180 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY QoS-Aware and Energy-Efficient Resource Management in OFDMA Femtocells

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1 180 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 QoS-Aware and Energy-Effient Resource Management in OFDMA Femtocells Long Bao Le, Senior Memer, IEEE, Dusit Niyato, Memer, IEEE, Ekram Hossain, Senior Memer, IEEE, Dong In Kim, Senior Memer, IEEE, and Dinh Thai Hoang Astract We consider the joint resource allocation and admission control prolem for Orthogonal Frequency-Division Multiple Access (OFDMA)-ased femtocell networks. We assume that Macrocell User Equipments (MUEs) can estalish connections with Femtocell Base Stations (FBSs) to mitigate the excessive cross-tier interference and achieve etter throughput. A crosslayer design model is considered where multiand opportunist scheduling at the Medium Access Control (MAC) layer and admission control at the network layer working at different time-scales are assumed. We assume that oth MUEs and Femtocell User Equipments (FUEs) have imum average rate constraints, whh depend on their geographal locations and their applation requirements. In addition, locking proaility constraints are imposed on each FUE so that the connections from MUEs only result in controllale performance degradation for FUEs. We present an optimal design for the admission control prolem y using the theory of Semi-Markov Decision Process (SMDP). Moreover, we devise a novel distriuted femtocell power adaptation algorithm, whh converges to the Nash equilirium of a corresponding power adaptation game. This power adaptation algorithm reduces energy consumption for femtocells while still maintaining individual cell throughput y adapting the FBS power to the traff load in the network. Finally, numeral results are presented to demonstrate the desirale operation of the optimal admission control solution, the signifant performance gain of the proposed hyrid access strategy with respect to the closed access counterpart, and the great power saving gain achieved y the proposed power adaptation algorithm. Index Terms Femtocell network, admission control, Markov decision process, locking proaility, channel assignment. I. INTRODUCTION SMALL cell deployment and inter-cell interference mitigation have een recognized as the key techniques to enhance the capacity of cellular wireless networks [1]. Due to Manuscript received January 29, 2012; revised May 27 and August 02, 2012; accepted Septemer 30, The associate editor coordinating the review of this paper and approving it for pulation is M. C. Gursoy. This work was supported in part y the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Strateg Grant Program and the MKE, Korea, under the ITRC support program supervised y the NIPA (NIPA-2012-(H )). This paper was presented in part at IEEE International Conference on Communations (IEEE ICC 2012), Ottawa, Ontario, Canada. L. B. Le is with the Institut National de la Recherche Scientifique - Énergie, Matériaux et Télécommunations (INRS-EMT), Université du Quéec, Montréal, Quéec, Canada ( long.le@emt.inrs.ca). D. Niyato and D. T. Hoang are with Nanyang Technologal University, Singapore ( {dniyato, thdinh}@ntu.edu.sg). E. Hossain is with University of Manitoa, Winnipeg, MB, Canada ( Ekram.Hossain@ad.umanitoa.ca). D. I. Kim is with Sungkyunkwan University (SKKU), Suwon, Korea ( dim@skku.ac.kr). Digital Oject Identifier /TWC /13$31.00 c 2013 IEEE imal installation and operation costs, emerging femtocells have een shown to e a viale technal solution for roadand wireless access in indoor environments [2]. However, since femtocells may operate on the same frequency spectrum as macrocells, mitigation of cross-tier interference is a very signifant research issue. To enale spectrum sharing etween macrocells and femtocells in Orthogonal Frequency-Division Multiple Access (OFDMA)-ased two-tier networks, one of the three access modes, namely, open, closed and hyrid access, can e employed [3]-[7]. In the open access mode, the MUEs are allowed to connect to either their own Macrocell BSs (MBS) or FBSs. In contrast, in the closed access mode, only certain users (suscriers) elonging to the so-called Closed Suscrier Group are allowed to connect to each FBS. The hyrid access mode alances the strengths and weaknesses of the closed and open access modes. In a typal hyrid access mode for OFDMA-ased two-tier network, the FUEs can use all availale suchannels when there is no connected MUE. However, limited spectrum access at each femtocell is granted for MUEs whh wish to estalish connections. An effient admission control poly is required in this case to coordinate spectrum sharing and admission control for oth types of users, whh should stre a alance etween achieving high spectrum utilization and protecting QoS requirements for FUEs. In this paper, we develop such a spectrum sharing and admission control mechanism for OFDMA-ased two-tier networks. There have een some recent works on resource allocation and performance analysis of OFDMA-ased femtocell networks. In [5], a stat frequency assignment scheme ased on fractional frequency reuse was proposed considering the handoff, coverage, and interference aspects of femtocell networks. In [8], a randomized frequency allocation strategy called F- ALOHA was proposed and its area spectral-effiency was analyzed for OFDMA-ased femtocell networks y using stochast geometry. Research studies in [9] suggested that open access can provide a throughput gain of more than 300% for CDMA-ased femtocell networks whereas the throughput performance of open and closed access modes for OFDMA femtocells depends on user density. Moreover, the admission control and handoff prolem for femtocell networks was studied y using simulations [4]. In [10], a hierarchal resource allocation framework for OFDMA-ased femtocell networks was proposed that includes three control loops, namely, maximum power setting for FUEs,

2 LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 181 target SINR assignment for FUEs, and instantaneous power control to achieve these target SINR values. In [11], a distriuted power control algorithm was proposed for femtocells to maximize the sum-rate achieved y FUEs. In [12], to design resource allocation algorithms, a game model was used, the equiliria of whh were shown to e fair and effient. In [13], a frequency scheduling algorithm ased on spectrum sensing was proposed for coexistence of MUEs and FUEs. In [14], distriuted admission control and spectrum allocation algorithms were developed using reinforcement learning, whh are, however, unale to provide performance guarantees for users of oth network tiers. There are existing works in the literature that investigated the admission control prolem ased on Markov Decision Process (MDP) and also the power control prolem for traditional one-tier CDMA wireless networks [16], [17], [21]. To the est of our knowledge, the prolem of optimal admission control with quality-of-serve (QoS) guarantee in multi-tier wireless cellular networks, whh is addressed in this paper, has not een well investigated in the literature. The contriutions of this paper can e summarized as follows: We develop a mathematal model for joint resource allocation and admission control design for dynam spectrum sharing in OFDMA-ased two-tier femtocell networks. This model considers the QoS requirements of MUEs and FUEs in terms of average rates and locking proailities in presence of oth co-tier and cross-tier interferences. We devise a cross-layer radio resource management framework for femtocells with a multiand proportionalfair scheduling scheme at the MAC layer and an admission control scheme at the network layer. Then, the optimal admission control solution is otained y using the theory of Semi-Markov Decision Process (SMDP). For energy-effient resource management, we propose a novel distriuted femtocell power adaptation algorithm y using game theory. We prove that the proposed femtocell power adaptation algorithm converges to the Nash equilirium (NE) of the game. We demonstrate the effacy of the proposed admission control scheme as well as the signifant power saving gains of the proposed power adaptation algorithm via numeral studies. The rest of this paper is organized as follows. In Section II, we present the system model. The cross-layer resource allocation and admission control framework is presented in Section III. We present the distriuted femtocell power adaptation algorithm in Section IV. Numeral results are presented in Section V whh is followed y conclusion in Section VI. A summary of key notations is presented in Tale I. II. SYSTEM MODEL We consider the downlink of a two-tier OFDMA-ased wireless network that employs Frequency-Division Duplexing (FDD). There are N suchannels shared y MUEs and FUEs for downlink communations 1.Itisassumedthatthereare 1 The structure of cross-tier interference in the uplink is quite different from that in the downlink. Analysis of the uplink scenario is left for our future work. Fig. 1. 2D Two-tier femtocell network. Macrocell MBS MUE MBS L500m FUE FBS FBS FUE FUE Femtocell J femtocells sharing these N suchannels with I macrocells. We further assume that a hyrid access poly is employed where MUEs can connect to a neary FBS. This can happen when MUEs suffer from undue cross-tier interference or they can achieve etter rates if connected with a neary FBS. The system model under consideration is illustrated in Fig. 1. We assume that each suchannel can e assigned to at most one FUE or MUE connecting to any FBS. Furthermore, we assume a full spatial reuse where all suchannels are utilized at each FBS. In addition, suchannels are assumed to e allocated to macrocells in such a way that interference among macrocells is properly controlled 2. We consider the scenario where users of oth network tiers demand some imum average rates whh are detered y their underlying applations and locations in the cell. In fact, location-dependent QoS constraints can e imposed to alance user throughput and fairness. For instance, cell-edge users may require a imum rate that is smaller than that of cell-center users so that the total cell throughput is not severely compromised. We assume that there are C 1 classes of FUEs and C 2 classes of MUEs connecting to any FBS. In addition, it is assumed that class-c MUEs and FUEs require their total average rates to e at least R (mc) and R (fc), respectively. To illustrate these QoS constraints, let us assume that longterm signal attenuation depends on the distance etween users and a BS symmetrally. Note however that this assumption can e relaxed as long as detailed path-loss information in each cell is availale. The area around each FBS can e divided into circular areas and users running the same applation (e.g., voe or video) in each circular area can e imposed the same imum average rate requirement. Each such imum rate is mapped to one user class. We dept this QoS modeling in Fig. 2 where the femtocell area is divided into cell-edge and cell-center regions. In addition, there is a circular region where MUEs inside that region would request to estalish connections with the underlying FBS (i.e., they switch their 2 Examples of suchannel allocation schemes include fractional frequency reuse and partial frequency reuse [15].

