control technique. They solve this problem using distributed auction game by considering FBS as an auctioneer and UEs as bidders. Although the approach has a low computational complexity, it assumes that an UE can have at most one channel. The authors in [19] propose a dynamic spectrum allocation scheme for FBS networks based on Q-learning. Most of the existing techniques in the literature [7] suggest the use of interference avoidance channel assignment schemes (based on FFR/FR) along with various power control techniques to achieve better system performance. These techniques usually operate in centralized fashion. Hence, these are a huge burden to the entire system. It can be inferred from Shannon’s capacity formula [20] that high data rate is not only dependent on high Signal to Interference plus Noise Ratio (SINR) but also on high PRB availability. In this regard, while a FR based PRB assignment provides high PRB availability at the cost of low SINR, FFR based PRB assignment offers a high SINR at the cost of low PRB availability. Hence, a balance between FR and FFR is needed to improve PRB availability and the received SINR simultaneously. In order to achieve this, location aware PRB allocation and power control is explored to obtain high system performance [8]. In this paper, we propose a location and traffic aware PRB assignment and power control technique to improve system throughput, blocking, energy efficiency, and PRB reuse ratio. While the PRBs are assigned without explicit negotiation from immediate neighboring FBSs, PRB transmit power is computed based on the set of immediate neighboring FBSs’ channel gain matrix. To summarize, our contributions are as follows, • We formulate a problem for joint PRB assignment and transmit power control. • We exploit the FBS observed indoor mobility model of UEs and calculate the location based traffic behavior. • We propose a set of distributed algorithms to determine the PRB reuse mode based on traffic behavior from immediate neighboring FBSs. • We determine the PRB transmit power utilizing immediate neighboring FBSs’ channel gain matrix.

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• Finally we simulate our technique by considering a scenario based on 3GPP specified building model [21] with close access FBSs and verify the results. The rest of the paper is organized as follows. We explain the system model in Section 3 along with channel model, indoor mobility model, energy efficiency, and location dependent PRB reuse. The problem formulation is discussed in Section 4 for PRB allocation and power control. Then we discuss our solution approach for PRB allocation using a greedy elimination algorithm and expected value transmit power control in Section 5. Section 6 presents the simulation scenario and obtained results. The work concludes in Section 7, with directions for future work. 3. System model We consider a two-tier Macro–Femto Heterogeneous Cellular Network (HetNet) (Fig. 1) with a Macro BS (MBS) deployed at the center of the MBS coverage area. The FBS tier consists of a few FBS clusters which are distributed randomly in the MBS coverage area. Each FBS cluster represents a building consisting of 5 × 5 apartments [21]. Each apartment has an FBS deployed randomly in any of its rooms. Let F be the set of all FBSs present in the MBS coverage area. The set of FBSs neighbor to FBS i is represented by F(i) and is discovered using the technique mentioned in [15]. Since the FBSs are closely deployed to each other, an UE can fall in the transmission range of two neighboring FBSs. 3.1. UE association We assume that the FBSs (F) operate in the closed access mode. An FBS i(∈ F) serves a Closed Subscribed Group (CSG) of UEs represented by U(i). The UEs (U(i)) move in the FBS i’s  U (i ) coverage area as described in Section 3.2. The set U =

represents the set of all FBS UEs. The Maximum Reference Signal Received Power (MaxRSRP) based UE to FBS association is not followed because the FBSs operate in closed access mode. Hence, if UE u(∈ U(i)) is not in the coverage area of FBS i, then it is associated with the MBS and is ignored in the analysis. 3.2. Indoor mobility model It has been observed in the recent studies that the existing macroscopic mobility models are not suitable to study the performance of resource allocation and interference mitigation techniques for FBS networks [22]. In order to evaluate the performance of the proposed technique, we develop a simple state transition diagram which mimics the movement of an UE in an apartment. Let us consider the apartment with FBS i, which has L(i ) rooms. A user can move from one room to another only through a door but not through walls. If we consider the rooms as nodes and doors connecting them as edges (ξ ), then the apartment mobility model can be represented as a graph G = (L, ξ ). There may not be a door between every pair of rooms but every room can be reached from every other room through a finite set of intermediate doors (edges) (Fig. 2). Therefore, G is a connected graph. Let pul ,l be the probability of UE u moving from room ls (∈ s d

L(i )) to room ld (∈ L(i )). If ls and ld are not connected to each other by a door then the transition probability pul ,l is 0. A s d

self-loop represents that an UE has a non-zero probability of being in the same room. Fig. 2 represents a six-room apartment. The overlaid graph shows the possible transitions from one room to another. We can observe that a room can be reached from any other room but only through a few finite set of intermediate doors.

i∈F

Fig. 1. Two tier Macro–Femto HetNet.

