Autonomous Opportunistic Spectrum Access in Distributed Femtocell Networks

Transcription

1 Autnmus Opprtunistic Spectrum Access in Distributed Femtcell Netwrks Ahmed Khattab, Khaled Elsayed Electrnics and Electrical Cmmunicatins Department, Cair University, Giza, Egypt 1 Abstract Femtcells randmly deplyed in a given macrcell cverage area share the wireless spectrum available t the macrcell. The unplanned and ad hc nature f the femtcell deplyment in the macrcell envirnment renders centralized frequency planning inapplicable. Furthermre, the femtcells are unable t apriri knw neither the channel assignment f their neighburs nr the impact f their transmissins n nearby macrcell users due t the lack f explicit crdinatin. In this paper, we present the distributed Autnmus Opprtunistic Channel Access (AOCA) framewrk that allws the femtcells t share the available spectrum with the verlaying macrcell withut any kind f crdinatin neither between the macrcell and femtcells nr amngst the femtcells. Furthermre, it prvides statistical guarantees n the perfrmance f the macrcell users. We frmulate the AOCA cnstrained spectrum access prblem as nn-linear prgram t find its ptimized parameters settings. Simulatin results shw that AOCA achieves multiple flds imprvement in the average femtcell netwrk rate due t its prbabilistic and nn-greedy access that enables multiple neighburing femtcells t simultaneusly use a given channel. Index Terms femtcell netwrks; pprtunistic spectrum access; spectrum sharing I. INTRODUCTION Femtcells als called hme base statins have recently emerged as a cst-effective slutin t imprve the indrs cverage and capacity f cellular netwrks. Typically, femtcells are deplyed and managed by custmers at hmes r in their ffices. Therefre, the deplyment f femtcells in a pre-existing cellular netwrk envirnment is uncntrllable and results in an unplanned ad hc femtcell netwrk that shares the wireless spectrum with the macrcell netwrk [1], [2]. Unfrtunately, having a dedicated spectrum fr the femtcell netwrk t eliminate the interference between the macrcell and femtcell netwrks (e.g., see [3] [6]) is typically nt feasible due t (1) the scarcity f the wireless spectrum, and (2) the lack f crdinatin between the macrcell and femtcells and between the femtcells themselves [1], [2]. Hence, it is mre favrable t perate the macrcell and femtcell netwrks in a shared-spectrum manner frm either an infrastructure, cst r spectrum availability perspectives [7]. Several appraches have recently emerged t address spectrum sharing in such a tw-tier femtcell netwrks given that centralized netwrk planning is increasingly less viable. A great This wrk is part f the 4G++ prject supprted by the Natinal Telecm Regulatry Authrity f Egypt.

2 2 deal f the literature fcuses n the design f pwer cntrl and interference mitigatin strategies [8] [10]. Cperative [11] and nn-cperative [7], [12], [13] gaming techniques have als been widely used t address the spectrum-sharing prblem. Hwever, such games require message exchange and crdinatin between the femtcells, fr instance fr interference price bargaining, which further deterirates the attainable femtcell netwrk thrughput. In cntrast, ur gal is t allw the femtcell netwrk t share the macrcell spectrum by having the individual femtcells lcally chsing their transmissin bands and strategies withut explicit crdinatin. The paper cntributins are: First, we present the Autnmus Opprtunistic Channel Access (AOCA) framewrk that allws the femtcell netwrk t share the macrcell spectrum while prviding statistical guarantees n the perfrmance f the macrcell users. The prpsed framewrk tackles the infeasibility f frequency planning and the lack f explicit spectrum allcatin crdinatin in such a netwrk by (1) having the individual femtcells randmly chsing their channels, (2) preventing a single femtcell frm exclusively using all f the capacity f the randmly-selected channel, and (3) having the femtcells individually adapt their transmissin pwers and channel selectins t maximize the average femtcell netwrk rate while satisfying the macrcell perfrmance requirements. Secnd, we analytically frmulate the resurce (spectrum and pwer) allcatin prblem accrding t the prpsed AOCA apprach as a nn-linear prgram in rder t derive the