3 182 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 TABLE I SUMMARY OF KEY NOTATIONS Notation I J N W C 1, C 2 R (fc), R(mc) g (fc) ijk, g(fc) ijk L(d ijk ) λ (f), λ(m) μ (f), μ(m) p i, p 0 β i PFBS max, P MBS max Γ (fc), Γ(mc) f (fc) y f (mc) y Γ (fc), Γ(mc) U (f), U (m) u (f), u(m) Δ (f), Δ(m) s (f), s(m) s (f), s(m) y (fc), y(mc) (x), F y (fc) (x), F (mc) y, r(mc) r (fc) r (fc), r(mc) B (f), B(m) P (fc), P (mc) a (f), a(m) A x τ x(a) z xa w (m), w (f) T i, T σ δ P i, F i (.) p xy(a) (x) (x) Physal meaning Numer of macrocells Numer of femtocells Numer of suchannels Bandwidth of one suchannel Numer of FUE/MUE serve classes Minumum required rate for class-c FUEs/MUEs Channel gain from FBS/MBS j to class-c user k in femtocell i Path-loss over distance d ijk Arrival rate of class-c FUEs/MUEs in femtocell i Serverateofclass-c FUEs/MUEs in femtocell i Transmission power on each suchannel from FBS/MBS i Transmission power ratio for femtocell i Maximum transmission power of FBS/MBS SINR of class-c FUE/MUE k in femtocell i Average SINR of class-c FUE/MUE k in femtocell i Set of class-c FUEs/MUEs in femtocell i Numer of class-c FUEs/MUEs in femtocell i Set of suchannels allocated for class-c FUEs/MUEs in femtocell i Numer of suchannels allocated for class-c FUEs/MUEs in femtocell i Required numer of suchannels for class-c FUEs/MUEs in femtocell i Equal Γ (fc) /Γ(fc) and Γ (mc) /Γ (mc), respectively Proaility density function and proaility distriution function for y (fc) Proaility density function and proaility distriution function for y (mc) Average rate achieved y class-c FUE/MUE k in femtocell i Minimum average rate achieved y class-c FUE/MUE k in femtocell i Blocking proaility for class-c FUEs/MUEs in femtocell i Target locking proaility for class-c FUEs/MUEs in femtocell i Control action of class-c FUEs/MUEs in femtocell i Admissile action space for system state x Expected time until the next decision epoch when action a is taken Rate of choosing action a in state x Weighting factors defining the cost function of the MDP formulation Throughput of femtocell i and total throughput Standard deviation of shadowing Power scaling factor Power and payoff function of femtocell i Transition proaility from state x to state y given action a e taken connections to the underlying FBS) 3. We assume that the distance from any user connecting with FBS i to other FBS/MBS j can e well approximated y the distance from FBS i to FBS/MBS j. This assumption would e valid ecause the size of a typal femtocell would e much smaller than the distance etween the BSs of either tier. Let g (fc) ijk and g (mc) ijk e the channel gains on a partular suchannel from FBS j and MBS j, respectively, to a partular class-c user k of either tier who is associated with femtocell i. For revity, the suchannel index is omitted in these notations. Channel gains are modeled considering pathloss, shadowing, and Rayleigh fading. Specifally, we can write g (xc) ijk (x stands for f or m) asg(xc) ijk L(d ijk)10 η/10 ω, where L(d ijk ) represents the path-loss over the corresponding distance d ijk, η is a Gaussian-distriuted random variale with zero mean and standard deviation σ, and ω represents the short-term Rayleigh fading gain. In addition, we assume that 3 MUEs typally achieve etter average SINRs and higher transmission rates when they enter this neighorhood and switch their connections to the underlying FBS. Fig. 2. Switching oundary for MUEs Femtocell oundary Serve-class oundary for FUEs FBS Location-dependent QoS classes and switching oundary for MUEs. connection requests of class-c FUEs and MUEs in femtocell i, whh are assumed to follow Poisson processes, arrive with rate λ (f) and λ (m), respectively. The connection duration is

4 LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 183 Fig. 3. Cross-layer Adaptation Arrival and Serve Rates Distriuted Opportunist Scheduling Admission Control With Rate and Blocking Proaility Constraints Distriuted Femtocell Power Adaptation User Average Rate and Required Bandwidth Blocking Proailities Instantaneous CSI and Co-tier/Crosstier Interference Cross-layer resource management model with time-scale separation. assumed to e exponentially distriuted with mean duration of 1/μ (f) and 1/μ (m) for class-c FUEs and MUEs, respectively. III. CROSS-LAYER RESOURCE ALLOCATION AND ADMISSION CONTROL FRAMEWORK We consider a cross-layer joint resource allocation and admission control framework for femtocells with the following network functionalities. A distriuted opportunist scheduling algorithm is assumed to e implemented at each FBS to exploit the multiuser diversity at a small time-scale. Depending on the channel dynams oserved y users in two tiers, the size of a scheduling time slot is assumed to e designed accordingly. In contrast, the admission controller operates at a larger timescale, whh captures the system dynams due to user arrivals and departures. Also, we design a distriuted power adaptation algorithm that adapts the transmission power of FBSs to the heterogeneous traff distriution over the network for QoSaware and energy-effient spectrum sharing etween the two network tiers. The cross-layer model under consideration is illustrated in Fig. 3. It is worth noting that we consider a dynam network model where users come and leave the network over time. Therefore, traditional resource allocation algorithms developed for a stat and snapshot network model with fixed network topology (i.e., fixed numer of users with known locations) cannot e applied to our setting. We assume that the MBSs have maximum transmission power of PMBS max while the maximum allowale power of FBSs is PFBS max whh is detered from outage proaility constraints for MUEs and will e descried in Section III-C. For simplity, we assume that the MBSs and FBSs perform uniform power allocation over the suchannels and FBS j uses 0 β j 1 fraction of its maximum power while the MBSs use their maximum power for downlink communations 4. These femtocell transmission power ratios β j will e employed y the distriuted power adaptation algorithm to e presented in Section IV. Therefore, the transmission power on any suchannel for users connecting to FBS j is p j β j PFBS max /N and the transmission power from any MBS on one suchannel is p 0 PMBS max /N. Given the power 4 We do not consider resource allocation for the macrocell tier in this paper. However, the proposed algorithms would e ale to adapt to the potential dynam operations of the macrocells. allocation for MBSs and FBSs, we present an opportunist scheduling algorithm and analyze its throughput performance in the following. A. Multi-and Opportunist Scheduling The signal-to-interference-plus-noise ratio (SINR) achieved y class-c FUE k associated with femtocell i on a partular suchannel can e written as Γ (fc) p i g (fc) i j1,j i g(fc) ijk p j + I j1 g(mc) ijk p 0 + N 0 p i g (fc) i j1,j i g(fc) ijk p j + IN (fc) where N 0 denotes the noise power and recall that g (fc) ijk and g (mc) are the channel gains from FBS j and MBS j to class-c ijk FUE k in femtocell i, respectively. The first and second terms in the denoator of (1) represent the total interference due to other FBSs and MBSs, respectively. In addition, IN (fc) I j1 g(mc) ijk (1) p 0 +N 0 denotes the total interference from MBSs and the noise power. Similarly, the SINR achieved y class-c MUE k connecting with FBS i can e written as Γ (mc) p i g (mc) i j1,j i g(fc) ijk p j + I j1,j j i g (mc) ijk p 0 + N 0 p i g (mc) i j1,j i g(fc) ijk p j + IN (mc) where IN (mc) I j1,j j i g (mc) ijk p 0+N 0 and j i is the nearest MBS of femtocell i. Here, we assume that suchannels allocated to MUEs connected with FBS i are not assigned to other MUEs connected with the nearest MBS of femtocell i. Hence, in the second term in the denoator of (2) we exclude the interference from this MBS in calculating the total noise and interference power. For revity, we omit the suchannel index in the SINR notations Γ (fc) and Γ (mc). We assume that the SINR-proportional fair opportunist scheduling algorithm [20], [22] is employed on each suchannel 5. In partular, time is divided into equal-size time slots and scheduling decisions are made in each time slot for all suchannels. Because the time slot interval is very small (e.g., typally few milliseconds) compared to the user dwelling time, the opportunist scheduling algorithm operates over a small timescale. Note that a partular user of either tier can e scheduled to transmit on multiple suchannels in each time slot. Let U (m) and U (f) denote the sets of class-c MUEs and FUEs in femtocell i and their cardinalities are denoted as u (m) U (m) and u (f) U (f), respectively. In addition, let Δ (f) and Δ (m) e the sets of suchannels allocated for class-c FUEs and MUEs in femtocell i, respectively. We assume that these sets are detered to meet the average rate requirements and they are only updated when the numers of active users (2) 5 Consideration of the proportional fair scheduling in the cross-layer model would e quite natural given that it has een adopted in practal wireless standards [20], [22]. Moreover, the framework considered in this paper can e readily extended to other scheduling schemes.

