... which depend on their geographical locations and maybe their running applications. In ... a novel distributed load-balancing algorithm to enhance the network ...
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Joint Load Balancing and Admission Control in OFDMA-Based Femtocell Networks Long Bao Le, Dinh Thai Hoang, Dusit Niyato, Ekram Hossain, and Dong In Kim
Abstract—In this paper, we consider the admission control problem for hybrid access in OFDMA-based femtocell networks. We assume that Macrocell User Equipments (MUEs) can establish connections with Femtocell Base Stations (FBSs) to improve their QoSs. Both MUEs and Femtocell User Equipments (FUEs) have minimum rate requirements, which depend on their geographical locations and maybe their running applications. In addition, blocking probability constraints are imposed on each FUE so that connections from MUEs only result in controllable performance degradation for FUEs. We show how to formulate the admission control problem as a Semi-Markov Decision Process (SMDP) and present a Linear Programming (LP) based solution approach. Moreover, we develop a novel femtocell power adaptation algorithm, which can be implemented in a distributed manner jointly with the proposed admission control scheme. This power adaptation algorithm enables to achieve better cell throughput and more energy-efficient operation of the femtocell network considering the heterogeneity of traffic load in the network. Finally, numerical results are presented to illustrate the desirable performance of the optimal admission control solution and the significant throughput and power saving gains of the proposed cross-layer solution.
Here, an efficient admission control policy is needed to coordinate spectrum sharing and admission control decisions for both types of users, which should strike to balance between achieving high spectrum utilization and protecting QoS requirements for FUEs. There are some existing works considering an admission control problem using MDP in the literature [8], [9]. However, these works investigate this problem in the traditional singlecarrier wireless cellular networks. Moreover, investigation of admission control and handoff issues have been recently conducted for femtocell networks by using the simulation approach [4]. In this paper, we present an optimal admission control scheme for OFDMA-based two-tier femtocell networks considering QoS constraints for FUEs. In addition, we devise a novel distributed load-balancing algorithm to enhance the network throughput performance and reduce energy expenditure of FBSs. We demonstrate desirable performance of the proposed admission control and a significant throughput and power saving gains of the power adaptation algorithm via numerical studies.
I. I NTRODUCTION To enable spectrum sharing between macrocells and femtocells in OFDMA-based two-tier networks, one of the three access modes can be employed, namely open, closed and hybrid access modes. In the open access mode, MUEs are allowed to connect to either their own Macrocell BS (MBS) or FBSs [1], [2], [3]. This access mode is more efficient that the other two counterparts in terms of interference mitigation, spectrum utilization, and QoS provisioning. However, this benefit comes at the cost of capacity reduction for FUEs as well as security problems [3], [4], [5], [6], [7]. In contrast, in the closed access mode, only certain users (subscribers) belonging to the socalled Closed Subscriber Group are allowed to connect to each FBS. These access restrictions result in severe cross-tier interference when both types of users operate on the same frequency band. The hybrid access mode balances strengths and weaknesses of both closed and open access modes. For a typical hybrid access mode in OFDMA-based two-tier networks, FUEs can employ all subchannels for their communications where there is no connected MUE. However, limited spectrum access at each femtocell is reserved for MUEs whose connections with their MBSs fail to support their required QoS performance.
II. S YSTEM M ODEL We consider the downlink of a two-tier OFDMA-based wireless network that employs Frequency Division Duplexing (FDD). There are N subchannels shared by MUEs and FUEs for downlink communications. It is assumed that there are J femtocells sharing these N subchannels with I macrocells. We further assume that a hybrid access policy is employed where MUEs can connect to a nearby FBS if needed (e.g., when they suffer from undue cross-tier interference). The considered system model is illustrated in Fig. 1. DĂĐƌŽĐĞůů
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Long Bao Le is with University of Quebec, Montreal, QC, Canada; Dinh Thai Hoang and Dusit Niyato are with Nanyang Technological University, Singapore; Ekram Hossain is with University of Manitoba, Winnipeg, MB, Canada; Dong In Kim is with Sungkyunkwan University, Korea. This research was supported by NSERC grants and the MKE, Korea, under the ITRC support program supervised by the NIPA (NIPA-2012-(C1090-1211-0005)) and the NRF grant funded by the Korea government (MEST) (No. 2011-0029329).