ptimal values f its parameters. The slutin f such a prgram prvides majr insights n the effects f different system parameters, such as the macrcell user density and femtcell netwrk density, the macrcell user perfrmance requirements, and the number/frequency f the macrcell frequency bands, n the perfrmance f the prpsed framewrk. Finally, we use simulatin results t shw that the AOCA apprach results in multiple flds imprvement in the average femtcell rate cmpared t crdinated frequency planning. Such a significant perfrmance gain is attributed t the prbabilistic and nn-greedy access mechanism f the prpsed apprach that (1) allws the femtcells t explit the spectral pprtunities that are typically unexplited by the deterministic crdinated frequency planning (which limits each femtcell t use a single channel), and (2) allws multiple neighburing femtcells t simultaneusly use a given channel withut explicit crdinatin, which increases the femtcell netwrk-wide gdput perfrmance. As the lad/denisty f bth netwrks apprach the spectrum saturatin level, centralized frequency planning achieves higher rates cmpared t ur apprach. Hwever, such centralized frequency planning is typically infeasible given the uncntrlled and ad hc nature f femtcell deplyment. The remainder f the paper is rganized as fllws. We define the system mdel and frmulate the pprtunistic spectrum access prblem in Sectin II. The prpsed AOCA apprach is presented in Sectin III. Then we analytically ptimize its parameters and evaluate its perfrmance in Sectin IV and Sectin V, respectively. We cnclude in Sectin VI. II. SYSTEM MODEL AND PROBLEM FORMULATION We cnsider the dwnlink f a tw-tier netwrk that cnsists f a single macrcell that serves a circular area f radius R, within which N femtcells are randmly deplyed by hme and ffice users. The macrcell prvides cellular access t M randmly lcated macrcell users (MUs). The randm distributin f bth the MUs and the femtcells within the macrcell service area are mdeled by hmgeneus spatial Pissn pint prcesses [1] with densities ρ MU and ρ F,

3 3 Fig. 1. Interference scenari in tw-tier femtcell netwrks. respectively. The femtcells share the macrcell spectrum that is divided int S nn-verlapping channels (e.g., a channel can refer a cmpnent carrier r a resurce blck in LTE systems). We mdel the macrcell transmissin activities carried ver each channel as an ON/OFF surce. We define the activity factr f the i th channel, a (i) M, as the fractin f time channel i is carrying MU traffic. A femtcell can access ne channel at any given time t serve its assciated femtcell user (FU). We assume a single FU per femtcell. Such an assumptin is cmmn in the literature due t the pprtunistic scheduling peratin in practice (which dedicates a channel t the user with the best respnse) and des nt vilate the generality f the mdel [8]. We als mdel the femtcell activity as an ON/OFF surce with activity factr a F. Withut lss f generality, we assume the activity factr f femtcells a F is fixed thrughut the netwrk regardless the used frequency. We d nt assume any kind f infrmatin exchange whatsever between the femtcells and the macrcell nr between femtcells amngst each ther. A. Interference Mdel Fr a given macrcell service area, we assume that the interference frm neighburing macrcells is negligible due t either explicit frequency planning r the use f inter-cell interference crdinatin (ICIC) schemes. Hence, the interference scenaris in the system at hand are limited t the fllwing scenaris depicted in Figure 1: Macrcell-t-femtcell interference: The received interference pwer frm the macrcell base statin at an FU perating ver channel i is ( ) α P (i) M F = P (i) d M γ (i), d d (i) d (i) (1) where d is the distance between the macrcell and the FU, d (i) is the clse in distance that is in the rder f the perating wavelength (i.e., few centimeters), α is the path lss expnent f the envirnment, P (i) M = P (i) M G(i) t G (i) r λ 2 i is the received pwer at the clse in distance d (i) (4πd (i) ) 2 where P (i) M is the macrcell transmissin pwer, G(i) t and G (i) r are the transmit and receive antenna gains, respectively, and λ i is the channel wavelength. Fr the assumed Rayleigh fading mdel, the nrmalized pwer gain f the fading prcess γ (i) is expnentially distributed.