5 184 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 u (m) and u (f) change. The SINR-proportional fair opportunist scheduling algorithm operates on a partular suchannel v Δ (f) as follows. FBS i chooses FUE k that achieves the largest ratio Γ (fc) (t)/γ(fc) for transmission in time slot t on this suchannel, i.e., k argmax (f) k U Γ (fc) (t)/γ(fc) where recall that Γ (fc) (t) and Γ(fc) are the instantaneous and average SINR of FUE k on the underlying suchannel, respectively. Similar operations are applied for suchannels in Δ (m) to schedule MUEs in the sets U (m). Now, we detere the average rate achieved y a partular FUE k U (f) on one partular suchannel. Toward this end, we need to descrie the proaility distriution of Γ (fc) (t)/γ(fc). It was shown in [19], [20] that the composite variaility of g (fc) ijk due to Rayleigh fading and lognormal shadowing can e approximated y a single lognormal distriution. In addition, it is well-known that a sum of lognormally-distriuted random variales can e represented y a single lognormal distriution [23], [32]. Also, the ratio of two lognormally-distriuted random variales is lognormally distriuted. Therefore, y (fc) Γ (fc) (t)/γ(fc) can e approximated y a lognormally-distriuted random variale whose mean and standard deviation can e calculated as in [20]. Then, the average rate achieved y FUE k U (f) on a partular suchannel can e written as follows 6 : r (fc) W 0 ( log 1+y (fc) Γ(fc) F y j U (f) i,c,j k (fc) ij ) (x) f (x)dx (3) y (fc) F y (fc) where W is the andwidth of one suchannel; f (fc) y (x) and (x) represent the proaility density function and proaility distriution function of y (fc), respectively. Similarly, the average rate achieved y MUE k U (m) on a partular suchannel can e written as follows: ( ) r (mc) W log 1+y (mc) Γ (mc) 0 F (mc) y (x) ij f (x)dx (4) y (mc) j U (m),j k where y (mc) Γ (mc) (t)/γ (mc) ; f (mc) y (x) and F (mc) y (x) represent the proaility density function and proaility distriution function of y (mc), respectively. B. QoS Constraints It can e verified that the average rate r (fc) calculated in (3) decreases with the path-loss L(d i ) for given power allocation and channel gain parameters. Moreover, r (fc) decreases with the numer of class-c FUEs u (f) ecause the proportional-fair 6 Assug that the long-term channel gains on different suchannels are the same and the typal user dwelling time is much larger than a scheduling time slot, the average rates achieved y a partular user on different suchannels are the same. scheduling allows equal long-term time-shares among users [18], [20] and each suchannel in Δ (f) is shared y u (f) FUEs. Recall that class-c MUEs and FUEs require their total average rates to e at least R (mc) and R (fc), respectively. To detere the imum numer of suchannels to meet the imum rate requirement, we consider the worst user with imum L(d i ) (or maximum d i ) for each serve class c in femtocell i. That is, the femtocell i is located at the edge of the corresponding serve class for symmetr path-loss. Let r (fc) i and r (mc) i e the imum rates achieved y any class-c FUE and MUE, respectively. These imum rates can e calculated y using (3) and (4) for the corresponding worst users. Let s (f) Δ (f) and s(m) Δ (m) e the numers of suchannels allocated for class-c FUEs and MUEs in femtocell i, respectively. To maintain the rate requirements for FUEs and MUEs of each serve class, we impose the following constraints 7 : R (fc) R (mc) s(f) s (m) r (fc) i (u (f) ) (5) r (mc) i (u (m) ) (6) where we explitly descrie the dependence of r (fc) i and on u (f) and u (m), respectively. These constraints ensure r (mc) i that the imum rate requirements are satisfied y any classc user. From these inequalities, we require that the numers of suchannels allocated for class-c MUE and FUE satisfy s (m) s (f) R (fc) r (fc) i (u (f) ) R (mc) r (mc) i (u (m) ) ( s (f) ( s (m) u (f) u (m) ) (7) ). (8) Therefore, the rate constraints in (5) and (6) hold if the following constraints for femtocell i are satisfied: C 1 N ( s (f) u (f) ) C 2 + ( s (m) u (m) ), i 1, 2,...,J. (9) This constraint means that the numer of availale suchannels should e large enough to support the required imum rates for all serve classes. This constraint will e used for admission control design. Since the MUEs degrade the performance of the FUEs connecting to the same FBS, the FUEs must e satisfactorily protected. Toward this end, we assume that a class-c FUE has the maximum tolerale locking proaility of P (fc).letb (f) denote the locking proaility of class-c FUEs in femtocell i. Then, the locking proaility constraints can e written as follows: B (f) P (fc), i, c. (10) The admission control and channel assignment should e performed in such a way that they can satisfy the channel and locking proaility constraints in (9) and (10), respectively. 7 Since the average rates achieved y any user on different suchannels are the same, only the numer of suchannels allocated to a partular serve class impacts the achievale average rates of its users. Note, however, that we have exploited the channel dynams to enhance the user throughput through employing the proportional fair scheduling.

