ENERGY-EFFICIENT DOWNLINK TRANSMISSION WITH BASE STATION CLOSING IN SMALL CELL NETWORKS. Liyan Su, Chenyang Yang, Zhikun Xu and Andreas F.

Transcription

1 ENERGY-EFFICIENT DOWNLINK TRANSMISSION WITH BASE STATION CLOSING IN SMALL CELL NETWORKS Lyan Su, Chenyang Yang, Zhkun Xu and Andreas F. Molsch Behang Unversty, Bejng, Chna Unversty of Southern Calforna, Los Angeles, USA Emal: ABSTRACT Shutdown of low traffc load base statons (BSs) s recognzed as a promsng approach to ncrease energy-effcency (EE) and reduce total power consumpton, especally for small cell networks (SCN). In ths paper, we study BS closng strateges for downlnk mult-antenna mult-carrer SCN supportng best effort traffcs. We formulate the optmzaton problem of long-term BS closng, BS-user assocaton and subcarrer allocaton to maxmze EE or mnmze total power consumpton under the constrants of average sum rate and rate proporton. We obtan an optmal soluton for maxmzng EE and a suboptmal soluton for mnmzng total power consumpton. Smulaton results show that the solutons provde substantal gan both n savng power consumpton and ncreasng EE, and mnmzng the total power consumpton wll not lead to the maxmal EE. 1. INTRODUCTION Energy-effcency (EE) s becomng an mportant desgn goal for cellular networks except for spectrum effcency (SE) [1]. Statstcal results n moble communcatons show that over 80% of the power s consumed by base statons (BSs) [2], and about 60% of the power consumed at each BS s taken up by processng crcuts and ar condtonng [3]. As a result, shuttng down the BSs wthout actve users s expected as an effcent way to reduce network power consumpton [4, 5]. Ths s practcally possble because the deployment of exstng cellular networks, usually optmzed for fully loaded traffcs, leads to very neffcent usage of B- Ss durng off-peak tme. Moreover, the daly traffc varaton due to user moblty and actvtes s predctable, whch ndcates that BS closng strateges can operate on a long-term tme scale, e.g., n hours. Several BS closng schemes based on traffc load and channel condtons were studed, e.g., [6]. Small cell networks (SCNs) are ganng wde popularty to mprove both SE and EE [7]. On one hand, dvdng a large (Macro) cell nto a number of small (Pco) cells brng Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna (No ) and by the Natonal Basc Research Program of Chna (No. 2012CB316003). the users closer to the BSs, whch s one of the most effectve ways to ncrease the network capacty. On the other hand, the dle BSs can be shut down to reduce power consumpton. To acheve hgh EE or low power consumpton whle ensurng the requred performance of a partcular system, the traffc feature should be consdered. For best effort traffcs, the requrement s to maxmze the sum rate and to ensure the farness n data rates among multple users. In ths paper, we nvestgate BS closng strateges for mult-nput-mult-output (MIMO)-orthogonal frequency duplex multple access (OFDMA). We consder downlnk SCN supportng best effort traffcs. We formulate the problem of BSs closng, BS-user assocaton and subcarrer allocaton toward dfferent optmzaton objectve functons, maxmze EE and mnmze total power consumpton, ensurng mnmal average sum rate requrement and proportonal rate farness. The total power ncludes the crcut power and transmt power. We obtan an optmal soluton for maxmzng EE. Consderng that the problem to mnmze total power consumpton s ntractable for large scale networks, we resort to sparse optmzaton [8] to fnd a suboptmal soluton. 2. SYSTEM AND POWER CONSUMPTION MODEL 2.1. System Model Consder a downlnk MIMO-OFDMA SCN, where B low power BSs each equpped wth N t antennas are deployed to serve M sngle-antenna users n the network wthout coordnaton. When a BS serves multple users, L subcarrers are shared wthout overlappng. Denote g mb,j = α mb h mb,j as the channel vector between BS b and user m at the jth subcarrer, where α mb s the large scale fadng gan ncludng path loss and shadowng, h mb,j C Nt 1 s the small scale fadng channel vector. Entres of dfferent subcarrers channel vector are assumed ndependent and dentcally dstrbuted (..d.). We assume perfect nstantaneous channel state nformaton (CSI) s avalable at each actve BS and the BS transmts to the user wth maxmal-rato transmsson (MRT) precodng. Snce a large porton of power s consumed by the crcuts of actve BSs, our man concern s how to save energy by closng unnecessary BSs. In SCN, the BSs transmt wth low