4 4 Femtcell-t-femtcell and femtcell-t-macrcell interference: These tw interference scenaris represent the cumulative interference frm all f the femtcells using channel i at a certain FU and MU, respectively. The tw interference scenaris have the same mdel as they are riginated by the same surce: the femtcell netwrk. Hwever, they represent the interference at different types f users. Fr a tagged nde, either a FU r a MU, the cumulative received interference pwer frm all the interfering femtcells, P (i) int randm variables P (i) l, i.e., where P (i) l, is the sum f the L i.i.d. P (i) int = P (i) 1 + P (i) P (i) L (2) is the received interference frm the l th femtcell cmputed similar t (1) with P (i) = P (i) F G (i) G (i) λ 2 l i is replaced by P (i) t r F (4πd (i) F l is the l th femtcell transmissin pwer, and L is a randm variable that dentes the number f interfering femtcells. Nte that the randm variable ) 2 as P (i) L is independent f the randm variables P (i) l. In a highly dense femtcell netwrk, the femtcell distributin is mdeled as a hmgeneus Pissn prcess [1]. Hence, the prbability f having l interfering femtcells in a circle f radius R int and area πrint 2 is given by P rb[l = l] = e ρ F πrint 2 (ρf πrint) 2 l, l = 0, 1, 2,... (3) l! where R int is the cverage radius f the femtcell which is the distance beynd which the femtcell interference is negligible, i.e., belw the receiver sensitivity f the FU and MU units. The distributin f the distance between the FU r MU lcated at the center f a circular area f radius R int and the randmly lcated interferers within is given by [14] f D (d l ) = 2d l, d Rint 2 l R int (4) Using the law f ttal prbability, the prbability distributin functin f P (i) int can be calculated as fllws: P rb[p (i) int ] = l=0 P rb[p (i) int \L = l]p rb[l = 1] (5) The cnditinal distributin f P (i) int is difficult t btain in clsed frm. Hwever, we use the analytical apprach presented in [15] in which we first cmpute the characteristic functin f the cnditinal distributin f P (i) int then reverse it t cmpute the uncnditinal distributin f P (i) int. We mit the detailed prf due t space limitatins. Accrdingly, we can apprximate the distributin f the femtcell-t-femtcell and the femtcell-t-macrcell interference with lgnrmal distributins. We cmpute the mean and variance f such lgnrmal distributins as: and E[P (i) int ] = 2πa F ρ F P (i) F d (i)2 2πa F ρ F P (i) F d(i)2 α 2 V ar[p (i) int ] = πa F ρ F α 1 [ 2P (i) e πa F ρ F d (i) 2 e πa F ρ F d (i) 2 F d (i)2 e πa F ρ F d (i) 2 ln R int, α = 2 d (i), α > 2 M (6) ] 2, α 2 (7) respectively. Nte that the abve distributin f P (i) int describes the ttal interference at any given FU r MU. We shall use the abve interference mdel shwn in Figure 1 in ur pprtunistic spectrum access prblem frmulatin.