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Fig. 1.
Two-tier network model.
2
We assume that each subchannel can be assigned to at most one FUE or MUE connecting to any FBS. Furthermore, we assume full spatial reuse where all subchannels are utilized at each FBS and MBS. We consider the scenario where users of both network tiers demand some minimum rates which are determined by their underlying applications and locations in the cell. This assumption can be justified by the fact that location-dependent QoS constraints are imposed to balance user throughput and fairness. In particular, the area around each FBS is divided into circular areas and users running the same application (e.g., voice or video users) in each circular area is assumed to have the same minimum rate requirement. Each such minimum rate is mapped to one user class. For example, the femtocell area is divided into cell-edge and cell-center regions. We assume there are C1 classes of FUEs and C2 classes of MUEs connecting to any femtocell. We assume that the coverage range of any femtocell is sufficiently small so that the distance from their associated users to other FBSs or MBSs can be well approximated by the distance between the corresponding BSs. In addition, only long-term channel gains averaged over short-term fading and shadowing are used for resource allocation and QoS fc mc provisioning.1 Let gij and gij be the long-term channel gains on any subchannel from FBS j or MBS j to a class-c user of either tier that are associated with femtocell i, respectively. FBSs and MBSs have maximum transmission power of max max PFBS and PMBS , respectively. For simplicity, we assume that the MBS and FBSs perform uniform power allocation over their subchannels and FBS j uses βj ≤ 1 fraction of its maximum power while MBSs use their maximum power for downlink communications. These power scaling factors βj will be employed by the distributed power adaptation algorithm to be presented in Section IV. Therefore, the transmission power on any subchannel for users connecting to FBS j is max pj = βj PFBS /N and the transmission power from any MBS max on one subchannel is p0 = PMBS /N . The minimum average Signal to Interference plus Noise Ratio (SINR) achieved by any class-c FUE associated with femtocell i on each allocated subchannel can be written as follows: (f )
pi g fiic I fc fc mc j=1,j=i gij pj + j=1 gij p0 + Ni
Γi,c = J
(1)
where g fiic is the minimum channel gain of any class-c FUEs which would be achieved by users located on the furthest circular boundary of this user class. The first and second terms in the denominator of (1) represent the total interference due to other FBSs and MBSs, respectively and Nif c is the Gaussian noise power for class-c FUEs connecting with FBS i. Similarly, the minimum average SINR achieved by any class-c MUE connecting with FBS i can be written as (m)
Γi,c = J
fc j=1 gij pj
+
p0 g mc ii I
mc j=1,j=i gij p0
+ Nimc
(2)
where g mc ii is the minimum channel gain of any class-c MUEs, Nimc is the Gaussian noise power for class-c MUEs connecting 1 The
worst effect of short-term fading can be mitigated by diversity and coding techniques, which is outside the scope of this paper.
with FBS i. We assume that connection requests of class(f ) c FUEs and MUEs in femtocell i occur with rate λi,c and (m) λi,c , respectively which are assumed to be Poisson processes. Connection duration is assumed to be exponentially distributed (f ) (m) with mean duration of 1/μi,c and 1/μi,c for class-c FUEs and MUEs, respectively. A. QoS Constraints We assume that class-c MUEs and FUEs require their total achievable rates due to all allocated subchannels to be at least fc fc mc mc Rmin and Rmin , respectively. Let Sik and Sik be the sets of subchannels allocated to class-c MUE k and FUE k associated with femtocell i, respectively. Then, the total minimum rates achieved by these users can be written as (m) mc Rik 1 + αΓ , (3) = W smc log 2 ik i,c (f ) fc = W sfikc log2 1 + αΓi,c (4) Rik where α ≤ 1 denotes the gap to the Shannon capacity, mc W is the bandwidth of one subchannel, smc ik = |Sik | and fc fc fc mc sik = |Sik | are the number of subchannels in Sik and Sik , respectively. Note that we have used the worst-case SINRs (m) (f ) Γi,c and Γi,c to calculate the total rates for class-c MUEs (m) (f ) and FUEs, respectively. Let Ui,c and Ui,c denote the sets of class-c MUEs and FUEs in femtocell i and their cardinalities (m) (m) (f ) (f ) are denoted as ui,c = |Ui,c | and ui,c = |Ui,c |, respectively. Then, the rate constraints for both types of users can be written as mc Rik fc Rik
≥ ≥
(m)
mc Rmin ,
∀i, c and k ∈ Ui,c ,
fc Rmin ,
∀i, c and k ∈
(f ) Ui,c .