2 power, the dle BSs are closed, and user dstrbuton s sparse [9]. Ths leads to neglgble nter-cell nterference and the scenaro s nose lmted. Then, f user m s served by BS b, the average data rate can be expressed as k mb R m =Δf E{log 2 (1 + Pα mb σ 2 h mb,j 2 )} (1) j=1 = k mb ΔfE{log 2 (1 + Pα mb σ 2 h mb,1 2 )} = k mb Δf r mb, where Δf s the subcarrer spacng, k mb s the number of subcarrers occuped by user m. We assume equal power allocaton across all the subcarrers, P and σ 2 are respectvely the transmt power and nose power at each subcarrer, r mb denotes the average SE of user m Power Consumpton Model A typcal power consumpton model for low power BSs such as pco and femto cells s provded n [9]. The total power consumed by a BS conssts of transmt power and crcut power. Denote η as the effcency of the power amplfer. Then, the transmt power consumpton of BS b s Ptr b = m S b k mb. Besdes a fxed crcut power consumpton P η to mantan the operaton of the BS, crcut power consumed for sgnal prossng depends on the number of subcarrers,.e., P b sp = p sp m S b k mb, where p sp s the sgnal processng power consumpton of each subcarrer. The total power consumpton at BS b s modeled as, P b tot = P b tr + P b sp + P b c,, B, (2) where Pc b s the fxed crcut power consumpton of the BS, and can be modeled by a pecewse functon as { Pc b Pca f BS = b s actve, 0 f BS b s closed. 3. BS CLOSING STRATEGIES In ths secton, we study BS closng strateges for best effort traffcs. We optmze the BS closng pattern, user access, and the subcarrer allocaton of actve BSs that maxmze the EE and mnmze the total power consumpton under the constrant of a mnmal average sum rate and rate farness EE Maxmzaton Defne BS-user assocaton vectors w m {0, 1} B 1, whose bth entry w mb s 1 f user m s connected to BS b and 0 otherwse. Then, the total power consumpton n the SCN can be expressed as P tot ({w, k } M =1) B = w m 0 +( P η + p sp) k T mw m (3), e T b where 0 denotes l 0 -norm, e b s a vector of zeros except that ts bth entry s one, k m R B 1 whose bth entry s k mb. Then, e T b M w m ndcates the number of users connected to BS b, and e T b M w m 0 =1ndcates that BS b s actve whle e T b M w m 0 =0ndcates t s dle and should be closed. Defne the EE as EE({w, k } M =1) = P tot ({w, k } M (4) =1 ), where = M R m s the sum rate. To support best effort traffcs for users, we formulate the optmzaton problem of BS closng, BS-user assocaton and subcarrer allocaton to maxmze the EE under the constrants of mnmal average sum rate and user rate farness as follows max EE({w, k } M =1) (5a) {w,k } M =1 R mn (5b) R m = β m 1 m M (5c) e T b k m e T b w m L, 1 b B (5d) 1 T w m =1, 1 m M (5e) w mb = 0 or 1, 1 m M,1 b B.(5f) where the farness factor β s a postve real number and M =1 β = 1, whch ensures the farness among the actve users wth a data rate proporton as n [10], (5d) ensures that each BS can at most allocate L subcarrers,.e., m S b k mb L, 1 s a vector of one, and (5e) ensures each user to be connected to a sngle BS. For gven BS-user assocaton vectors {w } M =1, constrant of (5c) leads to the followng long-term subcarrer allocaton for the actve BSs: k mb = βmrsum Δf r mb. By gnorng the mpact of cel operaton, the number of subcarrers s a lnear functon of the sum rate. Moreover, the frst term of (3) s a constant, and the second term s a lnear functon of. Then, (4) can be rewrtten as EE = Pc I = 1 + κ κ Pc I κpc I + κ 2, (6) where Pc I B M = et b w m 0 and κ = ( P η + p sp ) M B β m Δf r mb w mb does not depend on. Therefore, EE s an ncreasng functon of. It mples that n order to maxmze the EE, the average sum rate (.e., SE) should acheve the maxmal value. Ths suggests that each actve BS should employ avalable subcarrers as many as possble to serve the users connected to t. We consder sparse user dstrbuton and B M. The soluton of problem (5) s as follows: all the users should connect to ther local BSs wth strongest average receve sgnals, the dle BSs wthout users are closed, and at least one actve BS allocates all the subcarrers to serve the user accessed to t, other actve BSs allocate subcarrers accordng to (5c).