5 5 B. Opprtunistic Spectrum Access Prblem Frmulatin In this paper, we cnsider the pprtunistic spectrum access prblem that aims at maximizing the average rate f the femtcell netwrk while prviding statistical guarantees n the perfrmance f the macrcell users. In ur statistical mdel, we prbabilistically guarantee an upper bund n the femtcell interference at the macrcell users. Let Pint max and β define the maximum permissible interference that can be tlerated frm the femtcell netwrk and the maximum allwed utage prbability at the MUs, respectively. Let r n (i) dente the rate achieved by the n th FU ver channel i defined as: r (i) n = a F W (i) eff lg 2(1 + SINR (i) n ) (8) where SINR n (i) is the signal t interference plus nise rati experienced by n th FU ver channel i, and W (i) eff is the ith channel effective bandwidth equals t ηw (i), where W (i) is the bandwidth f channel i and η mdels the bandwidth efficiency f the used mdulatin and cding scheme. Typical values f η in LTE systems lie between 0.5 and 0.7 [16]. The generic cnstrained pprtunistic channel access prblem can be frmulated as fllws: maximize subject t 1 1 N S N S n=1 i=1 r (i) n, n = 1, 2,..., N P rb[p (i) int P max int ] β, i = 1, 2,..., S P min P (i) P max where P (i) is the maximum transmissin pwer f the n th femtcell, P min and P max are the lwer and upper bunds f the femtcell transmissin pwer, respectively. The lwer bund P min > 0 is t guarantee a minimum rate per femtcell in the wrst case. We next intrduce ur prpsed autnmus pprtunistic channel access apprach then refrmulate this generic prblem accrdingly t ptimize its perfrmance. (9) III. AUTONOMOUS OPPORTUNISTIC SPECTRUM ACCESS IN FEMTOCELL NETWORKS We prpse the Autnmus Opprtunistic Channel Access (AOCA) apprach that allws the femtcells t access the macrcell channels while statistically guaranteeing an upper bund n the perfrmance f the macrcell users. The main distinguishing feature f the prpsed AOCA apprach is that it des neither rely n any kind f explicit crdinatin amngst the femtcells each ther nr with the macrcell base statin. The prpsed OOSA framewrk has tw main cmpnents: (1) a randmized channel selectin cmpnent that addresses the inability t explicitly crdinate the individual channel selectins f the femtcells, cmbined with (2) a nn-greedy channel access mechanism which prbabilistically enables the femtcells t share the available wireless capacity in a distributed manner withut explicit crdinatin. A. Randmized Channel Selectin As we explained earlier, the randmly deplyed femtcells are unable t apriri knw the channel assignment f their neighburs due t the lack f explicit crdinatin. T cunter such limitatins, we prpse the fllwing randm channel selectin apprach. A femtcell randmly selects a channel t use frm the pl f available channels (if there des nt exist a preferred

6 6 channel that recently carried ut successful transmissins). Due t the inability f a femtcell t neither accurately assess the impact f its transmissin n nearby n-ging MUs nr knw the channel utilizatin prfile f the surrunding femtcells and MUs, a femtcell chses any channel with equal prbability. Hence, we use randmizatin t spread multiple femtcells ver different channels and alleviate the need fr explicit inter-femtcell crdinatin. Hwever, such a randmized channel selectin neither ensures the fair sharing f the available capacity between different femtcells nr guarantees certain levels f macrcell users perfrmance. In rder t achieve these gals, we present the fllwing prbabilistic transmissin scheme that cmplements such randmized channel selectin. B. Adaptive Prbabilistic Transmissin Recall that a femtcell des nt knw whether r nt its transmissin will interfere with any nearby n-ging MU receptins nr if ther nearby femtcells have als selected the same channel. We prpse the fllwing prbabilistic channel access mechanism which is cnservative and nn-greedy in expliting the randmly selected channel, and hence, it prbabilistically reduces MU utages due t miss inferring the existence f nearby MUs. Furthermre, such a prbabilistic apprach allws multiple femtcells t simultaneusly explit a given spectral pprtunity since it allws the femtcell t transmit at the maximum pwer level that can be used, P (i), nly with a certain prbability p. Hence, the AOCA apprach prbabilistically leaves a capacity margin that can be utilized by ther femtcells in the system that happened t simultaneusly select the same channel. On the ther hand, the AOCA apprach will have the femtcell using a lwer pwer between P min and ζp (i), where 0 < ζ < 1, with prbability (1 p). While ptentially degrading the femtcell rate, the use f lw pwer transmissin further reduces the prbability f intercepting unidentified macrcell transmissins. In additin, it allws multiple neighburing femtcells t simultaneusly use a given channel t increase the aggregate femtcell netwrk rate. Recall that a lwer transmissin pwer implies a lwer transmissin rate realized via a lw rder mdulatin scheme which is mre rbust t interference that cannt be explicitly nulled ut [17]. The AOCA prtcl realizatin starts frm the minimum transmissin pwer level, P min, and will is reached r a transmissin failure ccurs. Such a gradual reductin f the unutilized capacity margin is t nt sacrifice the average femtcell rate if there des nt exist any nearby MUs n the randmly-selected channel. Meanwhile, if a nearby femtcell uses the same channel, it will cause the high rate transmissin t fail. As lng as the high pwer transmissins are successful n the randmly-selected channel, the femtcell declares a channel as its favurite channel. Otherwise, the femtcell will randmly chse a new channel. Algrithm I utlines the AOCA apprach. increase the pwer used with prbability (1 p) until either ζp (i) IV. ANALYTICAL PERFORMANCE OPTIMIZATION In this sectin, we analyze the prpsed AOCA apprach in rder t derive its ptimal parameter values. Mre specifically, we refrmulate the generic cnstrained pprtunistic channel access prblem given in (9) t find the values f the prbability f high pwer transmissin p, the lw pwer margin ζ, and the maximum femtcell transmissin pwers ver different frequency channels P (1), P (2),..., P (S) that maximize the average femtcell netwrk rate while prviding statistical guarantees n the perfrmance f the macrcell users.