S. Mishra, C.S.R. Murthy / Computer Networks 94 (2016) 164–175

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3.4. Energy efficiency The energy consumption of FBS i is divided into two parts. First, the constant power consumption, E0 , that is the minimum power consumed at an FBS to keep the internal circuitry active, where as the second part depends on the sum transmit power of the FBS across all the PRBs.

E i = E0 +

 

aku,i Pik

(6)

u∈U (i ) k∈N

In order to analyze energy efficiency of the system, we calculate the ratio of total energy consumed to the system throughput. It is called as Energy Consumption Rating (ECR) [23].

ECR = Fig. 2. Transition probability graph of an UE in an apartment (L = 6).

Energy consumed E f f ective system capacity 

=   

The total spectrum available for the FBS tiers is divided into N non-overlapping PRBs. We have also assumed that the MBS and FBS tier operate in spectrum orthogonal to each other. Thus, there is no cross-tier interference. However, the co-tier interference among neighboring FBSs operating in the same spectrum is still very large. In our model, resources are assigned in terms of PRBs. Let aku,i be an indicator variable which represents, if PRB k(∈ N) is allocated to UE u associated with FBS i.



aku,i = 

Ei

i∈F

3.3. Channel model

1, PRB k is used by UE u ∈ U (i ) 0, otherwise

aku,i ≤ 1, ∀i, k

(1)

(7)

i∈F u∈U (i ) k∈N

k aku,i ru,i

(8)

4. Problem formulation We formulate an optimization problem to maximize the utilization of total PRBs (N) across all the FBSs (F) while minimizing the interference at UEs. 4.1. Location dependent PRB reuse We define an indicator variable ni, j which represents whether FBS i and FBS j are neighbors to each other,

(2)

⎧ ⎨1, i f F BS i & j are neighbors

0, i f F BS i & j aren t neighbors 0, i = j

u∈U (i )

ni, j =

Inequality Eq. (2), tells us that PRB k can be used at most once by FBS i. The down-link SINR of UE u(∈ U(i)) from FBS i on PRB k is,

We also define F(i), the set of all FBS (j ∈ F) neighbor to FBS i as follows,



k u,i

= 



aku,i Pik hu,i

j∈F (i ) v∈U ( j )

akv, j Pjk hu, j + W σ 2

,

∀u, i, k

(3)

where, Pik (Pjk ) is the per sub-channel transmit power of FBS

i(j), hu, i (hu, j ) is the channel gain of UE u from FBS i(j), and σ 2 is the white Gaussian noise power. W is the width of a PRB in Hz. Note that, we have ignored the interference from non neighboring FBSs F − F (i ) as it is insignificant when compared to that of neighboring FBSs F(i). k of UE u from FBS i on PRB k is The down-link data rate ru,i a function of SINR

k , u,i

k k ru,i = F (u,i )

(4)

F (. ) is the rate function and is assumed to be same for each FBS in the system. For a basic scenario, the rate function can be represented as follows, k k F (u,i ) = W ∗ log(1 + u,i ) ∀u, i, k

(5)

⎩

F (i ) = { j : j ∈ F and ni, j = 1}

(9)

(10)

The allocation of PRB k among two neighboring FBSs i and j (Fig. 3) can be done in two ways, (i) FFR and (ii) RPR, which are explained as follows. Fractional Frequency Reuse (FFR): An FBS i cannot reuse PRB k, if it is in use by any of its neighboring FBS j(∈ F(i)). The FFR of PRB k for any two UEs u(∈ U(i)) and v(∈ U ( j )) can be represented as follows,

aku,i akv, j ni, j = 1,

∀u, v, i, j, k

(11)

Inequality Eq. (11) eliminates interference at UEs u and

v from FBS j and i respectively, but at the cost of lower PRB availability at those neighboring FBSs. Hence, for a dense urban FBS deployment with high neighbor density, the effective PRB reuse will be very low. In our earlier work [8], we have shown that the location of UEs with respect to its neighboring FBS j plays an important role in increasing the PRB reuse. We have divided the coverage area between any two neighboring FBSs i and j as hidden (Ahi, j ) and exposed (Aei, j ) as shown in Fig. 3. It can be seen that

