Mall Cell Network - Power, Memory and Networking

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1 Slow admon and power control for mall cell network va dtrbuted optmzaton Sew Eng Na, Tony Q.S. Quek, Mérouane Debbah To cte th veron: Sew Eng Na, Tony Q.S. Quek, Mérouane Debbah. Slow admon and power control for mall cell network va dtrbuted optmzaton. WCNC 23, Apr 23, Shangha, Chna. pp , <.9/WCNC >. <hal-92776> HAL Id: hal Submtted on 3 Jan 24 HAL a mult-dcplnary open acce archve for the depot and demnaton of centfc reearch document, whether they are publhed or not. The document may come from teachng and reearch nttuton n France or abroad, or from publc or prvate reearch center. L archve ouverte plurdcplnare HAL, et detnée au dépôt et à la dffuon de document centfque de nveau recherche, publé ou non, émanant de établement d enegnement et de recherche frança ou étranger, de laboratore publc ou prvé.

2 Slow Admon and Power Control for Small Cell Network va Dtrbuted Optmzaton Sew Eng Na, Tony Q. S. Quek, and Mérouane Debbah Inttute for Infocomm Reearch, A STAR, Fuonopol Way, #2- Connex, Sngapore Sngapore Unverty of Technology and Degn, 2 Dover Drve, Sngapore SUPELEC, 3 rue Jolot-Cure, 992 Gf-ur-Yvette, France Abtract Although mall cell network are envronmentally frendly and can potentally mprove the coverage and capacty of cellular layer, t mperatve to control the nterference n uch network before overlayng them n a macrocell network on a large-cale ba. In recent work, we developed the jont admon and power control algorthm for two-ter mall cell network n whch the number of mall cell uer that can be admtted at ther qualty-of-ervce (QoS) contrant maxmzed wthout volatng the macrocell uer QoS contrant. The QoS metrc adopted outage probablty. In th paper, we nvetgate the dtrbuted mplementaton of the jont admon and power control problem where the mall cell can determne jontly ther admblty and tranmt power autonomouly. I. INTRODUCTION Energy conumpton and electromagnetc polluton are fat becomng problem that future communcaton nfratructure need to allevate. Toward th end, the degn of green cellular network ha been condered. One uch approach to overlay a macrocell network wth many mall cell [], [2]. Wth mall cell, uer can obtan better ndoor recepton and power avng due to the low tranmt power. In addton, mall cell can offload much data traffc from the macrocell network va backhaul. Th enhance the overall network coverage and capacty. However, one of the major mpedment to the ucce of two-ter mall cell network the preence of nterter and ntra-ter nterference. A gnfcant amount of reearch focued on managng nter-ter and ntra-ter nterference [3] [5]. In [3], nter-ter nterference between the macrocell and mall cell ter can be avoded by ung orthogonal pectrum allocaton. Clearly, th method neffcent gven a pare mall cell deployment ettng and a much hgher area pectrum effcency can be acheved by pectrum harng [4]. On the other hand, for pectrum harng n two-ter mall cell network, the nterter nterference ha to be properly controlled by ung technque uch a acce control [4] [7], power control [8] [], multple antenna [], [2], or cogntve rado [3] [5]. All thee cheme [3] [5] nvolve computatonal and gnallng overhead. If the et of actve mall cell change at the rate of Raylegh fadng, there wll be very frequent updatng and proceng at the macrocell bae taton (MBS) and mall cell acce pont (SAP). Therefore, we propoed an nterference management cheme wth jont admon and power control that track at a much lower hadowng tme-cale n [6]. In [6], we conder a two-ter mall cell network, where mall cell uer (SU) hare the ame pectrum wth the macrocell uer (MU). We aume that the MU ha a hgher pectrum acce prorty than the SU. The propoed jont admon and power control problem am to maxmze the number of mall cell admtted wth ther outage probablty contrant atfed and multaneouly, mnmze ther total tranmt power, whle guaranteeng the outage probablty contrant of the MU. Dfferent from conventonal work [7], [8] whch ue ntantaneou gnal-to-nterference-plunoe rato (SINR) contrant, we apply outage probablty contrant for the uer becaue th enable the admon and power updatng to be performed at a much lower lognormal hadowng tme-cale ntead of the Raylegh fadng tme-cale. A th formulaton NP-hard, convex relaxaton appled to obtan hgh qualty approxmate oluton that exhbt near optmal performance a hown n [6]. However, the centralzed approach n [6] dffcult to mplement n practce a the SAP are randomly deployed by ther ubcrber. In th paper, we nvetgate the decentralzed mplementaton of the algorthm n [6] whch developed va dual decompoton. The dtrbuted algorthm enable the mall cell to elf organze; the mall cell can determne jontly (on ther own) f they are admtted or rejected for communcaton and the repectve tranmt power hould they be admtted nto the ytem. The mulaton reult how the effectvene of our propoed dtrbuted algorthm. II. SYSTEM MODEL AND PROBLEM FORMULATION A hown n Fg., we conder an uplnk two-ter network where a macrocell network overlad wth N cloed acce mall cell. The MBS and the SAP are operatng n a common frequency band wth one MU and N SU. We aume that there one SU n each mall cell requetng to hare the pectrum wth the MU n order to communcate wth t SAP. Therefore, the receved SINR of the th SU can be wrtten a SINR = G F P G l F l P l +Gm Fm Pm +N o () A ngle MU condered for brevty of expoton. More QoS contrant can be added to nclude multple MU whch doe not alter the tructure of the propoed problem.