7 7 Algrithm 1 AOCA Pseudcde 1: if FavuriteChannel == Null then 1 Femtcell randmly selects channel i with prb. S 2: else Use FavuriteChannel 3: end if 4: Set transmissin pwer t: Maximum pwer P (i) with prb. p Lw pwer [P min, ζp (i) ] with prb. 1 p 5: Transmit data 6: if Data transmissin succeeds then FavuriteChannel = channel i Increase the lwer pwer up t ζp (i) G t 4: 7: else FavuriteChannel = Null G t 1: 8: end if A. Average Femtcell Rate Accrding t the AOCA apprach, the femtcell uses the highest pssible rate (btained when the femtcell is transmitting at the highest pwer P (i) ) with prbability p and a variable lwer rate with prbability (1 p). Cnsequently, the FU rate when using channel i can be expressed as where SINR n (i) be expressed as r (i) n = a F W (i) eff [ p lg 2 (1 + SINR (i) n ) +(1 p) lg 2 (1 + ζsinr (i) n ) ] (10) is the received signal t interference plus nise rati f the femtcell that can SINR (i) n = W (i) N + a (i) M P (i) ( ) α P (i) d F γ (i) d (i) ( d M M d (i) ) α γ (i) + P (i) int where d F and d M are the distances between the tagged FU and the femtcell and macrcell base statins, respectively, and N is the pwer spectral density f the white Gaussian nise. Nte that we d nt incrprate the ramp up frm the minimum pssible rate t the rate btained at in ur frmulatin. While such an assumptin slightly impacts the FU achievable rate, it des nt affect ur ptimizatin prblem as the maximum interference cnstraints depend nly n the maximum used pwer, P (i), and ζ. the steady state pwer ζp (i) (11)

8 8 B. Macrcell Statistical Perfrmance Guarantees Since we have apprximated P (i) (i) int with a lgnrmal distributin, the prbability that P int des nt exceed a certain margin Pint max is given by P rb[p (i) int P int max ] = 1 ( ) ln P max 2 erfc int µ (12) 2σ 2 where and ( ( ) µ = ln E[P (i) int ] 1 (i) 2 ln V ar[p int 1 + ] = ln 2πa F ρ F P (i) F l d (i)2 α 2 1 ( ) 2 ln (α 2)2 1 + (α 1)πa F ρ F ( ) (i) σ 2 V ar[p int = ln 1 + ] E[P (i) int ]2 = ln (1 + E[P (i) int ]2 e πa F ρ F d (i)2 (α 2)2 ) (α 1)πa F ρ F Nte that while µ depends lgarithmically n the femtcell maximum transmissin pwer thrugh P (i) F, σ2 l is independent f the value f the femtcell transmissin pwer. Hence, the cnstraint that P rb[p (i) int P int max ] β can be frmulated in terms f the femtcell transmissin pwer as P (i) < 2ln P max int + σ2 2 2σ 2 erfc 1 (2β) 2πa F ρ F d (i)2 e α 2 πa F ρ F d (i)2 (4πd (i) ) 2 G (i) t G (i) r λ 2 i Subsisting in (9), the AOCA cnstrained pprtunistic spectrum access prblem can be stated as ) (13) (14) (15) maximize 1 1 N S N S n=1 i=1 r (i) n, n = 1, 2,..., N subject t P min < ζ < 1, P max 0 p 1 P min P (i) P (i) P max i = 1, 2,..., S < 2ln P max int + σ2 2 2σ 2 erfc 1 (2β) 2πa F ρ F d (i)2 e α 2 πa F ρ F d (i)2 (4πd (i) ) 2 G (i) t G (i) r λ 2 i Slving this nn-linear ptimizatin prblem ff-line fr a given system parameters, we btain the AOCA p and ζ values alngside the maximum pwers P (1), P (2),..., P (S) t be used by the different femtcells in rder t maximize the average femtcell netwrk rate while prviding a statistical guarantee β n the interference caused at the MUs, Pint max. (16)