(5) (6)
By using the results in (3) and (4), we can see that the rate constraints in (5) and (6) hold if the numbers of allocated subchannels for class-c MUE and FUE satisfy ⎤ ⎡ mc R (f ) ⎢ ⎥ s(m) min smc ∀k ∈ Ui,c , (7) ik ≥ ⎢ i,c , (m) ⎥ ⎢ W log 1 + Γi,c ⎥ ⎤ ⎡ fc R (f ) (f ) min ⎥ si,c sfikc ≥ ⎢ , ∀k ∈ Ui,c . (8) ⎢ (f ) ⎥ ⎢ W log 1 + Γi,c ⎥ Therefore, the rate constraints in (5) and (6) hold if the following constraints for femtocell i is satisfied N≥
C1 c=1
(f ) (f )
si,c ui,c +
C2 c=1
(m) (m)
si,c ui,c ,
∀i = 1, 2, . . . , J.
(9)
This constraint will be used for admission control design in (f ) this paper. Let Bi,c denote the blocking probability of classc FUEs in femtocell i. Then, we impose following blocking probability constraints to protect FUEs (f )
Bi,c
≤
Pbc ,
∀i, c.
(10)
Admission control and channel assignment should be performed in such a way that it can maintain these channel and blocking probability constraints in (9) and (10).
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III. O PTIMAL A DMISSION C ONTROL D ESIGN A. Description of SMDP Note that admission control can be performed separately in each cell. Without loss of generality, we will consider a particular femtocell i in the following. Decision epochs of the underlying SMDP are arrival and departure instants of either FUE or MUE in the considered femtocell i. We define a general system state at decision epoch t as follows:
(f ) (f ) (m) (m) x(t) ui,1 (t), . . . , ui,C1 (t), ui,1 (t), . . . , ui,C2 (t) (11) (f )
(m)
where recall that ui,c (t) and ui,c (t) are the number of class-c FUEs and MUEs at decision epoch t, respectively. Then, the state space X is defined as X {x : constraints in (9) hold}. At each decision epoch when the system changes its state, an admission control action is determined for the next decision epoch. In fact, an admission control action is only taken for a newly arriving user of either type. At a departure instant of any connection, state transition occurs and no action is needed. We define a general action a at decision epoch t as follows:
(f ) (f ) (m) (m) a(t) ai,1 (t), . . . , ai,C1 (t), ai,c (t), . . . , ai,C2 (t) (12) (f )
for a ∈ Ax . Transition probability pxy (a) of the underlying embedded Markov chain can be calculated by noting that the probability of a certain event (e.g., connection arrival and departure) is equal to the ratio between the rate of that event and the total cumulative event rate 1/τx (a). Specifically, pxy (a) can be determined as ⎧ (f ) (f ) (f ) ⎪ λi,c ai,c τx (a), if y = x + ei,c ⎪ ⎪ ⎪ ⎪ (m) (m) (m) ⎪ ⎪ λi,c ai,c τx (a), if y = x + ei,c ⎨ (f ) (f ) (f ) (15) pxy (a) = μi,c ui,c τx (a), if y = x − ei,c ⎪ ⎪ ⎪ (m) (m) (m) ⎪ ⎪ μi,c ui,c τx (a), if y = x − ei,c ⎪ ⎪ ⎩ 0, otherwise. where for simplicity we omit user index i in both τx (a) and pxy (a). B. Formulation of the Admission Control Problem We formulate the admission control problem by minimizing a cost function, which is defined as the weighted sum of blocking probabilities
(m)
where ai,c (t) and ai,c (t) denote the admission control action when an arrival occurs for class-c FUEs and MUEs in (f ) (m) femtocell i, respectively where ai,c (t) = 1 (ai,c (t) = 1) if a newly arriving FUE (MUE) is admitted. Otherwise, we (f ) (m) have ai,c (t) = 0 (ai,c (t) = 0). The action