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S. Mishra, C.S.R. Murthy / Computer Networks 94 (2016) 164–175 Table 1 Reuse of PRB k between UEs u and v. Scenario

Hu, i, j

Hv, j,i

PRB usage

Hidden Hidden Hidden Exposed

1 1 0 0

1 0 1 0

FFR FFR FFR RPR

rewrite Eq. 16 with power control as follows,

   

i∈F u∈U (i ) j∈F (i ) v∈U ( j )

hu, j Pjk Xu,i, j Xv, j,i aku,i akv, j ni, j ≤ Ith , ∀k (17)

0 ≤ Pik aku,i

PF ≤ tx , N

∀u, i, k

(18)

Inequality Eq. (17) represents that the sum interference at UE u due to neighboring FBS F(i) on PRB k is always below an interference threshold Ith . Inequality Eq. (18) tells us that the transmit power on a PRB is positive and it cannot exceed F denotes the maximum sub-channel transmit power. Here, Ptx maximum transmit power of an FBS.

Fig. 3. Hidden and exposed region for overlapping FBSs.

4.2. PRB assignment UE u associated with FBS i belongs to the exposed region Aei, j with respect to the neighboring FBS j. Let Hu, i, j be the indicator variable that represents if UE u is hidden from FBS j as follows,



Hu,i, j =

1, i f u ∈ Ahi, j 0, otherwise

(12)

Similarly, we can also define Xu, i, j , as an indicator variable that represents if UE u belongs to the exposed region (Aei, j ) between FBSs i and j.



Xu,i, j =

1, i f u ∈ Aei, j 0, otherwise

(13)

Ahi, j and Aei, j are non-overlapping. Hence, UE u can either belong to the hidden or to the exposed region between FBSs i and j but not both. Moreover, Hu, i, j can be defined in terms of Xu, i, j as follows,

Hu,i, j = 1 − Xu,i, j , ∀u, i, j

(14)

Now, we can rewrite Eq. 11 using Xu, i, j (Fig. 3) as follows,

(1 − Xu,i, j Xv, j,i )aku,i akv, j ni, j = 1, ∀i, j, u, v, k

(15)

Inequality Eq. (15), represents that if either UE u or UE v belongs to the hidden region, then only one of them should be allocated to PRB k. Reduced Power Reuse (RPR): A PRB can be used at UEs u and v (Fig. 3), iff they both belong to the exposed region (Fig. 3). The RPR for PRB k can be represented as follows,

aku,i akv, j Xu,i, j Xv, j,i ni, j

=1

(16)

Since the aggressive reuse of PRBs at neighboring FBSs will increase the interference, necessary transmit power control is undertaken at the neighboring FBSs. Thus, we can

Table 1 shows the different possible reuse scenarios of PRB k for any two UEs u and v associated with FBSs i and j(∈ F(i)) respectively. It can be observed from the above table that both FFR and RPR assignment techniques are effective in terms of interference mitigation but not completely effective in maximizing PRB reuse and system throughput, respectively. While FFR does a strict PRB allocation among neighboring FBSs leading to a low PRB reuse, exclusive use of RPR PRBs lowers the sum SINR leading to lower system throughput. Thus, we exploit both the PRB allocation techniques (FFR, RPR) to achieve higher PRB reuse and system throughput. From Inequality Eq. (17), it is observed that allocation of RPR PRBs with reduced power just to meet the necessary interference threshold, does not maximize the transmit power on RPR PRBs which is directly proportional to SINR and system throughput. Thus, in order to achieve an optimum PRB reuse without affecting the system throughput, our objective should be to maximize the overall transmit power of all the PRBs in use. However, this objective does not impact FFR system throughput as well as PRB reuse, as per the PRB transmit power is always constant and equal to the per sub-channel transmit power. The complete PRB assignment problem that takes care of both FFR and RPR with power control can be written as follows:

Maximize :

 

Pik aku,i

(19)

k∈N i∈F u∈U (i )

such that,  aku,i ≤ N, ∀i, k

(20)

u∈U k∈N



k F (u,i )aku,i ≥ Ru ,

k∈N

and Eqs. (2,15,17,18).