9 9 TABLE I SIMULATION PARAMETERS Parameter Value Path lss expnent (α) 4 Number f channels (S) 4 Channel bandwidth 10 MHz AWGN pwer density (N ) -160 dbm/hz Maximum allwed interference Pint max -67 dbm Statistical MU utage guarantee (β) 1 % Transmit and receive antenna gains (G t, G r ) 0 db Macrcell radius 500 m Macrcell pwer 20 W Femtcell radius 20 m Maximum femtcell pwer (P max ) 20 mw Minimum femtcell pwer (P min ) 1.8 mw Femtcell bandwidth efficiency (η) 0.5 m V. PERFORMANCE EVALUATION Here, we evaluate the perfrmance f the prpsed AOCA apprach via MATLAB simulatins. We cnsider a single macrcell with a 500 meters cverage radius with 4 frequency channels, each f bandwidth 10 MHz. The MUs and femtcells are distributed within the macrcell cverage area accrding t hmgeneus spatial Pissn pint prcesses. While the MU densities per channel are simulatin variables, we set the femtcell density t its maximum value f 625 femtcells/km 2 fr a 20 meters femtcell cverage radius. We cnsider tight MU statistical guarantees: Pint max = 67 dbm and β = 1%. The simulatins parameters are listed in Table I. Our perfrmance benchmark is a crdinated channel access apprach that explits centralized frequency planning t eliminate the femtcell-t-femtcell interference based n the availability f the glbal netwrk-wide infrmatin. Given the crdinated channel allcatin f such a frequency plan, we slve the generic cnstrained femtcell perfrmance ptimizatin prblem given in (9) t cmpute the maximum femtcell transmissin pwers satisfying the MU perfrmance requirement. Such a benchmark represents the upper bund f the perfrmance f the wide set f existing schemes that assume explicit crdinatin within femtcell netwrk (e.g., explicit interference crdinatin schemes) and/r crdinatin with the macrcell. We cmpare the perfrmance f ur prpsed autnmus prbabilistic apprach (which allws a femtcell t pprtunistically explit the entire macrcell spectrum) against such a crdinated deterministic apprach (which allcates a single channel per femtcell) in rder t demnstrate the AOCA perfrmance gains despite the absence f any kind f crdinatin in such a tw-tier netwrk. A. Impact f Macrcell users and Femtcell densities In this sectin, we study the impact f the macrcell (assuming equal activity factr fr all MUs) and femtcell densities/lads n the AOCA perfrmance. At lw MU densities, the average femtcell rate linearly increases with the femtcell activity as the case with crdinated access due t the absence f significant femtcell interference. Hwever, the AOCA average femtcell rate is multiple flds f the benchmark rate (e.g., Figure 2 shws up t 310% gain). Such a gain dubles when the femtcell density decreases. Recall that, these results are fr the maximum femtcell density.