6 LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 185 C. Maximum Power Constraints Under Closed and Hyrid Access Let d MU e the radius of the circular area centered around each FBS where MUEs inside this region will connect with the corresponding FBS under the proposed hyrid access scheme. Also, let d F e the radius of the coverage area of any femtocell. We consider oth closed and hyrid access strategies and derive the corresponding maximum power constraints for FBSs so that MUEs whh are connected with MBSs and close to FBSs are protected from excessive cross-tier interference. Specifally, it is required that the transmission powers of FBSs must e smaller than some maximum value so that outage proaility of MUEs is smaller than a desirale value. Toward this end, let us consider a partular MUE k that connects with a neary MBS and FBS i is its closest FBS. Let h (m) e the channel gain etween the considered MUE k and its connecting MBS. Then, we can express the SINR of this MUE k as γ (m) p 0 h (m) j1 g(fc) ijk p j + I j1,j j i g (mc) ijk p 0 + N 0 p 0 h (m) j1 g(fc) ijk p. (11) j + IN (mc) Note that all femtocells including femtocell i create cross-tier interference for the considered MUE k. In addition, MUEs are not allowed to connect with neary FBSs under the closed access. To calculate the maximum allowale power for FBSs under the closed access, we impose the outage proaility constraints for the worst MUE k whose distance from FBS i is exactly d F.Letγ 0 e the target SINR of the considered MUE k then the outage proaility constraint can e expressed as { } Pr γ (m) (d F ) <γ 0 <P o (m) (12) where γ (m) (d F) denotes the SINR of the MUE whose distance to the nearest FBS is d F and P o (m) represents the target outage proaility. The LHS of this inequality denotes the outage proaility for the considered MUE. Recall that γ (m) can e modeled as a lognormally distriuted random variale with mean and standard variation (in db) of μ m and η m, respectively, whh can e calculated as in [20]. The outage proaility in the left hand side of (12) can e expressed as [20] { } Pr γ (m) (d F ) <γ ( ) 10 2 erfc log10 γ 0 μ m (13) 2ηm where erfc(x) denotes the complementary error function, defined as erfc(x) 2 π x exp( y2 )dy. Then, we assume that the transmission power of any FBS is constrained y a common maximum value PFBS max so that outage proaility constraints in (12) are satisfied for neighoring MUEs of all femtocells. This kind of outage proaility constraints has een considered in several recent works [27], [28]. For the proposed hyrid access, any MUE whose distance from the nearest FBS is less than d MU will connect with the FBS. Therefore, the outage proaility constraints in this case can e expressed as { } Pr γ (m) (d MU) <γ 0 <P o (m). (14) The outage proaility in (14) can e calculated as in (13) with the corresponding mean and standard deviation values. And the maximum transmission power PFBS max of all FBS under the hyrid access can e calculated so that the outage proaility constraints in (14) are satisfied. The maximum transmission power PFBS max under either access scheme is assumed to e estimated y FBSs during a network startup phase. D. SMDP-Based Distriuted Admission Control in Femtocells Given the considered physal and network layer models, admission control is performed at the network layer considering user dynams at the call level. It turns out that admission control can e performed separately in each cell, whh enales distriuted implementation. We will present and analyze the performance of an optimal admission control scheme for a partular femtocell i. In fact, we can formulate the admission control prolem as an SMDP [33]. We proceed y descriing the state and action spaces for the underlying SMDP. The 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: [ ] x(t) u (f) i1 (t),...,u(f) ic 1 (t),u (m) i1 (t),...,u(m) ic 2 (t) (15) where recall that u (f) (t) and u(m) (t) are the numers of classc FUEs and MUEs at decision epoch t, respectively. Then, the state space X is defined as follows: X {x : constraint (9) holds}. (16) At each decision epoch when the system changes its state, an admission control action is detered 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 [ ] a(t) a (f) i1 (t),...,a(f) ic 1 (t),a (m) i1 (t),...,a(m) ic 2 (t) (17) where a (f) (t) and a(m) (t) denote the admission control action when an arrival occurs for class-c FUEs and MUEs in femtocell i, respectively, whh are defined as follows: { 1, if a newly arriving FUE is admitted a (f) (18) 0, otherwise a (m) { 1, if a newly arriving MUE is admitted 0, otherwise. (19) The action state } space can e defined as A {a : a {0, 1} C1+C2. Given these system and action state spaces, we can detere the transition proailities for the underlying emedded Markov chains ased on whh the optimal solution can e otained (see Appendix A). Let B (f) and B (m) e the locking proailities for class-c FUEs and

7 186 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 MUEs, respectively, whh can e calculated from the SMDPased admission control solution presented in Appendix A. Then, we can calculate the achievale call throughput of femtocell i as follows: C 1 C 2 T i (1 B (f) )λ(f) + (1 B (m) )λ (m) (20) where we have taken locked arrivals into consideration. Finally, the total network throughput achieved y all femtocells can e calculated as T i1 T i. The admission control framework developed in this section will e used in the design of a femtocell power adaptation algorithm in the next section. IV. DISTRIBUTED POWER ADAPTATION ALGORITHM High transmission power at an FBS may severely degrade the performance of other highly-loaded femtocells and macrocells ecause of excessive inter-cell and cross-tier interference. To address this issue, we develop an effient power adaption mechanism y using game theory 8. The proposed power adaptation algorithm aims to adapt transmission powers of FBSs to spatial traff load over the network [31] 9. Therefore, it is only activated when the traff load descried y user arrival rates changes. Femtocell Power Adaptation Game (FPAG): Players: J FBSs. Strategies: Each FBS i can select its total transmission power P i [0,PFBS max] (the transmission power ratio β i for FBS i is in [0, 1]) to maximize its payoff. Payoffs: F i (P i,p i ) for each FBS i is F i (P i,p i ) P i,wherep i [P 1,...,P i 1,P i+1,...,p J ] denotes a vector containing transmission powers of other FBSs excluding FBS i. It is assumed that all FBSs are required to satisfy the channel and locking proaility constraints in (9) and (10), respectively, while maximizing their payoffs. In addition, we require that each FBS i that wishes to reduce its transmission power must satisfy the following locking proaility constraints for their MUEs B (m) P (mc), 1 c C 2 (21) given that these constraints are satisfied when the maximum power PFBS max (mc) is used. Here P s are some predetered values. These additional constraints ensure that satisfactory performance in terms of locking proailities is achieved for users of oth network tiers while the payoffs of all the FBSs are maximized. Remark 1: We assume that only FBSs partipate in the power adaptation game. In general, this formulation can e readily extended to the scenario where MBSs are also players of the game. However, MBSs are typally inter-connected y high-speed links, whh enale them to achieve certain gloal 8 In general, femtocell owners would e interested in maximizing their own enefits while maintaining required QoS for their users. Therefore, use of non-cooperative game theory in designing the power adaptation algorithm for femtocells arises quite naturally. 9 The related research tops including design of FPGA, power circuitry, and sleep mode strategies are other aspects of cross-layer design in attaining the energy effiency, whh are out of the scope of this paper. ojectives. Investigation of power control issues for MBSs are, therefore, eyond the scope of this paper. One important concept in game theory is the Nash equilirium (NE), whh is defined in the following. Definition 1: A transmission power vector P is called the NE of the FPAG if for each FBS i, F i (Pi,P i ) F i(p i,p i ), P i [0,PFBS max]. In the following, we develop a femtocell power adaptation algorithm that converges to the NE of the FPAG. In partular, FBSs, whose required locking proaility constraints are still maintained, decrease their transmission powers y a factor δ< 1 iteratively. Toward this end, we present some preliary results that characterize the system ehavior under these power scaling operations. Proposition 1: Given the channel gains for all users, we have the following properties: 1) For any FUE and MUE, whose FBS scales down power, the SINR given in (1) and (2) decreases; 2) For any FUE and MUE, whose FBS does not scale down power, the SINR given in (1) and (2) increases. Proof: To prove the first property of this proposition, let us consider the SINR on any suchannel achieved y a class-c FUEs associated with FBS i whh scales down power y a factor δ. LetΩ e the set of FBSs whh scale down their transmission powers excluding FBS i in the current iteration. Then, we can rewrite the SINR of FUE i as follows: Γ (fc) δp (p) i g (fc) i j Ω g(fc) ijk δp(p) j + j/ Ω g(fc) ijk p(p) j j Ω g(fc) ijk p(p) j p (p) i g (fc) i + j/ Ω g(fc) p (p) j ijk δ p (p) i g (fc) i j Ω g(fc) ijk p(p) j + j/ Ω g(fc) ijk p(p) j + IN (fc) + IN(fc) δ + IN (fc) (22) where p (p) j β j PFBS max /N is the transmission power on any suchannel in femtocell j in the previous iteration. The last inequality in (22) holds ecause δ<1. It can e oserved that the quantity in the right hand side of (22) is indeed the SINR of class-c FUEs in femtocell i in the previous iteration. Similarly, we can prove the decrease of SINR of MUEs. Therefore, the first property stated in the proposition holds. The second property in the proposition can e proved similarly. In partular, for any FBS whh does not scale down power, the received powers of its FUEs remain the same. However, the total received interference can only decrease due to the decreases in transmission powers of some other FBSs. The results in Proposition 1 descrie how the power updates of FBSs impact the SINRs of users in the network. We now state further results on the average rates achieved y the opportunist scheduling scheme under power adaptation. Proposition 2: We have the following results for the average rates achieved y the SINR-proportional fair scheduling scheme: 1) For any FUE and MUE whose FBS scales down power, the average rate given in (3) and (4) decreases;