state space
min
zx,a ≥0
+
We now analyze the dynamics of this SMDP, which is characterized by the state transition probabilities of the Markov chain obtained by embedding the system at arrival and departure instants. Specifically, we will determine transition probability pxy (a) from state x to state y when action a is taken. Toward this end, let τx (a) denote the expected time until the next decision epoch after action a is taken at system state x. Then, τx (a) can be calculated as the inverse of the cumulative arrival and departure rate with blocked arrivals taken into account. In particular, τx (a) can be calculated as follows [8], [10]: C C1 1 (f ) (f ) (f ) (f ) τx (a) = λi,c ai,c + μi,c ui,c c=1
c=1
+
C2 c=1
(m) (m) λi,c ai,c
+
C2 c=1
−1 (m) (m) μi,c ui,c
(14)
x∈X a∈Ax c=1 C2 x∈X a∈Ax c=1
C +C
can be defined as A = a : a ∈ {0, 1} 1 2 . In addition, admissible action space Ax given a system state x comprises all possible actions that do not result in transition into a state that is not allowed (i.e., not in allowable state space X). In addition, if x = 0, then it is required that action a = 0 is excluded from Ax to prevent the system to be trapped in the (f ) (m) zero state forever. Let ei,c (ei,c ) be a vector of dimension C1 + C2 , which is the same size as that of the general state vector x(t) having all zeros except the one at the same position (f ) (m) of xi,c (xi,c ) in (11). Then, we can write Ax as follows: (f ) (f ) / X; Ax a ∈ A : ai,c = 0 if x + ei,c ∈
(m) (m) / X; and a = 0 if x = 0 . (13) ai,c = 0 if x + ei,c ∈
C1
(f )
(f )
wi,c (1 − ai,c )zx,a τx (a) (m)
(m)
wi,c (1 − ai,c )zx,a τx (a)
(16)
where zx,a denotes the rate of choosing action a in state x; (m) (f ) wi,c > 0 and wi,c > 0 are weighting factors controlling desired performance tradeoff. In addition, the blocking probability constraints for FUEs can be written as follows: (f ) (f ) Bi,c = (1 − ai,c )zx,a τx (a) ≤ Pbc , c = 1, . . . , C1 . (17) x∈X a∈Ax
We impose other standard constraints for a MDP as follows [10]: zy,a − pxy (a)zx,a = 0, ∀y ∈ X (18) a∈Ay
x∈X a∈Ax
zx,a τx (a) = 1
(19)
x∈X a∈Ax
where (18) describes the balance equation and (19) captures the normalization condition where the sum of the steadystate probabilities should be equal to 1 [10]. We can calcu∗ late optimal zx,a by solving the Linear Program (16)-(19). Then, we can determine an optimal randomized admission control policy as follows: for each system state x the probability of choosing action a ∈ Ax can be calculated as ∗ ∗ θx (a) = zx,a τx (a)/ a zx,a τx (a). These probabilities can be calculated offline and applied for online admission control for different system states. In addition, the blocking probability for (f ) class-c FUEs in cell i (Bi,c ) is given in (17) and the blocking probability for MUEs can be calculated similarly as follows: (m) (m) Bi,c = (1 − ai,c )zx,a τx (a). (20) x∈X a∈Ax
4
Then, we can calculate achievable throughput in femtocell i as follows: Ti =
C1 c=1
(f )
(f )
(1 − Bi,c )λi,c +
C2 c=1
(m)
(m)
(1 − Bi,c )λi,c
(21)
where we have taken blocked arrivals into consideration. Finally, the total network J throughput achieved by FUEs can be calculated as T = i=1 Ti .