10 10 Average Femtcell Rate [Mbps] MU/km MU/km MU/km MU/km 2 Crdinated Femtcell Activity Factr Maximum Transmit Pwer [mw] Prpsed (90% MU Actv.) Crd. (90% MU Actv.) Prpsed (50% MU Actv.) Crd. (50% MU Actv.) Prpsed (10% MU Actv.) Crd. (10% MU Actv.) Maximum Interference Bund [dbm] Fig. 2. Average femtcell rate increases with the femtcell activity factrs fr different per channel MU densities. Fig. 3. AOCA prbabilistic access mechanism allws the femtcell t use higher pwer cmpared t the crdinated access apprach. Femtcell Rate Gain [%] Femtcell Activity Factr [%] 700 MHz 1.8 GHz 2.1 GHz 3 GHz Fig. 4. AOCA gain increases with the perating frequency f the band t which all 4 channels belng t fr 300 MU/km 2 and 90% MU activity. Maximum Transmit Pwer [mw] Channel 1 (700 MHz) Channel 2 (1.8 GHz) Channel 3 (2.1 GHz) Channel 4 (3 GHz) Femtcell Activity Factr [%] Fig. 5. The AOCA apprach allcates mre pwer t channels with higher frequency when the channels belng t different frequency bands. As the MU density increases, the AOCA gain decreases. Furthermre, the average AOCA femtcell rate tends t saturate with the increase f the femtcell activity. Such a decrement in the average AOCA rate with the increase f either the femtcell activity r the macrcell density is attributed t the reductin in the AOCA transmissin parameters p and ζ as well as the femtcell transmissin pwers satisfying the MU perfrmance cnstraint. Hence, crdinated access utperfrms the prpsed scheme when the system if fully laded. Hwever, crdinated frequency planning is based upn unrealistic system assumptins unlike the AOCA apprach that des nt assume cperatin neither between the femtcells each ther nr with the macrcell. Next, we vary the activity f the MUs. While the AOCA gain exhibits similar trends fr varius MU activity patterns, the gain increases with the increase in the MU activities - despite the reductin in the average femtcell rate.

11 11 B. Impact f Macrcell Perfrmance Cnstraints We evaluate the impact f the MU perfrmance cnstraints ver the AOCA parameters. Namely, we study hw the maximum allwed interference limit, Pint max, and the statistical utage cnstraint, β, affect the ptimal AOCA parameter values. The maximum femtcell transmissin pwer accrding t bth AOCA and the crdinated frequency planning increases with the relaxatin f the MU cnstraints (i.e., higher Pint max r β values). Hwever, the AOCA apprach allws the femtcells t use higher pwer cmpared t the crdinated access apprach as shwn in Figure 3. This is attributed t the AOCA prbabilistic transmissin mechanism that allws the femtcell t use the maximum pwer nly with prbability p. C. Impact f Operating Frequency Finally, we assess the impact f the perating frequency. We study the cases in which (1) all the channels belng t the same LTE band and vary the band frequency, and (2) each f the S channels belngs t a different band. We cnsider the 700 MHz, 1.8 GHz, 2.1 GHz, and the 3 GHz LTE bands. In bth cases, the AOCA gain increases with the perating frequency regardless f the MU density r activity pattern (e.g., see Figure 4). Such a behavir is attributed t the better prpagatin characteristics f lwer frequencies that extends the transmissin range fr a given transmissin pwer. Cnsequently, the number f the femtcells that can simultaneusly share a spectrum due t AOCA decreases with the decrease f the perating frequency, and hence, the AOCA gain decreases due t the reductin in the values p and ζ as well as the maximum femtcell pwers btained by slving (16). Figure 5 depicts the maximum pwer allcated t different channels in the latter case in which each channel belngs t a different band. While we nly present the results fr S equals t 4, similar perfrmance trends were btained fr different S [1, 5]. The nly impact f the increase in S is an increase f the AOCA gain. VI. CONCLUSIONS In this paper, we have presented the autnmus pprtunistic channel access framewrk. The framewrk allws the randmly deplyed femtcell netwrk t share the channels available t the verlaying macrcell netwrk withut any kind f crdinatin between neither the femtcells amngst each ther nr with the macrcell base statin. The prpsed AOCA apprach adpts prbabilistic channel access mechanism that allws the femtcells t explit the spectral pprtunities in a way that maximizes the average femtcell rate while prviding statistical guarantees n the perfrmance experienced at the macrcell users. Simulatin results have shwn that the prpsed apprach achieves multi-fld imprvement in the average femtcell rate gain when the macrcell ffered lad des nt saturate the capacity f the available channels. REFERENCES [1] V. Chandrasekhar, J. G. Andrews, and A. Gatherer, Femtcell netwrks: a survey, IEEE Cmmunicatins Mag., vl. 46, pp , Sep [2] H. Claussen, Perfrmance f macr- and c-channel femtcells in a hierarchical cell structure, in Prc. f IEEE PIMRC07, Athens, Greece, Sep [3] L. Garcia, K. Pedersen, and P. Mgensen, Autnmus cmpnent carrier selectin: Interference management in lcal area envirnments fr LTE-advanced, IEEE Cmmunicatins Mag., vl. 47, n. 9, pp , Sep [4] F. Sanchez-Mya, J. Villalba-Espinsa, L. G. U. Garcia, K. I. Pedersen, and P. E. Mgensen, On the impact f explicit uplink infrmatin n autnmus cmpnent carrier selectin fr LTE-A femtcells, in Prc. f IEEE VTC 2011-Spring, Budapest, Hungary, May 2011.