8 LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 187 2) For any FUE and MUE whose FBS does not scale down power, the average rate given in (3) and (4) increases. Proof: From Proposition 1, for any FUE and MUE whose connecting FBS scales down the transmission power, its average SINR and rate in each scheduled slot decreases. In addition, one important principle of the proportional fair scheduling is that it allows equal long-term time shares among competing users on each suchannel [18], [20]. Therefore, for the fixed numer of users of either type (i.e., FUEs or MUEs) in a partular serve class, each user is asymptotally scheduled for the same fraction of time. Since the average rate of each user in each scheduled slot decreases with the decreasing FBS transmission power, its long-term average rate decreases. Therefore, the first property in Proposition 2 holds. The second property can e proved similarly y using the fact that the average SINR and rate achieved y any FUE or MUE in each scheduled slot increases in this case. According to (7) and (8), the numer of suchannels required to support certain target imum rates can increase or decrease if the average rates of the corresponding user class decrease or increase, respectively. In turn, the channel requirements for different user classes impact the channel constraint in (9) and the corresponding admission control performance. Because we are interested in the throughput performance at the network layer, the impacts of power adaptation on the admission [ control performance must] e characterized. Let u i u (f) i1,...,u(f) ic 1,u (m) i1,...,u(m) ic 2 e the vector whose elements represent [ the numer of users of] different classes and let s i s (f) i1,...,s(f) ic 1,s (m) i1,...,s(m) ic 2 e the required numers of suchannels to support the imum rate requirements in (7) and (8), respectively. Definition 2: A vector s i is said to doate another vector s i written as s i s i if we have s(f) s (f),c 1,...,C 1, s (m) s (m),c 1,...,C 2, and there is at least one strt inequality in these inequalities. We are ready to state an important result that descries the interaction of the physal and network layer performance of the proposed cross-layer design model. Proposition 3: Consider the performance of the SMDPased optimal admission control descried in Section III.C under two different channel requirement vectors s i and s i where s i s i. Let B(f), B(m) and B (f), B (m) e the optimal locking proailities that are attained with the two different channel requirement vectors s i and s i, respectively. Suppose that arrival rates are suffiently high so that B (f) B (f) P (fc) control 10. Then, we have B (m), 1 c C 1 under the SMDP-ased admission B (m). Proof: Let us rewrite the cost function F π in (29) for a partular stationary poly π as C 1 F π w (f) B(f) + C 2 w (m) B (m) (23) where recall that B (f) and B (m) denote the locking proailities of class-c FUEs and MUEs, respectively. 10 As will e seen in the numeral results, these proaility constraints for FUEs are met with equality for suffiently large arrival rates. Let π denote the optimal poly of the system with the channel requirement vector s i and let B (f) and B (m) e the optimal locking proailities achieved y this optimal poly for FUEs and MUEs, respectively. Refer to Appendix A for further details on how to calculate the optimal admission control solution for a given channel requirement vector. Suppose we apply this poly π for another system with the channel requirement vector s i. Since we assume s i s i, such poly utilization can maintain the suchannel constraint in (9) and the achievale locking proailities satisfy B (f) B (f) P (fc) (the second equality holds due to the assumption of the proposition) and B (m) B (m). Now, let us compare the locking proailities B (m) otained aove with the locking proailities B (m) attained y the optimal solution for the system with the channel requirement vector s (m) i.wemusthaveb B (m) since B (m) is due to the optimal poly for the system with the channel requirement vector s i. Therefore, we have (m) B B (m) B (m). This completes the proof of the proposition. The results in Proposition 2 and Proposition 3 estalish the foundation to develop the power adaptation algorithm. Specifally, we can allow lightly-loaded FBSs to reduce their transmission powers, whh in turn increases the locking proailities of their users as long as the resulting locking proailities satisfy the constraints in (10) and (21). The reduction of transmission powers in lightly-loaded FBSs will increase transmission rates for femtocells with high traff load. This can potentially decrease channel requirement vector s i for other highly-loaded femtocell i. This can result in an improvement in locking proailities and the total throughput in these highly-loaded femtocells. The proposed power adaptation algorithm is descried in details in Algorithm 1. In steps 3-5, each FBS in set A f attempts to reduce its transmission power y a factor δ. Parameter P (mc) in (21) is introduced to maintain the performance of MUEs connecting with lightly-loaded FBSs. When multiple femtocells scale down their powers at the same time there may e a suset of these femtocells failing to maintain their locking proaility requirements (i.e., constraints (10) and (21)). In steps 7-9 of Algorithm 1, the femtocells whh fail to maintain their locking proaility requirements scale up their powers y a factor 1/δ to do so. There are sutle interactions among femtocells after step 9. Specifally, the power scaleup of femtocells in steps 7-9 may make other femtocells violate their locking proaility requirements. This is ecause a larger transmission power of any femtocell results in higher interference and therefore lower transmission rates for users in other femtocells. In steps of Algorithm 1, any violating femtocell scales up its transmission power to maintain its locking proaility requirement. This is performed until the locking proaility requirements in all femtocells are satisfied. The proposed algorithm can e implemented in a distriuted fashion ecause each FBS only needs to know the average rates achieved y its FUEs and MUEs of different classes. This can e attained y letting FUEs and MUEs of all classes

9 188 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 Algorithm 1 FEMTOCELL POWER ADAPTATION 1: Initialization: Each FBS uses its maximum power for downlink communations. Moreover, each FBS calculates its admission control performance using the analytal model presented in Section III.C. 2: Let A f e the set of active femtocells who can maintain its locking proaility requirements in (10) and (21). 3: for each FBS i in A f do 4: FBS i scales down its transmission power y a factor δ<1 (i.e., FBS i performs the following update: β i : δβ i and transmits with power β i PFBS max). 5: end for 6: Each FBS re-calculates its admission control solution ased on the current perceived SINRs of its user classes where additional constraints (33) are imposed for each FBS i if constraints in (21) for FBS i hold in the previous iteration. 7: for each FBS j whh scales down its transmission power in the current iteration and cannot maintain the locking proaility constraints in (10) or (21) do 8: FBS j scales up the transmission power y a factor 1/δ (i.e., go ack to the previous power level). 9: end for 10: while there are any femtocells whh scale up their transmission power do 11: Each FBS re-calculates its admission control solution ased on the current perceived SINRs of its user classes where additional constraints in (33) are imposed for each FBS i if constraints in (21) for FBS i hold in the previous iteration. 12: for each FBS j whh scales down its transmission power in the current iteration and cannot maintain the locking proaility constraints in (10) or (21) do 13: FBS j scales up the transmission power y a factor 1/δ (i.e., go ack to the previous power level). 14: end for 15: end while 16: Update the set A f to contain all femtocells who successfully maintain their locking proaility requirements in (10) and (21) after power scale-down in the current iteration or those that fail to do so K iterations efore where K is a predetered numer. 17: Go to step 2 until convergence. to feedack the estimated mean and standard variation of the lognormally distriuted variales representing their SINRs to each FBS i, whh are used to calculate the average rates and channel requirement vector s i. The channel requirement vectors are used to calculate the admission control performance for users of oth tiers in each femtocell. The convergence of Algorithm 1 is stated in the following theorem. Theorem 4: We have the following results for Algorithm 1: 1) The locking proaility requirements in (10) and (21) are satisfied at the end of each iteration. 2) Algorithm 1 converges to an equilirium. 3) If δ is suffiently close to 1 then the achieved equilirium tends to the NE of the FPAG. Proof: Note that the interference received y any FUEs and MUEs does not increase over iterations; therefore, if a femtocell goes ack to its power level in the previous iteration their locking proaility constraints must e satisfied. Also, since the locking proaility requirements of all lightlyloaded femtocells are satisfied in the first iteration and there is a finite numer of femtocells, the inner loop corresponding to steps of Algorithm 1 must terate in a finite numer of su-iterations (ounded y the numer of femtocells). Therefore, the locking proaility requirements in (10) and (21) for all femtocells are satisfied at the end of each iteration (i.e., after step 15). Hence, we have completed the proof for the first property of this theorem. We now prove the convergence of Algorithm 1. In each iteration, each femtocell either utilizes the same power level as in the previous iteration or scales down its power y a factor δ < 1 in Algorithm 1. Recall that the power adaptation operations performed in Algorithm 1 can maintain the locking proaility constraints (10) and (21) for all femtocells in any iteration (the first property of the theorem). In order to maintain these constraints, the average achieved rates of associated users must e strtly larger than zero (since the locking proailities of any user class tend to one if the average achieved rate of that user class tends to zero (i.e., zero serve rate)). Since each FUE and MUE receive nonzero total noise and interference power from other MBSs, the transmission power of any FBS must e strtly larger than zero to achieve non-zero average rates for its associated users. This implies that Algorithm 1 must converge to an equilirium at whh no femtocell can scale down its power further. Finally, we prove that the achieved equilirium tends to the NE of the FPAG for δ suffiently close to 1 y contradtion. Specifally, suppose that the achieved equilirium is not a NE. Then there must exist an FBS whh can increase its payoff or slightly decrease its transmission power while still maintaining the constraints in (10) and (21) given the transmission powers of other FBSs. However, this contradts to the fact that Algorithm 1 cannot decrease the transmission power of any FBS further at the equilirium. Therefore, the achieved equilirium must e close to the NE of the FPAG if δ is suffiently close to 1. Let βi,i1,...,j e the femtocell transmission power ratios otained y Algorithm 1 at convergence. Then, we can calculate the power saving with respect to the maximum allowed transmission power as follows: S p 100 JPmax FBS i1 β i P FBS max JPFBS max 100 J J i1 β i J (24) One may want to compare the admission control performance at the equilirium attained y Algorithm 1 with that achieved y using the maximum power. We characterize these results in the following theorem. Theorem 5: We have the following results for the equilirium achieved y Algorithm 1. 1) Throughput reduction ΔT i of a lightly-loaded femtocell i, whh scales down its transmission power, can e upper-ounded as ΔT i C 1 λ (f) P (fc) +.