3) Algorithm 1 converges to an equilibrium in a finite number of iterations. Proof: To prove first property of this proposition, let us consider the SINR on any subchannel for class-c FUEs in FBS i who scales down power by a factor δ. Let Ω be set FBSs who scale down their powers excluding FBS i in the current iteration. Then, we can write down the SINR of FUE i as (p)
(f )
Γi,c =
IV. D ISTRIBUTED F EMTOCELL P OWER A DAPTATION High transmission powers of FBSs may severely degrade the performance of other highly-loaded femtocells because of excessive inter-cell interference. In addition, using low transmission power in lightly-loaded femtocells may result in significant throughput enhancement for other femtocells serving high traffic load, which ultimately leads to total network throughput improvement. Motivated by these observations, we develop an efficient power adaption mechanism for FBSs. Algorithm 1 FBS P OWER A DAPTATION 1: Initialization: Each FBS uses maximum power for downlink communications and calculates its admission control and throughput performance. 2: if FBS j can maintain its blocking probability require(m) (m) ments and has Bj,c ≤ P j for all classes c then 3: FBS j scales down its transmit power by a factor δ < 1 (i.e., FBS j performs the following update: βj := δβj max and transmits with power βj PFBS ) 4: end if 5: Each FBS re-calculates its admission control solution under the current SINRs of its associated users. 6: if FBS j who scales down its transmission power in the current iteration cannot achieve its blocking probability (m) (m) constraints for any FUE class or has Bj,c > P j for any class c then 7: It scales up the transmission power by a factor 1/δ (i.e., go back to the previous power level) and does not perform any power scaling operation in subsequent iterations. 8: end if 9: Go to step 2 until convergence. The proposed power adaptation algorithm is described in (m) details in Algorithm 1. Parameters P j in steps 2 and 6 are blocking probability thresholds based on which the proposed power adaptation mechanism is activated and terminated. The proposed power adaptation algorithm can be implemented in a distributed fashion. This is because each FBS only needs to collect SINR levels received by its FUEs and MUEs of differ(f ) ent classes based on which each FBS can calculate si,c and (m) si,c and the admission control performance. The convergence of Algorithm is stated in the following proposition. Proposition: Algorithm 1 has the following properties 1) The SINR of any FUE whose FBS scales down power decreases; 2) The SINR of any FUE whose FBS does not scale down power increases;
=
≤
f c (p) j∈Ω gij δpj
fc δpi gii
f c (p) j ∈Ω / gij pj (p) f c pi gii (p) f c (p) f c pj j∈Ω gij pj + j ∈Ω / gij δ (p) f c pi gii f c (p) f c (p) j∈Ω gij pj + j ∈Ω / gij pj
+
+
+ +
I
mc j=1 gij p0
I
mc p0 j=1 gij δ
I
mc j=1 gij p0
+ Nif c +
Nif c δ
+ Nif c
(p)
max where pj = βj PFBS /N is the transmission power on any subchannel in femtocell j in the previous iteration. The last inequality holds since δ < 1. It can be observed that the last quantity is indeed the SINR for class-c FUEs in femtocell i in the previous iteration. Therefore, the first property stated in the proposition holds. The second property in the proposition can be proved similarly. We can now prove the convergence of Algorithm 1. Note that the proposed power scaling operation in one particular FBS results in the decrease in SINRs of its FUEs according to the first property and, therefore, the potential decrease in achievable rates of its FUEs over consecutive iterations. The (c) minimum number of required subchannels si,c for any classc FUEs in femtocell i that performs power scaling operation can potentially increase over consecutive iterations. In turn, (m) this will increase the blocking probability for MUEs Bi,c as soon as blocking probability constraints for FUEs in (17) (m) are met with equality. Then, as soon as the condition Bi,c ≤ (m) P i is violated, which surely occurs, FBS i will terminate its power scaling operation. Therefore, any FBS must terminate its power scaling operations in a finite number of iterations.