∀u, i

(21)

S. Mishra, C.S.R. Murthy / Computer Networks 94 (2016) 164–175

As discussed above, the objective (Eq. 19) maximizes the sum transmit power in the system which implicitly maximizes PRB reuse. In orthogonal PRBs there is no interference hence, Pik behaves like a constant. Inequality Eq. (20) tells us that the total PRB reuse at any FBS will be below the maximum available PRBs (N) for FBS tier. Inequality Eq. (21) ensures that UE u achieves the required data-rate Ru from its serving FBS i. 5. Proposed solution The above optimization (Eq. 19) is a Mixed Integer Non Linear Programming (MINLP) problem which is NP-hard. In [8], we had proposed a two-step approach that runs at the FMG. First, we found the PRB assignments for FBSs using modified Greedy graph coloring technique to increase PRB reuse factor. Then, in order to mitigate co-tier interference for the PRBs used in the exposed region, we proposed a transmission power control by exploiting inter-FBS distance using path loss model [24]. However, owing to the exponential increase in FBS density in near future, such centralized RRM techniques are not efficient in terms of load balancing at the FMG. Hence, we propose a distributed RRM technique in this section. 5.1. PRB discovery The Greedy Graph Coloring algorithm used in [8] has been amended to find all possible available PRB (F F R_PRB and RPR_PRB) assignments for u ∈ U(i) at location l using simple set difference and union operations. Algorithm 1 presents the pseudo-code to find all the PRBs for u at l that can be used in FFR (F F R_PRB) and RPR Algorithm 1 FFR and RPR PRBs available for u ∈ U(i). Require: Set of PRBs for the FBS-tier: N Require: Location l of UE u 1: F F R_PRB ← N − get_PRBs (i ) 2: RPR_PRB = φ 3: for all j ∈ F (i ) do 4: F F R_PRB ← F F R_PRB − get_PRBs( j ) 5: if j ∈ getExp(l ) then 6: RPR_PRB ← RPR_PRB ∪ getRPR_PRBs( j ) 7: end if 8: end for 9: RPR_PRB ← RPR_PRB − getRPR_PRBs (i ) (RPR_PRB) mode. It first discovers all the unallocated PRBs at FBS i and denote it as F F R_PRB, then it sequentially eliminates all the PRBs in use at each of the neighboring FBSs j ∈ F(i). The RPR_PRB is set to φ at the beginning of the algorithm. Then, for every FBS j ∈ F(i) exposed with respect to u at l the RPR PRBs used at j are added to RPR_PRB. getRPR_PRBs(i ) and get_PRBs(i ) return all the RPR PRBs and total set of PRBs already in use at FBS i respectively. get Exp(l)) returns the set of FBSs exposed to an UE at location l ∈ L ( i ). Every FBS broadcasts, (i) the list of PRBs allocated, and (ii) their reuse modes in the down-link control channel, which is assumed to be interference free. This broadcast helps the

169

neighboring FBSs to discover F F R_PRB and RPR_PRB without any coordination or involvement from the FGW. Algorithm 1 iterates over the list of PRBs allocated by all its neighboring FBSs F(i) to determine the PRBs available (F F R_PRB and RPR_PRB) for UE u ∈ U(i) at location l (∈ L(i )). Hence, the computational complexity of Algorithm 1 is O(E[F(i)]), where E[F(i)] is the expected number of neighboring FBSs. We can observe that if no FBS uses RPR PRBs pro-actively then the Algorithm 1 cannot discover any RPR PRBs. The Algorithm 1 in [8] uses PRBs in RPR mode with respect to j, iff UE u ∈ U(i) is present in the exposed region with respect to FBS j ∈ F(i). But, if the RPR PRBs are not used at the neighboring FBSs then the subsequent aggressive power control over RPR PRBs will reduce the achievable data-rate at u. In order to avoid this, we propose a probabilistic approach to decide if UE u at location l should use F F R_PRB or RPR_PRB PRBs for its data-rate requirement in the following section.