10 LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 189 C2 P (mc) λ (m). 2) Let s i and s i e channel requirement vectors of a partular highly-loaded femtocell i under maximum power and at the equilirium attained y Algorithm 1. Suppose the arrival rates of the considered femtocell are suffiently large such that the constraints in (10) are met with equality when the maximum power is used. In addition, assume that we have s i s i. Then, Algorithm 1 results in etter throughput for the considered femtocell i compared to that achieved y using the maximum power. Proof: The first result of this theorem can e proved y noting that a lightly-loaded femtocell i only decreases its transmission power as long as the locking proaility constraints in (10) and (21) are still satisfied. Using the fact that the locking proailities for FUEs and MUEs are upperounded y P (fc) and P (mc), respectively, the upper-ound in throughput reduction can e otained y consulting the throughput formula in (20). The second result of this theorem can e proved y using the results in Proposition 3. In partular, the locking proailities for FUEs and MUEs decrease under Algorithm 1 ecause we have s i s i. Therefore, the second result follows y using these results and the throughput formula in (20). Remark 2: The power adaptation operations can e implemented asynchronously without impacting its convergence. In fact, in the arguments employed to prove the convergence of Algorithm 1 we do not impose any restrtion on the numer of femtocells that scale down transmission powers in any iteration. Therefore, the convergence holds for oth synchronous and asynchronous power updates. Moreover, the choe of parameter δ in Algorithm 1 impacts the tradeoff etween convergence speed and the transmission powers at the equilirium. In partular, fast convergence can e achieved y smaller δ at the cost of larger transmission powers at the equilirium. Remark 3: Let us define λ tot C 1 λ(f) + C 2 λ(m). Suppose we choose P (fc) P (mc) P ; then, the throughput loss of a lightly-loaded femtocell i presented in Theorem 5 can e rewritten as ΔT i P λ tot.sinceλ tot is ounded in stale systems we can achieve any desirale throughput loss y choosing P suffiently small. This implies that the NE achieved y Algorithm 1 indeed results in etter energy effiency for the femtocell network with improved throughput for highly-loaded femtocells and negligile throughput loss for lightly-loaded femtocells. Therefore, the achieved NE is a desirale operating point. Remark 4: Although the NE may not e very effient compared to certain gloally optimal solution, choosing NE as an operating point for the femtocells can e justified y the following facts. Firstly, femtocells owners would e typally selfish and only interested in optimizing their own enefits. Hence, NE would e an appropriate solution concept that enales us to realize this expectation. Secondly, the proposed power adaptation algorithm (i.e., Algorithm 1), whh converges to the NE of the underlying game, can e implemented in a distriuted manner. This is very desirale as ackhaul links over whh signaling information can e exchanged typally have limited capacity. Thirdly, development of a distriuted algorithm to reach a certain gloally optimal solution for the considered multi-layer resource allocation and admission control prolem seems to e non-tractale. In fact, it has een well-known that the utility maximization prolem for multell OFDMA setting even under the stat scenario (i.e., fixed numer of users without dynam user arrival and departure) is NP-hard and very complex to solve up to optimality [29]. Therefore, formulating the power adaption as a game where we can reach the NE in a distriuted manner would e a natural design approach for the femtocell network. Remark 5: We can calculate the energy effiency for the proposed hyrid access scheme in terms of energy per it [24], [25], [26]. Assume that users of each serve class transmit data at the required imum rates, i.e., class-c MUEs and FUEs transmit at rates R (mc) and R (fc), respectively. Let N (fc) i and N (mc) i e the average numers of class-c FUEs and MUEs connected with FBS i. Then, we can calculate the average numers of its transmitted y FBS i in one second as C 1 S i N (fc) i R (mc) C 2 + N (mc) i R (fc). (25) Recall that FBS i transmits at the power level P i β i PFBS max. Therefore, we can calculate the overall energy effiency of all femtocells as i1 E P i i1 S i i1 β ipfbs max i1 ( C1 N (fc) i R (mc) + C 2 N (mc) i R (fc) This implies that we can calculate the energy effiency if we can calculate N (fc) i and N (mc) i for a given power usage profile of all femtocells (i.e., β i for all femtocells i 1,...,J) and an admission control poly. Unfortunately, it seems nontractale to find closed-form expressions of N (fc) i and N (mc) i for the proposed optimal admission control poly. However, we can quantify the performance gain of the proposed power adaptation algorithm (i.e., Algorithm 1) in terms of energy effiency with respect to the scenario where the maximum transmission power P max is used if we can calculate the ratio ( FBS C1 of S tot i1 + C 2 under these two power usage profiles (i.e., Stot/S 1 tot 2 where Stot 1 and S2 tot denote the values of S tot under the two power usage profiles, respectively). We can argue that the values of S tot are approximately the same under these two power usage profiles. In fact, Algorithm 1 only scales down powers of lightly-loaded femtocells to the extent that the locking proailities of all associated MUEs and FUEs are elow the predetered small target locking proailities. In addition, any femtocell having higher average serve rate compared to other femtocells reduces its transmission power. Since the interference decreases with the transmission power, all femtocells would have roughly the same serve rates under oth power usage profiles. Since the energy effiency given in (26) is inversely proportional to S tot, whh is approximately the same under oth power usage N (fc) i R (mc) ). N (mc) i R (fc) )

11 190 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 profiles, the performance gains in terms of power saving and energy effiency are approximately the same. V. NUMERICAL RESULTS We present numeral results to illustrate the performance of the proposed admission control and power adaptation algorithms. The network setting is shown in Fig. 1 where there are 9 femtocells located at the edge of the central macrocell in a cluster of macrocells. The distance etween two neighoring 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 circular regions whose radii from the corresponding FBS are 15m and 30m, respectively. To calculate the required numer of suchannels for FUEs of each class (i.e., s (f) i,c in (7)), we consider the worst case where FUEs are located on the oundary of the corresponding inner and outer regions (i.e., distances from these worst class-1 and class-2 FUEs to their FBS are 15m and 30m, respectively). Moreover, we assume that MUEs will attempt to connect with a nearest FBS when they enter a circular area whose radius is 40m from the underlying FBS. To calculate the rate requirements for MUEs in (8), we also assume the worst case where MUEs are located on the oundary of this circular area. We calculate the long-term channel gains ased on the corresponding distance. We assume that the distance d ij from BS j to MUEs or FUEs associated with femtocell i can e approximated y the distance from BS j to FBS i. Also, the path-loss in db corresponding to d ijk is calculated as [15]: L(d ijk ) [ log 10 (h BS )] log 10 (d ijk ) log 10 (h BS ) + 23 log 10 (f c /5) + n ijk W ijk where h BS is the BS height, whh is chosen to e 25m and 10m for MBSs and FBSs, respectively (i.e., depending on whether BS j in this loss calculation corresponds to MBSs or FBSs); f c is the carrier frequency in GHz whh is set to 2 GHz. In addition, W ijk is the wall loss, and n ijk denotes the numer of walls. For communations from an FBS to its associated FUEs, we choose W ijk 5dB (i.e., indoor light walls) and n ijk 1; for communations from an FBS to an indoor FUE connected with a different FBS, we assume W ijk 12dB and n ijk 2; for other cases we assume W ijk 12dB and n ijk 1. The path loss in the linear scale corresponding to L(d ijk ) in db is 10 L(dijk)/10. Other system parameters are set as follows: FUEs and MUEs average serve time μ (f) i,c μ (m) i,c 1 ute, i, c; arrival rates for all FUEs and MUEs are chosen to e the same (i.e., λ (f) i,c λ (m) i,c, i, c); maximum power of an MBS PMBS max 80W; weighting factors in (29) are w (m) i,c w (f) i,c 1( i, c); standard deviation of shadowing σ 8dB; power scaling factor for Algorithm 1 δ 0.9;total numer of availale