V. N UMERICAL R ESULTS We consider the network setting shown in Fig. 1 where there are 25 femtocells located at the center cell edge of a cluster of 19 macrocells. The radii of each femtocell and macrocell are chosen to be 20m and 1000m, respectively. The distance between two neighboring femtocells is 120m. We assume there are 2 classes of FUEs in each femtocell where class-one and class-two FUEs are located in the inner and outer regions separated by a circle with radius 10m from the FBS. Moreover, we assume that MUEs will attempt to connect with a nearest FBS when they enter a circular area whose radius is 30m centered around the underlying FBS. To calculate the required number of subchannels for FUEs and MUEs of each class, we consider the worst case where FUEs and MUEs are located on the boundary of the corresponding regions (i.e., distances from these worst class-1, class-2 FUEs and MUEs to their FBS are 10m, 20m, and 30m respectively). We will calculate the long-term channel gains based on the corresponding distance. The path loss corresponding to
5
1
1 Class−1 FUEs Class−2 FUEs MUEs
0.8 Blocking probability
Blocking probability
0.8
0.6
0.4
0.2
0
Class−1 FUEs Class−2 FUEs MUEs
0.6
0.4
0.2
0.2
0.4 0.6 0.8 Arrival rate (users/min)
0 0.1
1
0.15
0.2 0.25 Arrival rate (users/min)
(a)
0.3
0.35
(b)
Fig. 2. Blocking probability for optimal admission control (a) s1i = 2 and s2i = 1 (b) s1i = 2 and s2i = 3 70
2.4 Without Power Adaptation, N =16
2
With Power Adaptation, N =16 L
60
Without Power Adaptation, NL=8 Without Power Adaptation, NL=8
Power saving (%)
Average throughput (users/min)
L
2.2
1.8 1.6 1.4
50
40
min f2
L
Rmin=6, NL=16
1.2
30 1 0.8 0.3
Rf2 =6, N =8
Rf2 =8, N =8 min f2
L
Rmin=8, NL=16 0.4
0.5
0.6
0.7
0.8
Arrival rate (users/min)
(a)
0.9
1
20 0.3
0.4
0.5 0.6 Arrival rate (users/min)
(b)
Fig. 3. (a) Throughput performance (b) Power saving due to power adaptation
dij is calculated as Lij = (44.9 − 6.55 log10 (dij ) + 34.46 + 5.83 log10 (hBS ) + 23 log10 (fc /5) + WL [dB] where hBS is the BS height, which is chosen to be 25m and 10m for MBS and FBS, respectively; fc is the carrier frequency in GHz which is set to 2GHz; and WL is the potential wall loss for transmissions from FBSs to users of either type or from MBSs to FUEs, which is chosen to be 15dB. The long-term channel gains can be calculated from Lij as gij = 10−Lij /10 . Other system parameters are set as follows: noise power Nif c = Nimc = 10−15 W (∀i, c); FUEs’ and MUEs’ average (f ) (m) service time are chosen to be μi,c = μi,c = 1 minute (∀i, c); all FUEs’ and MUEs’ arrival rates are chosen to be the same (f ) (m) (i.e., λi,c = λi,c (∀i, c)); maximum powers of FBSs and max max MBSs PFBS = 40mW and PMBS = 15W; target blocking (m) c probabilities Pb = P j = 0.05 (∀j, c); weighting factors in (m) (f ) (16) are chosen as wi,c = wi,c = 1 (∀i, c); α = 1 (i.e., we can achieve the Shannon capacity); the power scaling factor for Algorithm 1 δ = 0.85; and the total number of available subchannels N = 8. Moreover, the minimum required rates for f1 mc MUEs and FUEs are Rmin /W = 2 (b/s/Hz), Rmin /W = 10.5 f2 /W = 6 (b/s/Hz) unless stated otherwise. (b/s/Hz), and Rmin Figs. 2(a)-2(b) show the blocking probabilities achieved by the optimal admission control versus arrival rates. These figures confirm that the QoS requirements of FUEs in terms of blocking probabilities can be maintained. As the network becomes sufficiently congested, blocking probabilities of FUEs reach the target values (i.e., Pbc = 0.05) while the blocking probability of MUEs increases slowly then sharply. In addition, the “critical” arrival rate beyond which the blocking probabilities of MUEs start increasing sharply is larger in the (f ) (f ) (f ) (f ) case (si,1 , si,2 ) = (2,1) compared to the case (si,1 , si,2 ) = (m)
(2,3) for si,1 =2, which are about 0.58 and 0.26, respectively.