5.2. Location dependent PRB reuse mode selection The RPR PRBs can achieve very high PRB reuse but an FBS needs to provide relatively more number of RPR PRBs compared to FFR PRBs to fulfill the data-rate request of an UE. We would like to exploit the observed aggregate traffic behavior of UEs (U(i)) at indoor locations (L(i )) to determine, if RPR at location l ∈ L(i ) can increase the overall PRB reuse as follows: • Partition FBS i’s apartment area into L(i ) locations [25]. • Let χ u (l) be the probability of u making call at location l ∈ L(i ) as observed by FBS i. • Let π u (l) be the probability of u being at location l as observed by FBS i using pul ,l as discussed in Section 3.2. s d

• Calculate Prhi (Prei ) which represents the weight (rank) of neighboring FBSs being hidden (exposed) to calls at different locations in FBS i using Algorithm 2. Algorithm 2 Calculate Prhi and Prei . Require: χ u ∀u ∈ U (i ) Require: π u ∀u ∈ U (i ) h 1: Pri {1, 2, . . . ,F (i )} ← 0 e 2: Pri {1, 2, . . . ,F (i )} ← 0 3: for all l ∈ L (i ) do 4: t←0 5: for all u ∈ U (i ) do 6: t = t + χ u ( l )π u ( l ) 7: end for 8: for all j ∈ getHid (l ) do 9: Prhi ( j ) ← Prhi ( j ) + t 10: end for 11: for all j ∈ getExp(l ) do 12: Prei ( j ) ← Prei ( j ) + t 13: end for 14: end for • FBS i periodically updates Prhi ( j ) and Prei ( j ) to FBS j(∈ F(i)).

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• FBS i after receiving probability vectors Prhj (i ) and Prej (i ) from all the neighboring FBSs j ∈ F(i), decides the reuse mode for PRBs. Algorithm 2 calculates Prhi and Prei from χ and π . It first finds the aggregate probability of all UEs being at location l and subsequently making a call. We call it as location specific call probability (denoted as t). The weight Prhi ( j ) (Prei ( j )) of a hidden (exposed) FBS j ∈ F(i) is incremented by t if j is a hidden (exposed) FBS with respect to location l. This procedure is repeated for all l ∈ L(i ) to obtain the final weight vectors Prhi and Prei . Hence, the computational complexity of Algorithm 2 is O(E[L(i )](E[F (i )] + E[U (i )] )), where E[L(i )] is expected number of indoor locations. Each and every FBS executes Algorithm 2 and periodically communicates Prhi and Prei to its neighboring FBSs. After receiving the vectors Prhi and Prei from all the neighboring FBSs, FBS i executes Algorithm 3 to calculate the

Fig. 4. Maximum FFR of PRB k in a cluster of 7 FBSs.

Algorithm 3 Determine PRB reuse mode for u at location l ∈ L ( i ). Require: Prhj (i ), ∀ j ∈ F (i ) Require: Prej (i ), ∀ j ∈ F (i ) 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13:

h ← 0 e ← 0

for all j ∈ getHid (l ) do h (l ) ← h (l ) + Prhj (i ) end for for all j ∈ getExp(l ) do e (l ) ← e (l ) + Prej (i ) end for if e ≥ h then Use RPR PRBs f or u else Use F F R PRBs f or u end if

RPR profit (loss) e (h ). The computational complexity of Algorithm 3 is O(E[F(i)]) because it iterates over the list Prhi and Prei of size F(i). In Algorithms 2 and 3 getHid(l) returns the set of FBSs hidden to an UE at location l (∈ L(i )).

Fig. 5. Maximum RPR of PRB k in a cluster of 7 FBSs.

reuse the same PRB. Hence, the maximum reuse ratio of FFR of PRB k in a cluster of 7 FBSs (Fig. 4) is 17 . 5.4. PRB transmit power

5.3. Analyzing average reuse of PRB k We now analyze the maximum possible reuse of PRB k in a hexagonal deployment of FBSs for both FFR (Fig. 4) and RPR (Fig. 5). The scenario under consideration has 6 neighboring FBSs with respect to the FBS in the center (Fig. 4 and 5). All the FBSs are equally loaded and want to maximize the reuse of PRB k given that it is already in use by the FBS at the center of the cluster of 7 FBSs. If the FBS in the center uses PRB k in the RPR mode then there can be at most 3 neighboring FBSs that can reuse the same PRB in RPR mode (Fig. 5). Hence, the maximum reuse ratio of RPR of PRB k in a cluster of 7 FBSs is 47 . However, if the FBS in the center uses PRB k in the FFR mode then there cannot be any neighboring FBSs that can

Once a PRB that can be used in the reduced power mode is discovered, a proper transmit power needs to be calculated such that the sum interference at UEs reusing PRB k is below threshold Ith (Eq. 17). For any UE u reusing PRB k at FBS i, the transmit power Pik can be calculated as follows,

Pik =

Ith hmin i, j

k k hmin i, j = min{hi, j : au,i av, j = 1, ∀ j ∈ F (i ), v ∈ U ( j )}

(22)

(23)

where, hi, j is the channel gain of FBS i from FBS j. Eq. 23 finds the minimum channel gain among all the neighboring FBSs reusing PRB k. The value hmin ensures that the received power i, j from FBS i at all UEs v ∈ U ( j ) ∀ j ∈ F (i ) is below Ith .