3 SU SU SAP SAP Router Router Backhaul MU Backhaul MBS Fg.. Two-ter network where a macrocell network overlad wth mall cell. The traght arrow ndcate the dered lnk whle the wavy arrow ndcate nter-ter and ntra-ter nterferng lnk. where G l and Fl denote the low and fat fadng gan from the lth SU to the th SAP, repectvely. In the followng, we conder the low fadng gan to nclude the effect of propagaton path lo and hadowng, and the fat fadng gan modeled a exponental power fadng whch correpond to Raylegh fadng aumpton. Smlarly, G m and Fm refer to the low and fat fadng gan from the MU (agned ndex ) to the th SAP, repectvely. The tranmt power of the lth SU Pl, the tranmt power of the MU P m, whch aumed to be fxed a the MU doe not cooperate wth the SU, and the noe power N o. Wth the Raylegh fadng aumpton on the fat fadng gan, Fj kl are ndependent exponentally dtrbuted random varable wth unt mean. Thu, the outage contrant of the th SU gven by Pr(SINR γ,th ρ,th and derved a [] b N o P + ln(+ b G l P l P +ln(+ b Gm Pm P ) ) ln( ρ,th (2) where γ,th and ρ,th denote the pre-pecfed SINR and outage probablty threhold of the th SU, repectvely, and for notatonal convenence, b γ,th /G. When SU are operatng, the receved SINR of the MU where G mm M SINR m = and Fmm M the MU to the MBS and G m M G mm M Fmm M Pm Gm M Fm M P +N o (3) are the low and fat fadng gan from and Fm M are the low and fat fadng gan from the th SU to the MBS. The outage contrant of the MU then gven by Pr(SINR m γ m,th ) ρ m,th and derved a ln(+b m MP ) lnµ m (4) where ρ m,th the pre-pecfed outage probablty threhold of the MU, µ m = ( ρ m )/( ρ m,th ), ρ m the outage probablty of the MU n the abence of SU, and for notatonal convenence, b m M (γm,th G m M/(Gmm The objectve of th work to maxmze the number of SU that can be admtted wth a guaranteed QoS whle guaranteeng the QoS of the MU and multaneouly mnmze the total tranmon power of the SU. In th paper, the QoS provded to the MU a well a the SU outage probablty contrant. Followng the approach n [7], we can provde a compact and elegant ngle-tage framework [6] whch gven by mn P,.t. M Pm ). ǫ P +( ǫ) b No P P P,max, [,], + +ln(+ b Gm Pm P + ln(+ b G l P l P ) (5a) (5b) (5c) ) ln( ρ,th, (5d) ln(+bm M P lnµm (5e) where the auxlary chedulng varable are [,],P,max the maxmum tranmt power of each SU, the value of determne the admblty of the th SU and f the outage contrant of the th SU taken nto conderaton n the power control part of the jont admon and power control problem. If =, the th SU rejected and (5d) reduce to the trval nequalty ln( ρ,th ; f =, the th SU cheduled for admon and (5d) become an actve contrant. The cot functon cont of the weghted um of tranmt power of the SU whch bounded and the admon cot whch dcrete-valued. Intutvely, the weghng parameter ǫ < ǫ ha to be mall enough n order to enure that admon control alway prortzed before power control. The choce of ǫ can be undertood by the followng nterpretaton that droppng any uer cot more than can pobly be aved by total power mnmzaton [7]. Remark : By choong ǫ < ǫ = /(2NP,max +), the oluton of (5) equvalent to frtly, fndng the optmal et S that contan the larget number of SU that can be admtted ubject to tranmt power contrant (5b), outage probablty contrant of the SU (2), and outage probablty contrant of the MU (4) and latly, mnmzng the total tranmt power of the SU n S ubject to the ame contrant (5b), (2), and (4). Proof: The proof omtted for brevty. Dfferent from [7] whch contran the ntantaneou SINR of the SU, the propoed formulaton contran the outage probablte of the MU and SU. Conequently, the objectve functon, weghng parameter ǫ, and the effect that the chedulng varable exert on the contrant n (5) are entrely dfferent from thoe n [7]. III. CONVEX RELAXATION The ngle-tage reformulaton n (5) non-convex due to the bnary contrant (5c) and the term /( + ) n the