0.7
In Fig. 3(a), we show the average throughput per femtocell achieved by the optimal admission control scheme with and without power adaptation where the arrival rates of NL (f ) (m) lowly-loaded femtocells are fixed at λi,c = λi,c = 0.3 (users/min) and the arrival rates of the remaining highly-loaded femtocells are varied. This figure shows that the proposed power adaptation algorithm can indeed increase the average throughput when the arrival rates of highly-loaded femtocells are sufficiently high. In particular, the maximum throughput gains achieved for both NL =8 and NL =16 are larger than 10%. Finally, we present the power saving achieved by Algorithm 1 versus the arrival rates of highly-loaded femtocells in Fig. 3(b) when the number of lowly-loaded femtocells is NL = m1 8, 16 and minimum required rates are Rmin /W = 2 (b/s/Hz), f1 f2 Rmin /W = 10.5 (b/s/Hz) and Rmin /W = 6, 8 (b/s/Hz). This figure shows that a significant power saving of more than 60% can be achieved by the proposed power adaptation algorithm when the arrival rates of highly-loaded femtocells are below f2 0.5 and 0.56 (users/min) for Rmin /W =8 (b/s/Hz) and 6 (b/s/Hz), respectively. Moreover, when the arrival rates of highly-loaded femtocells are large, the power saving drops to about 23% and 43% for NL =8 and NL =16, respectively. The power saving for NL =16 is larger than that for NL =8 for high arrival rates since most of the power saving comes from the reduction in transmission power of lowly-loaded femtocells. VI. C ONCLUSION We have proposed an optimal admission control solution for spectrum sharing in OFDMA-based femtocell networks. Moreover, we have developed a novel distributed power adaptation algorithm, which can be integrated with the proposed admission control scheme. R EFERENCES [1] V. Chandrasekhar, J. G. Andrews, and A. Gatherer, “Femtocell networks: A survey,” IEEE Commun. Mag., vol. 46, no. 9, pp. 59–67, Sept. 2008. [2] D. Lopez-Perez, A. Valcarce, G. de la Roche, and J. Zhang, “OFDMA femtocells: A roadmap on interference avoidance,” IEEE Commun. Mag., vol. 47, no. 9, pp. 41–48 , Sept. 2009. [3] G. d. l. Roche, A. Valcarce, D. Lopez-Perez, and J. Zhang, “Access control mechanisms for femtocells,” IEEE Commun. Mag., vol. 48, no. 1, pp. 33–39 , Jan. 2010. [4] D. Lopez-Perez, A. Valcarce, A. Ladanyi, G. d. l. Roche, and J. Zhang, “Intracell handover for interference and handover mitigation in OFDMA two-tier macrocell-femtocell networks,” EURASIP J. Wireless Commun. Netw., 2010. [5] D. Choi, P. Monajemi, S. Kang, and J. Villasenor, “Dealing with loud neighbors: The benefits and tradeoffs of adaptive femtocell access,” in Proc. IEEE GLOBECOM, Dec. 2008. [6] I. Guvenc, M. R. Jeong, F. Watanabe, and H. Inamura, “A hybrid frequency assignment for femtocells and coverage area analysis for cochannel operation,” IEEE Commun. Letters, vol. 12, no. 12, pp. 880– 882, Dec. 2008. [7] D. T. Ngo, L. B. Le, T. Le-Ngoc, E. Hossain, and D. I. Kim, “Distributed interference management in femtocell networks,” in Proc. IEEE VTCFall 2011, Sept. 2011. [8] J. Choi, T. Kwon, Y. Choi, and M. Naghshineh, “Call admission control for multimedia services in mobile cellular networks: A Markov decision approach,” in IEEE Int. Symp. Comput. Commun. (IEEE ISCC), July 2000. [9] S. Singh, V. Krishnamurthy, and H. V. Poor, “Integrated voice/data call admission control for wireless DS-CDMA systems,” IEEE Trans. Sig. Processing, vol. 50, no. 6, pp. 1483–1495, June 2002. [10] M. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming. Hoboken, NJ: Wiley, 1994.