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The above approximation for transmit power for FBS i may appear too aggressive, if the closest FBS j ∈ F(i) does not use PRB k for its UEs. But if it uses PRB k sometime in future then the transmit power value of FBS i needs to be adjusted as per the closest FBS that has reused PRB k. This may result in variation in data rate and higher interference at some v(∈ U ( j ) : j ∈ F (i )). Algorithm 4 calculates the transmit power of FBS i on RPR_PRB k with respect to the probability of neighboring FBSs

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Table 2 Simulation parameters. Parameter

Value

Femto system bandwidth Number of UEs per FBS PRB size Carrier frequency FBS coverage radius FBS transmit power Gaussian noise figure (σ 2 )

2MHz 1–6 180KHz 2GHz 20 m 0.1Watt −174 dBm/Hz

Algorithm 4 Calculate Pik for UE u at location l. Require: Prej (i ), ∀ j ∈ F (i ) Require: hi, j , ∀ j ∈ F (i ) Require: location l of UE u 1: t {1, 2, ...F ( j )} ← 0 2: for all j ∈ getExp(l ) do 3: t ( j ) ← hi, j Prej (i ) 4: end for 5: P k = Ith /E[t] i (getExp(l)) becoming exposed to the call at location l. E[t] represents the expected value of vector t. The number of iterations of Algorithm 4 depends on the expected number of neighboring FBSs (E[F(i)]) and in the worst case all the neighboring FBSs are exposed. Hence, its computational complexity is O(E[F(i)]). The PRB allocation at FBS i is not affected by Algorithm 2 because the variables Prh (i ) and Pre (i ) required for PRB allocation are received from the neighboring FBSs (F(i)). Hence, it does not add to the computational complexity of the proposed heuristic. The remaining Algorithms 1, 3, and 4 required for PRB allocation can be partitioned into, (i) Algorithm 1 and (ii) Algorithms 3 and 4 in terms of data dependency; algorithms in these two groups can be executed simultaneously. Thus, the computational complexity of the proposed heuristic is O(E[F(i)]), which is linear in terms of expected number of neighboring FBSs. All the information required for PRB allocation is either available or can be accessed at the FBS. There are at most 8 neighboring FBSs in the indoor scenario under consideration. Hence, in the worst case the FBS has to iterate over the information of these 8 FBSs for the PRB allocation. 6. Performance evaluation We have considered a dense urban FBS scenario consisting of a few apartment blocks. Each block consists of 5 strips of 5 apartments each (Fig. 2). The dimensions of each apartment are 10 m × 10 m. Each apartment contains an FBS deployed at a random location by the user. The coverage radius of each FBS is assumed to be 20 m. Since FBSs are densely deployed, their coverage area may overlap with one another. The FBSs operate in closed access mode, each serving a set of UEs registered with it. The number of these CSG UEs vary from 1 to 6 per apartment. Each UE moves in an apartment where its movement is modeled using the indoor mobility model discussed in Section 3.2. To analyze the performance improvement, we plot average blocking, average system throughput, ECR, and PRB reuse