4 objectve functon beng nether a poynomal nor a monomal. Therefore, we apply the technque of convex relaxaton. Frt, we relax the bnary contrant to allow to take on any real value wthn the nterval [, ]. Next, we approxmate f( = /( + ) wth a monomal,.e., c α =.5 2 (detal are kpped for brevty) uch that the entre optmzaton problem can be cat a a geometrc programmng (GP) problem. Fnally, the new convex ngle-tage formulaton obtaned a follow: mn ǫ P P +c( ǫ) α (6),.t., (5b),(5d),(5e) whch clearly a GP and t can be olved globally and effcently. After (6) olved, f all =, t mean that all the MU and SU can be erved whle atfyng ther outage contrant. Otherwe, the removal of SU trggered n order to admt the maxmum number of SU wth ther outage contrant and that of the MU met. In th paper, the teratve removal algorthm ued to remove the SU wth the mnmal (one by one) at each teraton of (6). The algorthm termnate when = for all the remanng SU. IV. DISTRIBUTED OPTIMIZATION Although (6) can be effcently olved n polynomal tme, t tll requre a centralzed network controller to olve the optmzaton problem. Due to the random deployment of the mall cell, dtrbuted algorthm are epecally favoured o that the mall cell can determne ther own admblty and tranmt power (f they are admtted for communcaton). To th end, the dual decompoton approach appled [9]. A (5d) coupled wth the tranmt power of other SU, an auxlary varable z l = G l P l and an addtonal equalty (7d) are ntroduced. Let = ln, P = lnp, and z l = lnz l, then we can rewrte (6) a follow: mn ǫ P exp( P )+c( ǫ) N (exp( )) α (7a),.t. exp( )b No P lnp,max,, z l lng l P l =, l + ln(+ exp( )b exp( z l) ) exp( P ) +ln(+ exp( )b Gm Pm exp( P ) (7b) (7c) (7d) ) ln( ρ,th, (7e) ln(+bm M ) lnµm. (7f) Let γ l be the contency prce correpondng to (7d), ζ and λ be the dual varable for (7e) and (7f), repectvely o the partal Lagrangan for (7) can be wrtten a L( P,, z l ) = ǫ N exp( P )+c( ǫ) (exp( ) α [ exp( b + ζ N o ( + ln + exp( )b exp( z ) l) +ln (+ exp( )b ) ] Gm Pm exp( P ) +ln( ρ,th +λ [ N + ln(+b m M ) lnµm] where for each SU, =,,N, we have γ l [ z l lng l P l ] (8) L ( P,, z l ) = ǫ )+c( ǫ)(exp( ) α [ exp( b +ζ N o exp( P ) ( + ln + exp( )b exp( z ) l) +ln (+ exp( )b )] Gm Pm +λln(+b m Mexp( P )) + γ l z l ( γ l P. (9) The contency prce γ l and Lagrange multpler ζ and λ can be updated accordng to the followng equaton: γ l (t+) = γ l (t)+δ γ (t)[ z l lng l P l ], () [ exp( b ζ (t+) = ζ (t)+δ ζ (t) N o exp( P ) ( + ln + exp( )b exp( z ) l) +ln (+ exp( )b Gm λ(t+) = λ(t)+δ λ (t) [ N Pm ) ] +ln( ρ,th, () ln(+b m M ) lnµm] (2) where t the teraton ndex and δ γ, δ ζ, and δ λ are tep ze, repectvely. Incorporatng all the above equaton, we ummarze our propoed dtrbuted jont admon and power control algorthm a follow:

5 ) At t =, ntalze γ l = for,l, λ >, ζ >, and z l =. Frt, each SAPetmate the nterference from the MU,.e.,G m Pm, and channel gan from other SU,.e., G l. Each SAP can get γm,th, G mm M, Pm, and µ m from the MBS ung the backhaul. Each SU can obtan G m M va etmatng Gm M when the MBS broadcatng or tranmttng, after whch t nform t SAP. 2) At t, each SAP olve (9) ubject to t tranmt power contrant (7b) for P and ung nteror pont method. 3) Each SAP check f P and have converged. If o, go to Step (5). Otherwe, the SAP broadcat t P or pae th nformaton to other SAP over a low-rate control channel. 