suchannels N 6; and parameter K in step 16 of Algorithm 1 is chosen as K 3. Moreover, the imum required rate for MUEs is R (m1) /W 6/s/Hz; the imum required rates for class-1 and class-2 FUEs are R (f1) /W 10/s/Hz and R(f2) /W 4/s/Hz, respectively. The target locking proailities used in Algorithm 1 are chosen as P (mc) P (fc) 0.05, c; targetsinrofmuesis γ 0 3dB; and target outage proaility for MUEs in (12) is Blocking proaility Class 1 FUE Class 2 FUE Class 1 MUE Arrival rate (users/) Fig. 4. Blocking proailities in femtocell 1 when all FBSs use their maximum allowed power. Blocking proaility Class 1 FUE Class 2 FUE Class 1 MUE Arrival rate (users/) Fig. 5. Blocking proailities in femtocell 2 when all FBSs use their maximum allowed power We assume that the noise power and interference power from MBSs except the closest MBS of femtocell i for SINR calculations in (1) and (2) are negligile compared to the interference powers from femtocells and the closest MBS. By using the techniques presented in Section III.C, the maximum allowale powers of each FBS for whh we can still maintain P (m) o 0.15 are FBS FBS 1.5mW for the hyrid and closed access strategies, respectively. Fig. 4 and Fig. 5 show the locking proailities achieved y the optimal admission control versus arrival rates in femtocells 1 and 2, respectively, as all FBSs use their maximum allowale transmission power under the hyrid access, whh is the target outage proaility of the MUEs P o (m) P max max 3.5mW and P 3.5mW to meet the target outage proaility P o (m) These figures confirm that the QoS requirements of FUEs in terms of locking proailities are always satisfied. As the network ecomes congested, locking proailities of FUEs reach the target values (i.e., P (fc) 0.05) while the locking proaility of MUEs increases slowly, and then it increases sharply efore the system ecomes unstale (i.e., it is not possile to support the target locking proailities of FUEs). In addition, the locking proaility of MUEs in Fig. 4 is much larger than that in Fig. 5 since users connecting equal to P max FBS

12 LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 191 Femtocell call throughput (users/) Hyrid access Closed access Arrival rate (users/) Fig. 6. Call throughput of femtocell 2 under the closed and proposed hyrid access strategies. Transmission power ratio β i Femto Femto 2 Femto 3 Femto Femto 8 Femto Iteration Fig. 8. Convergence of transmission power ratios under Algorithm 1. Call throughput (users/) Femto, R (f2) /W4 Macro, R (f2) /W4 Femto, R (f2) /W6 Macro, R (f2) /W Arrival rate (users/) Fig. 7. Call throughput of FUEs and MUEs in femtocell 2 under different imum rate constraints. with FBS 1 receive relatively stronger interference from the nearest MBS compared to users connecting with FBS 2. This confirms the results in Proposition 3. In Fig. 6, we plot the average call throughput achieved y all FUEs in femtocell 2 versus the arrival rate under the closed and proposed hyrid access strategies. This figure shows that the proposed hyrid access strategy achieves signifantly higher call throughput than that due to the closed access strategy when the arrival rate is high. This performance gain comes from the fact that the maximum allowale transmission power of FBSs under the hyrid access is consideraly larger than that under the closed access (P max 3.5mW and PFBS max FBS 1.5mW, respectively). Hence, even though FBSs must reserve some andwidth for connecting MUEs under the hyrid access, the overall throughput achieved y FUEs is still higher than that under the closed access. The proposed hyrid access is, therefore, the win-win strategy for users of oth network tiers. To demonstrate the impacts of imum rate requirements on the spectrum sharing etween users of oth tiers, we show the call throughputs achieved y FUEs and MUEs versus the arrival rate for femtocell 2 in Fig. 7 for R (f2) /W 4/s/Hz and R (f2) /W 6/s/Hz while rate requirements for other Fig. 9. Average call throughput (users/) Without power adaptation, N L 3 With power adaptation, N L 3 Without power adaptation, N L 6 With power adaptation, N L λ (users/) 0 Average throughput per femtocell with and without power adaptation. user classes are R (m1) /W 6/s/Hz and R(f1) /W 10 /s/hz. As is evident from this figure, while the call throughput achieved y FUEs remains almost the same, the call throughput of MUEs ecomes much smaller in the high arrival rate regime as R (f2) /W increases from 4 /s/hz to 6 /s/hz. This means the proposed hyrid access strategy enales MUEs to appropriately exploit the radio resources eyond what is needed to support the required QoSs of FUEs. We show the evolutions of the femtocell transmission power ratios β i for different femtocells under the synchronous power updates whh demonstrate the convergence of Algorithm 1 in Fig. 8. There are N L 6 lowly-loaded femtocells (femtocells 1 to 6) with λ (f) i,c λ (m) i,c 0.2 users/ and the arrival [ rates of the] remaining 3 highlyloaded femtocells are λ (f) 7,c,λ(f) 8,c,λ(f) 9,c [λ 0, 3λ 0, 4.5λ 0 ] where λ users/. To keep the figure readale, we only show the transmission power ratios for 6 femtocells. In Fig. 9, we illustrate the average call throughput per femtocell achieved y the optimal admission control scheme with and without the power adaptation algorithm (i.e., Algorithm 1) where the arrival rates of N L lowly-loaded femtocells (femtocells 1 to N L ) are fixed at λ (f) i,c λ (m) i,c 0.2 users/ and the arrival rates of the remaining highlyloaded femtocells are varied y using a parameter λ 0. Here, the arrival rates of highly-loaded femtocells are chosen as

13 192 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 Fig. 10. Power saving (%) λ 0 (users/) Power saving due to femtocell power adaptation. [ ] λ (f) 4,c,λ(f) 5,c,...,λ(f) 9,c [λ 0, 3λ 0, 4.5λ 0,λ 0, 3λ 0, 4.5λ 0 ] and [ ] λ (f) 4,c,λ(f) 5,c,λ(f) 6,c [λ 0, 3λ 0, 4.5λ 0 ] for N L 3, 6, respectively. This figure shows that the proposed power adaptation algorithm can indeed maintain the average throughput for different values of arrival rates in the highly-loaded femtocells. In fact, Algorithm 1 slightly increases the average throughput for some values of arrival rates. The increase of throughput in highly-loaded femtocells is offset y slight decrease of throughput in other lightly-loaded femtocells. Therefore, the average throughput per femtocell remains almost the same for different values of arrival rates. Finally, we present the power saving achieved y Algorithm 1 with the parameter λ 0 in Fig. 10 when the numers of lowly-loaded femtocells are N L 3 and 6. This figure confirms that signifant power saving can e achieved y the proposed power adaptation algorithm when λ 0 is small, whh are aout 50% and 60% for λ users/ and N L 3 and 6, respectively. Moreover, when the arrival rates of highlyloaded femtocells ecome larger, the power saving drops to aout 22% and 41% for N L 3andN L 6, respectively. In fact, the power saving for N L 6 is larger than that for N L 3 with high arrival rates ecause most of the power saving comes from the reduction in transmission powers of lightly-loaded femtocells. VI. CONCLUSION We have considered the cross-layer resource allocation and admission control prolem for OFDMA-ased femtocell networks. Specifally, we have developed a unified model that captures co-tier and cross-tier interference as well as rate and locking proaility requirements for users of oth tiers. Moreover, we have presented a novel distriuted power adaptation algorithm, whh has een proved to converge to the NE of the corresponding power adaptation game. Via numeral studies, we have demonstrated the desirale performance of the optimal admission control scheme in maintaining the QoS requirements for FUEs and optimally using the spectrum resources. Finally, it has een confirmed that a signifant power saving can e achieved y the proposed joint admission control and power adaptation algorithm. N L 3 N L 6 APPENDIX A SMDP-BASED ADMISSION CONTROL Given the system and action state spaces descried in Section III.C, we are partularly interested in the admissile action space A x for a given system state x. In fact, A x comprises all possile actions that do not result in transition into a state that is not allowed (i.e., not in allowale state space X in (16)). In addition, if x 0, then it is required that action a 0is excluded from A x to prevent the system to e trapped in the zero state forever. Let e (f) (e (m) ) e a vector of dimension C 1 + C 2, whh is of the same size as that of the general state vector x(t) having all zeros except the one at the same position of x (f) (x (m) ) in (15). Then, we can write A x as follows: { A x a A : a (f) 0if x + e (f) / X; } a (m) 0if x + e (m) / X; and