12 12 [5] L. G. U. Garcia, I. Z. Kvacs, K. I. Pedersen, G. W. O. Csta, and P. E. Mgensen, Autnmus cmpnent carrier selectin fr 4G femtcells - a fresh lk at an ld prblem, IEEE Jurnal n Sel. Areas in Cmm., vl. 30, n. 3, pp , Apr [6] V. Chandrasekhar and J. G. Andrews, Spectrum allcatin in tiered cellular netwrks, IEEE Trans. n Cmmunicatins, vl. 57, n. 10, pp , Oct [7] X. Kang, R. Zhang, and M. Mtani, Price-based resurce allcatin fr spectrum-sharing femtcell netwrks: A stackelberg game apprach, IEEE Jurnal f Sel. Areas in Cmm., vl. 30, n. 3, pp , Apr [8] V. Chandrasekhar, J. G. Andrews, T. Muharemvic, Z. Shen, and A. Gatherer, Pwer cntrl in tw-tier femtcell netwrks, IEEE Wireless Cmmunicatins, vl. 8, n. 8, pp , Aug [9] H.-S. J, C. Mun, J. Mn, and J.-G. Yk, Interference mitigatin using uplink pwer cntrl fr tw-tier femtcell netwrks, IEEE Trans. n Wireless Cmmunicatins, vl. 8, n. 10, pp , Oct [10] S. Rangan and R. Madan, Belief prpagatin methds fr intercell interference crdinatin in femtcell netwrks, IEEE Jurnal n Sel. Areas in Cmm., vl. 30, n. 3, pp , Apr [11] O. N. Gharehshiran, A. Attar, and V. Krishnamurthy, Cllabrative sub-channel allcatin in cgnitive LTE femt-cells: A cperative game-theretic apprach, IEEE Trans. n Cmmunicatins, vl. 16, n. 1, pp , Jan [12] M. Rasti, A. R. Sharafat, and B. Seyfe, Paret-efficient and gal driven pwer cntrl in wireless netwrks: A gametheretic apprach with a nvel pricing scheme, IEEE/ACM Trans. n Netwrking, vl. 17, n. 2, pp , Apr [13] S. Ren, J. Park, and M. Schaar, Entry and spectrum sharing scheme selectin in femtcell cmmunicatins markets, IEEE/ACM Trans. n Netwrking, vl. 21, n. 1, pp , Feb [14] E. Susa and J. Silvester, Optimum transmissin ranges in a directsequence spread-spectrum multihp packet radi netwrk, IEEE Jurnal f Sel. Areas in Cmm., vl. 8, n. 5, pp , Jun [15] H. B. Salameh, M. Krunz,, and O. Yunis, MAC prtcl fr pprtunistic cgnitive radi netwrks with sft guarantees, IEEE Trans. n Mbile Cmputing, vl. 8, n. 10, pp , Oct [16] P. Mgensen, W. Na, I. Kvacs, F. Frederiksen, A. Pkhariyal, K. Pedersen, T. Klding, K. Hugl, and M. Kuusela, LTE capacity cmpared t the shannn bund, in Prc. f IEEE VTC 2007-Spring, Dublin, Ireland, Apr [17] T. Rappaprt, Wireless Cmmunicatins, Principles & Practice. Prentice Hall, 1996.