4) The SAP can appont one of themelve a an actng SAP controller to pa ther G m M to. The actng SAP controller update λ and nform the other SAP of λ va the low-rate control channel. Each SAP update z l, γ l, and ζ. Go to Step (2). 5) After P and have converged, each SAP can calculate P and. If =, the SU admtted to hare the pectrum wth the MU and the SU then tranmt at P to communcate wth the repectve SAP. If =, the SU rejected and t doe not tranmt at all. V. SIMULATION RESULTS The performance of our propoed dtrbuted jont admon and power control algorthm nvetgated for a code dvon multple acce ytem. The MBS located n the centre of a quare area of length 2m. The mall cell are randomly located n the ame area excludng a quare area of length m centred at the MBS. The SAP located at the centre of each mall cell (quare area) and the SU randomly located at ether one of the four corner of the cell at a dtance of 2m. The mall cell are eparated from each other by at leat m. The MU randomly located outde the mall cell by at leat m. The noe power at the MBS and SAP N o = W. The tranmt power and SINR threhold of the MU are P m = 4W and γ m,th = db, repectvely. The total number of requetng SU 3. The SINR threhold of the SU 25dB. The maxmum tranmt power of the SU P,max = W. The proceng gan of the MBS and SAP are PG m = and PG =, repectvely. The MU and SU have an outage probablty threhold ρ m,th = % and = %. The low fadng gan between tranmtter j and ρ,th recever modeled a G j = K βj/ d η j where d j the dtance between them, K = 3 a factor to nclude the effect of antenna gan and carrer frequency, β j a Gauan random varable wth zero mean and tandard devaton of 4dB to account for log-normal hadowng effect, and the path lo exponent η = 3 except that η = 4 for G. We tudy the performance of the propoed dtrbuted jont admon and power control algorthm by comparng wth t centralzed counterpart. In the frt example n Fg. 2, the centralzed algorthm admt all the requetng SU whle n the econd example n Fg. 3, the centralzed algorthm admt Value of of SU Tranmt power of SU (W).8 SU 2 Iteraton ndex.5.3. (a) SU Iteraton ndex Fg. 2. (a) Value of of SU obtaned by the propoed dtrbuted algorthm veru teraton ndex. All SU are admtted. Note that the x- ax on a logarthm cale. (b) Tranmt power of SU obtaned by the propoed dtrbuted algorthm veru teraton ndex. The old lne ndcate the tranmt power of the repectve SU a obtaned by the centralzed algorthm. only 2 SU whch are and. Fg. 2(a) and Fg. 3(a) how that the dtrbuted algorthm admt the ame SU a that of the centralzed algorthm. Note that the x-ax of Fg. 2(a) on a logarthm cale. Fg. 2(b) and Fg. 3(b) how that the tranmt power of the admtted SU converge to thoe obtaned by the centralzed algorthm (a ndcated by the old lne). In Fg. 3(b), the tranmt power of SU after the convergence of the dtrbuted algorthm not mportant becaue t not admtted for communcaton nce n Fg. 3(a), hence SU wll not tranmt at all. (b)

6 tranmt power f they are admtted. Value of of SU Tranmt power of SU (W).8 SU Iteraton ndex.8 SU (a) Iteraton ndex Fg. 3. (a) Value of of SU obtaned by the propoed dtrbuted algorthm veru teraton ndex. Only and are admtted. (b) Tranmt power of SU obtaned by the propoed dtrbuted algorthm veru teraton ndex. The old lne ndcate the tranmt power of the repectve SU a obtaned by the centralzed algorthm. (b) VI. CONCLUSION In th paper, we nvetgated the dtrbuted mplementaton of a hadowng tme-cale baed jont admon and power control algorthm n two-ter mall cell network. In partcular, the number of mall cell uer that can be admtted at ther outage probablty pecfcaton maxmzed and ther total tranmt