a 0if x 0. (26) We now analyze the dynams of this SMDP, whh is characterized y the state transition proailities of the Markov chain otained y emedding the system at arrival and departure instants. Specifally, we will detere transition proaility p xy (a) from state x to state y when action a is taken. Toward this end, let τ x (a) denote the expected time until the next decision epoch after action a is taken at system state x. Then, τ x (a) can e calculated as the inverse of the cumulative arrival and departure rate with locked arrivals taken into account. In partular, τ x (a) can e calculated as follows [16], [33]: τ x (a) [ C1 C 1 C 2 λ (f) a(f) + μ (f) u(f) + C 2 + λ (m) a (m) μ (m) u (m) ] 1 (27) for a A x. We are now ready to calculate transition proaility p xy (a) of the underlying emedded Markov chain. This can e done y noting that the proaility of a certain event (e.g., connection arrival and departure) is equal to the ratio etween the rate of that event and the total cumulative event rate 1/τ x (a). Therefore, the transition proaility p xy (a) can e detered as follows: p xy (a) λ (f) a(f) τ x(a), if y x + e (f) λ (m) a (m) τ x (a), if y x + e (m) μ (f) u(f) τ x(a), if y x e (f) μ (m) u (m) τ x (a), if y x e (m) 0, otherwise (28) where for simplity we omit user index i in oth τ x (a) and p xy (a). In the following, we formulate the optimal admission control prolem using the aove description of the underlying SMDP. We formulate the admission control prolem y defining a cost function as the weighted sum of locking proailities. In partular, we are interested in imizing the following

14 LE et al.: QOS-AWARE AND ENERGY-EFFICIENT RESOURCE MANAGEMENT IN OFDMA FEMTOCELLS 193 cost function: z xa 0 C 1 w (f) C 2 + w (m) (1 a (f) i,c )z xaτ x (a) x X a A x (1 a (m) )z xa τ x (a) (29) x X a A x where z xa denotes the rate of choosing action a in state x; w (m) > 0 and w (f) > 0 are weighting factors controlling the desired performance tradeoff. In this cost function, B (f) x X a A x (1 a (f) )z xaτ x (a) and B (m) x X a A x (1 a (m) )z xa τ x (a) express the locking proailities of class-c FUEs and MUEs, respectively, where z xa τ x (a) represents the proaility that action a is taken for a given system state x. In addition, we impose locking proaility constraints for FUEs as follows: B (f) (1 a (f) (fc) )zxaτx(a) P, 1 c C 1. (30) x X a A x Moreover, we impose other standard constraints for an MDP as follows [33]: z ya p xy (a)z x,a 0, y X (31) a A y x X a A x z xa τ x (a) 1 (32) x X a A x whh descrie the alance equation and the normalization condition, respectively [33]. The optimal admission control poly can e otained as follows. We calculate optimal zxa y solving the linear program (29)-(32). Then, we can detere an optimal randomized admission control poly as follows: for each system state x the proaility of choosing action a A x can e calculated as θ x (a) zxa τ x(a)/ a z xa τ x(a). These proailities can e calculated offline and applied for online admission control for different system states. In the aove model, we do not impose locking proaility constraints for MUEs. However, these additional constraints can e easily added to the model. Specifally, if P (mc) is the maximum tolerale locking proaility for class-c MUEs, then additional locking proaility constraints can e written as B (m) (1 a (m) )z xa τ x (a) P (mc), x X a A x 1 c C 2. (33) Then, we can calculate optimal z xa y solving the linear program (29)-(32), (33), and find the optimal admission solution accordingly. This calculation is indeed used in Algorithm 1. REFERENCES [1] G. 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15 194 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 1, JANUARY 2013 IEEE Trans. Wireless Commun., vol. 10, no. 12, pp , Dec [28] W. C. Chung, T. Q. S. Quek, and M. Kountouris, Throughput optimization, spectrum allocation, and access control in two-tier femtocell networks, IEEE J. Sel. Areas Commun., vol. 30, no. 3, pp , Apr [29] Z. Q. Luo and S. Zhang, Dynam spectrum management: complexity and duality, IEEE J. Sel. Tops Signal Process., vol. 2, no. 1, pp , Fe [30] 3GPP TR V0.0.9, Overview of 3GPP Release 11, Jan Availale: [31] Z. Niu, TANGO: traff-aware network planning and green operation, IEEE Wireless Commun., vol. 18, no. 5, pp , [32] G. L. Stuer, Principles of Moile Communation. Kluwer Academ, [33] M. Puterman, Markov Decision Processes: Discrete Stochast Dynam Programg. Wiley, Long Bao Le (S 04-M 07-SM 12) received the B.Eng. (with Highest Distinction) degree from Ho Chi Minh City University of Technology, Vietnam, in 1999, the M.Eng. degree from Asian Institute of Technology, Pathumthani, Thailand, in 2002, and the Ph.D. degree from the University of Manitoa, Winnipeg, MB, Canada, in From 2008 to 2010, he was a postdoctoral research associate with Massachusetts Institute of Technology, Camridge, MA. Since 2010, he has een an assistant professor with the Institut National de la Recherche Scientifique (INRS), Université du Quéec, Montreal, QC, Canada, where he leads a research group working on cognitive radio and dynam spectrum sharing, radio resource management, network control and optimization. Dr. Le is a memer of the editorial oard of IEEE COMMUNICATIONS SURVEYS AND TUTORIALS and IEEE WIRELESS COMMUNICATIONS LET- TERS. He has served as technal program committee co-chairs of the Wireless Networks track at IEEE VTC2011-Fall and the Cognitive Radio and Spectrum Management track at IEEE PIMRC2011. He is a Senior Memer of the IEEE. Dusit Niyato (M 09) received the BE degree from King Mongkuts Institute of Technology Ladkraang (KMITL), Bangkok, Thailand in 1999, and the PhD degree in electral and computer engineering from the University of Manitoa, Canada, in He is currently an assistant professor in the School of Computer Engineering at the Nanyang Technologal University, Singapore. His research interests are in the area of radio resource management in cognitive radio networks and roadand wireless access networks. He is a memer of the IEEE. Ekram Hossain (S 98-M 01-SM 06) is a Full Professor in the Department of Electral and Computer Engineering at University of Manitoa, Winnipeg, Canada. He received his Ph.D. in Electral Engineering from University of Vtoria, Canada, in Dr. Hossain s current research interests include design, analysis, and optimization of wireless/moile communations networks, cognitive radio systems, and network economs. He has authored/edited several ooks in these areas ( ekram). Dr. Hossain serves as the Editor-in-Chief for the IEEE COMMUNICATIONS SURVEYS AND TUTORIALS (for the term ) and an Editor for IEEE Wireless Communations. Previously, he served as the Area Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS in the area of Resource Management and Multiple Access from and an Editor for the IEEE TRANSACTIONS ON MOBILE COMPUTING from Dr. Hossain has won several research awards including the University of Manitoa Merit Award in 2010 (for Research and Scholarly Activities), the 2011 IEEE Communations Society Fred Ellersk Prize Paper Award, and the IEEE Wireless Communations and Networking Conference 2012 (WCNC 12) Best Paper Award. He is a registered Professional Engineer in the province of Manitoa, Canada. Dong In Kim (S 89-M 91-SM 02) received the Ph.D. degree in electral engineering from the University of Southern California, Los Angeles, in He was a tenured Professor with the School of Engineering Science, Simon Fraser University, Burnay, BC, Canada. Since 2007, he has een with Sungkyunkwan University (SKKU), Suwon, Korea, where he is currently a Professor with the School of Information and Communation Engineering. His research interests include wireless cellular, relay networks, and cross-layer design. Dr. Kim has served as an Editor and a Founding Area Editor of Cross- Layer Design and Optimization for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS from 2002 to From 2008 to 2011, he served as the Co-Editor-in-Chief for the Journal of Communations and Networks. He is currently an Editor of Spread Spectrum Transmission and Access for the IEEE TRANSACTIONS ON COMMUNICATIONS and the Founding Editor-in- Chief for the IEEE WIRELESS COMMUNICATIONS LETTERS. Dinh Thai Hoang received his Bachelor degree in Electrons and Telecommunations from Hanoi University of Technology (HUT), Vietnam in From 2010 to 2012 he worked as a research assistant at Nanyang Technologal University (NTU), Singapore. He has received the NTU research scholarship and he is currently working toward his Ph.D. degree in School of Computer Engineering, NTU under Professor Dusit Niyato s supervision. His research interests include cooperative networked systems, and resource allocation for wired and wireless networks.