ratio while varying UE density per apartment. Performance analysis is done for three different PRB assignment techniques viz., FR, FFR and proposed (joint FFR and RPR). In FR every FBS uses the complete set of sub-channels available for the FBS-tier, where as in FFR two neighboring FBS cannot use the same set of sub-channels. The rest of the simulation parameters are mentioned in Table 2. Fig. 6 depicts the blocking probability of the system for all three PRB assignment techniques. It can be seen that the blocking probability is minimum for the proposed technique due to better reuse of PRBs with power control. There is a non-zero blocking for FR technique with 1 UE per FBS. This is because of high interference from the neighboring FBSs coupled with UEs’ demand for high data-rate. However, on increasing the density of UEs system blocking increases as FBSs now have to support more UEs with limited number of PRBs. We can observe that the blocking for FFR increases over FR as the PRB availability decreases with an increase in the number of UEs in case of FFR. Fig. 7 shows that the proposed technique gives a better throughput than FR and FFR techniques. This is due to the fact that higher reuse of PRBs along with power control in the proposed technique improves per FBS PRB availability. Note that initially the system throughput for FR and proposed techniques is almost similar. However, there is a significant improvement in ECR (Fig. 9). This is due to high PRB availability in FR at the initial phase but with an increase in UE density the proposed technique achieves higher throughput due to low interference compared to FR from neighboring FBSs. Fig. 8 shows the PRB reuse ratio with an increase in UE density. We can see that the proposed technique and FR outperform FFR and the PRB reuse ratio increases with an increase in UE density. This is a direct consequence of aggressive resource partitioning in FFR, which reduces the total available PRBs per FBS. Also, observe that highest PRB reuse ratio is provided by the FR technique. This is because the PRB assignment in an FBS has no impact on its neighboring FBSs PRB allocation. Finally, we analyze the ECR aspect of the candidate PRB assignment techniques. Fig. 9 shows a significant improvement in ECR for our proposed technique. The ECR of FR is higher than that of the FFR and proposed technique, because FR does an aggressive PRB reuse without interference management. Fig. 9 also depicts that ECR of FFR is higher than that of the proposed technique, because (i) it achieves higher PRB reuse as compared to FFR and (ii) it amends power control on those location aware aggressively reused PRBs to achieve higher throughput and lower ECR simultaneously.

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FR

FFR

Proposed

0.6

0.5

Probability of blocking

0.4

0.3

0.2

0.1

0 1

2

3

4

5

6

5

6

UEs per FBS Fig. 6. Average system blocking.

FR

FFR

Proposed

50

45

System throughput (Mbps)

40

35

30

25

20

15

10 1

2

3

4

UEs per FBS Fig. 7. Average system throughput.

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FR

FFR

173

Proposed

10

9

7

6

5

4

3

2 1

2

3

4

5

6

UEs per FBS Fig. 8. Average PRB reuse.

FR

FFR

Proposed

0.023 0.022

0.021

0.02

ECR (Watts/Mbps)

PRB reuse ratio

8

0.019

0.018

0.017

0.016

0.015 1

2

3

4

UEs per FBS Fig. 9. Average system ECR.

5

6

174

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7. Conclusion Co-tier interference is an important problem in a dense FBS network, which can dramatically reduce system throughput and energy efficiency. FFR promises to eliminate interference but it also reduces available bandwidth for UEs whereas, RPR achieves higher PRB reuse than FFR while keeping interference below a threshold. In this paper, we formulated a joint optimization for PRB reuse mode selection and power control as a MINLP which is NP-hard. We presented a distributed technique which can adaptively decide PRB reuse mode and transmit power values to maximize system throughput and energy efficiency. We established that location based PRB reuse mode selection and power control achieve improved system performance. Hence, the proposed technique is designed to exploit the FBS observed indoor mobility of CSG UEs. We analyzed average system blocking, system throughput, PRB reuse ratio, and energy efficiency for different resource assignment techniques and demonstrated the superiority of our proposed technique. Future extensions of this work can analyze hybrid access FBS with adaptive priority for its CSG UEs over non-CSG UEs to achieve fairness. In this study, we have considered all the FBSs to be uniform, working together to increase system throughput and energy efficiency. It will be interesting to study the system performance and fairness in the presence of a few rouge FBSs which share wrong information with their neighboring FBSs to derive undue performance benefits to their CSG UEs. Acknowledgment The authors thank the anonymous reviewers for their valuable comments and suggestions. This work was supported by the Department of Science and Technology (DST), New Delhi, India (Grant Number: SB/S3/EECE/0150/2013). References [1] A. Damnjanovic, J. Montojo, Y. Wei, T. Ji, T. Luo, M. Vajapeyam, T. Yoo, O. Song, D. Malladi, A survey on 3GPP heterogeneous networks, IEEE Wirel. Commun. 18 (3) (2011) 10–21. [2] V. Chandrasekhar, J. Andrews, A. Gatherer, Femtocell networks: A survey, IEEE Commun. Mag. 46 (9) (2008) 59–67, doi:10.1109/MCOM.2008. 4623708. [3] T. Zahir, K. Arshad, A. Nakata, K. Moessner, Interference management in femtocells, IEEE Commun. Surv. Tutor. 15 (1) (2013) 293–311, doi:10. 1109/SURV.2012.020212.00101. [4] Cisco, Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2014–2019, Technical Report, Cisco, 2015. [5] I. Hwang, B. Song, S. Soliman, A holistic view on hyper-dense heterogeneous and small cell networks, IEEE Commun. Mag. 51 (6) (2013) 20– 27, doi:10.1109/MCOM.2013.6525591. [6] A. Golaup, M. Mustapha, L. Patanapongpibul, Femtocell access control strategy in UMTS and LTE, IEEE Commun. Mag. 47 (9) (2009) 117–123. [7] Y.L. Lee, T.C. Chuah, J. Loo, A. Vinel, Recent advances in radio resource management for heterogeneous LTE/LTE-A networks, IEEE Commun. Surv. Tutor. 16 (4) (2014) 2142–2180. [8] S. Mishra, R. Thakur, C.S.R. Murthy, An efficient physical resource block assignment for dense femtocell networks, in: Proceedings of the 2014 IEEE Seventy-Ninth Vehicular Technology Conference (VTC Spring), 2014, pp. 1–5, doi:10.1109/VTCSpring.2014.7022819. [9] D. Lopez-Perez, A. Juttner, J. Zhang, Dynamic frequency planning versus frequency reuse schemes in OFDMA networks, in: IEEE Vehicular Technology Conference (VTC Spring), 2009, pp. 1–5, doi:10.1109/VETECS. 2009.5073515.