power mnmzed whle guaranteeng the outage probablty pecfcaton of the macrocell uer. A th jont admon and power control problem NP-hard, convex relaxaton appled to obtan hgh qualty approxmate oluton. The dtrbuted mplementaton developed by applyng dual decompoton technque whch empower the mall cell to determne ther own admblty nto the ytem and the ACKNOWLEGEMENT Th work wa upported by the SRG ISTD and the CAS Fellowhp for Young Internatonal Scentt. REFERENCES [] J. Hoyd, M. Kobayah, and M. Debbah, Green mall-cell network, IEEE Veh. Technol. Mag., vol. 6, no., pp , Mar. 2. [2] D. López-Pérez, İ. Güvenc, G. de la Roche, M. Kountour, T. Q. S. Quek, and J. Zhang, Enhanced ntercell nterference coordnaton challenge n heterogeneou network, IEEE Wrele Commun., vol. 8, no. 3, pp. 22 3, Jun. 2. [3] V. Chandraekhar and J. G. Andrew, Spectrum allocaton n tered cellular network, IEEE Tran. Commun., vol. 57, no., pp , Oct. 29. [4] W. C. Cheung, T. Q. S. Quek, and M. Kountour, Throughput optmzaton, pectrum allocaton, and acce control n two-ter femtocell network, IEEE J. Sel. Area Commun., vol. 3, no. 3, pp , Apr. 22. [5] A.-H. Ta, L.-C. Wang, J.-H. Huang, and R.-B. Hwang, Hgh-capacty OFDMA femtocell by drectonal antenna and locaton awarene, IEEE Syt. J., vol. 6, no. 2, pp , Jun. 22. [6] C.-H. Ko and H.-Y. We, On-demand reource-harng mechanm degn n two-ter OFDMA femtocell network, IEEE Tran. Veh. Technol., vol. 6, no. 3, pp. 59 7, Mar. 2. [7] P. Xa, V. Chandraekhar, and J. G. Andrew, Open v. cloed ace femtocell n the uplnk, IEEE Tran. Wrele Commun., vol. 9, no. 2, pp , Dec. 2. [8] V. Chandraekhar, J. G. Andrew, T. Muharemovc, Z. Shen, and A. Gatherer, Power control n two-ter femtocell network, IEEE Tran. Wrele Commun., vol. 8, no. 8, pp , Aug. 29. [9] C. W. Tan, S. Fredland, and S. H. Low, Spectrum management n multuer cogntve wrele network: Optmalty and algorthm, IEEE J. Sel. Area Commun., vol. 29, no. 2, pp , Feb. 2. [] C. W. Tan, Optmal power control n Raylegh-fadng heterogeneou network, n Proc. IEEE Int. Conf. Comput. Commun., Shangha, Chna, Apr. 2, pp [] S. Park, W. Seo, Y. Km, S. Lm, and D. Hong, Beam ubet electon trategy for nterference reducton n two-ter femtocell network, IEEE Tran. Wrele Commun., vol. 9, no., pp , Nov. 2. [2] Y. Jeong, T. Q. S. Quek, and H. Shn, Beamformng optmzaton for multuer two-ter network, J. Commun. Netw., vol. 3, no. 4, pp , Aug. 2. [3] S.-M. Cheng, S.-Y. Len, F.-S. Chu, and K.-C. Chen, On explotng cogntve rado to mtgate nterference n macro/femto heterogeneou network, IEEE Wrele Commun., vol. 8, no. 3, pp. 4 47, Jun. 2. [4] S.-Y. Len, Y.-Y. Ln, and K.-C. Chen, Cogntve and game-theoretcal rado reource management for autonomou femtocell wth QoS guarantee, IEEE Tran. Wrele Commun., vol., no. 7, pp , Jul. 2. [5] A. Adhkary, V. Ntrano, and G. Care, Cogntve femtocell: Breakng the patal reue barrer of cellular ytem, n Proc. Inform. Theory Appl. Workhop, San Dego, CA, Feb. 2, pp.. [6] S. E. Na, T. Q. S. Quek, and M. Debbah, Shadowng tme-cale admon and power control for mall cell network, n Proc. IEEE Int. Symp. Wrele Per. Multmeda Commun., Tape, Tawan, Sep. 22. [7] E. Matkan, N. D. Sdropoulo, Z.-Q. Luo, and L. Taula, Convex approxmaton technque for jont multuer downlnk beamformng and admon control, IEEE Tran. Wrele Commun., vol. 7, no. 7, pp , Jul. 28. [8] I. Mtlagka, N. D. Sdropoulo, and A. Swam, Jont power and admon control for ad-hoc and cogntve underlay network: Convex approxmaton and dtrbuted mplementaton, IEEE Tran. Wrele Commun., vol., no. 2, pp. 4 42, Dec. 2. [9] M. Chang, Geometrc Programmng for Communcaton Sytem. Hanover, MA: Now Publher Inc., 25.