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Sudeepta Mishra is currently a Ph.D. student in the High Performance Computing and Networking Lab at Indian Institute of Technology Madras, India. He completed his Bachelor of Engineering in Computer Science from National Institute of Science and Technology, Odisha, India and Master of Technology in Computer Science and Engineering from Kalinga Institute of Industrial Technology, Odisha, India. His research interests include radio resource allocation and interference management in smallcells and heterogeneous cellular networks.

S. Mishra, C.S.R. Murthy / Computer Networks 94 (2016) 164–175 C. Siva Ram Murthy earned his B.Tech. degree in Electronics and Communication Engineering from Regional Engineering College (now National Institute of Technology), Warangal in 1982, M.Tech. degree in Computer Engineering from the Indian Institute of Technology (IIT), Kharagpur in 1984, and Ph.D. degree in Computer Science from the Indian Institute of Science, Bangalore in 1988. Since September 1988, he has been with the Department of Computer Science and Engineering at IIT Madras where he is currently a Professor. He has served as Head (Chairman) of the Department from 2010 to 2013 and held the Indian National Academy of Engineering (INAE) Chair Professorship during 2012–14. He is a co-author of the textbooks Parallel Computers: Architecture and Programming (Prentice-Hall of India, India), New Parallel Algorithms for Direct Solution of Linear Equations (John Wiley & Sons, Inc., USA), Resource Management in Real-time Systems and Networks (MIT Press, USA), WDM Optical

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Networks: Concepts, Design, and Algorithms (Prentice Hall, USA), An Analytical Approach to Optical Burst Switched Networks (Springer, USA), and Ad Hoc Wireless Networks: Architectures and Protocols (Prentice Hall, USA). His research interests include wireless networks, lightwave networks, real-time systems, and parallel and distributed computing. Dr. Murthy is a co-recipient of Best Paper Awards from the 5th IEEE International Workshop on Parallel and Distributed Real-Time Systems (WPDRTS), 6th and also 11th IEEE Annual International Conference on High Performance Computing (HiPC), and 14th and also 19th IEEE International Conference on Networks (ICON). He has served as an Associate Editor of the IEEE Transactions on Computers and as a Subject Area Editor for the Journal of Parallel and Distributed Computing (JPDC). He is currently an Associate Editor of the IEEE Transactions on Mobile Computing. He is a recipient of Best Ph.D. Thesis Award from the Indian Institute of Science, INSA Medal for Young Scientists, Dr. Vikram Sarabhai Research Award, IBM (USA) Real-Time Innovation Award, and Erasmus Mundus Academic Staff Scholarship. He is an elected Fellow of Institute of Electrical and Electronics Engineers (IEEE, USA), Indian National Science Academy (INSA) and Indian National Academy of Engineering (INAE).