3 3.2. Total Power Mnmzaton The BS closng strategy maxmzng the EE does not necessarly lead to the mnmzaton of the total power consumpton. In realstc systems, we need to reduce the total power consumpton. When the equalty n (5b) holds, the total power consumpton wll acheve the mnmal. Further consderng (5c), the two constrants of (5b) and (5c) lead to the followng long-term subcarrer allocaton for the actve BSs: k mb = βmrmn Δf r mb. Then, the optmzaton problem of BS closng and BS-user assocaton to mnmze the total power consumpton under the constrants of mnmal average sum rate and farness can be formulated as mn {w } M =1 P tot ({w } M =1) (7) (5d), (5e), (5f). We ntroduce sparse concave relaxaton to solve ths problem. A standard approach to solve the sparse optmzaton problem s to relax the l 0 -norm n objectve functon. The followng relaton for any gven scalar a>0s gven n [8], ln(1+aɛ a 0 = lm 1 ) ɛ 0 ln(1+ɛ 1 ). We gnore the lmt and relax the l 0 -norm as follows a 0 μ ln(1 + aθ 1 ) ln(1 + θ 1 ), (8) where θ>0s a small constant, μ (0, 1] s a parameter to control the accuracy of the approxmaton. By usng (8), relaxng the bnary nteger constrants (5f) and normalzng the coeffcent, problem (7) becomes mn {w } M =1 f({w } M =1) +λ B ln(1 + e T b k T mw m w m θ 1 ) (9a) (5d), (5e), 0 w mb 1, 1 m M,1 b B, (9b) where λ =( P η + p sp)ln(1+θ 1 )/(μ ). The objectve functon s concave and dfferentable. We can use the majorzaton-mnmzaton (MM) algorthm [11] to fnd a sequence of vectors {w (n) } M =1 ) f({w(n) ). Denote f({w (n+1) + } M =1 g({w } M =1, {w (n) (w w (n) =1 } M =1 } M =1) =f({w (n) such that } M =1) ) T f({w(n) } M =1 ), (10) w (n) as the majorzng functon used by the MM algorthm, where f({w (n) } M =1 ) = w (n) B θ + e T b e b M w(n) m + λk. (11) Durng the teraton, w (n+1) can be obtaned by solvng the followng problem mn w g({w } M =1, {w (n) } M =1) (12a) B ( e T b w 0 e T b =1 (5d), (5e), (9b), =1 w (n) 0 ) 2 1, (12b) where constrant (12b) ensures that n each teraton, at most one BS can change ts operaton mode. To solve problem (12) wthout loss of optmalty, we frst solve the problem for a gven BS whose mode has changed, whch s a lnear programmng problem and can be solved effcently. Next, we fnd whch BS should change mode by exhaustve searchng. We termnate the algorthm when f({w (n) } M =1 ) f({w(n+1) } M =1 ) <ε, and obtan the suboptmal soluton {w }M =1 ), where ε > 0 s a small value. It s not hard to prove the monotoncty and boundedness of f({w (n) } M =1 ), then the algorthm s convergent. Due to the relaxng of (5f), some entres of {w }M =1 ) are not ntegers. We map the entres onto bnary ntegers n the followng way. Frst, we connect user m to BS b f w mb =1. Then, for the remanng users, say, user j, t s assgned to BS f w j s the largest entry less than 1 and BS stll has subcarrers not yet allocated, j m, b. If a user can not be assgned to any actve BS, the nearest BS should be actvated to serve the user. The ntalzaton of the MM algorthm s crucal to the performance. We fnd the ntal value by searchng as follows. For all values of w (0) that ensure the number of actve BSs less than B 0, compare all correspondng suboptmal solutons and select one wth mnmal total power consumpton. We refer to such an algorthm to fnd the soluton of BS closng, BS-user assocaton and subcarrer allocaton toward total power mnmzaton as suboptmal BS closng method. 4. SIMULATION RESULTS In ths secton, we evaluate the power consumpton and EE of the two BS closng methods. The smulaton setup s based on the parameters of a pco cell setup n [9]. The SCN ncludes 19 (three-ter) small cells. The radus of small cells s 50 m. N t =2, L = 1024, and Δf = 15 khz. η = 8.0%, p sp = 0.4 mw, P c,a s ether 2.2 Wor4 W [12]. Two propagaton models are consdered, and 10 m s the transton dstance. In short-or long-range model, the large-scale fadng model s log d (db) [13] or logd (db) [14]. The standard devaton of shadowng s 6 db. When a BS s actve, the transmt power s 21 dbm. To compare wth the optmal soluton of problem (7) obtaned by exhaustve searchng that s of hgh complexty, we set 5 users n the SCN. In the concave relaxaton, θ = 0.1 and μ = θ ln(1 + θ 1 )=0.24, but the performance s

4 not senstve to these parameters. In the MM algorthm, ε = 0.1 and B 0 =2. All the smulaton results are obtaned by averagng over 100 realzatons of small scale fadng channels and 100 random locatons of the users. Power Consumpton (W) = 4 W = 2.2 W Tradtonal BS closng method 8 Suboptmal BS closng method Optmal method Fg. 1. Total power consumptons versus SE. SE EE = 23 bps/hz, Ptot EE = 19 W for 2.2 W, and Ptot EE =28Wfor4W. EE (bts/j/hz) Optmal method Suboptmal BS closng method Tradtonal BS closng method SCN wthout BS closng =2.2W =4W Fg. 2. EE versus SE. SE EE = 23 bps/hz, EE EE = 1.2 bts/j/hz for 2.2 W, and EE EE = 0.8 bts/j/hz for 4 W. Power Consumpton (W) Tradtonal BS closng method Suboptmal BS closng method Absolutely farness Resource farness Fg. 3. Impact of farness on total power consumpton. In Fg. 1, we compare the total power consumptons of the followng strateges: 1) tradtonal BS closng method, where all the users connect to ther local BSs, the dle B- Ss are closed, and each actve BS allocates the subcarrers to ensure the requred average data rate of each user, 2) suboptmal BS closng method, 3) optmal soluton of problem (7), whch s obtaned by exhaustve searchng, and 4) optmal soluton of problem (5), whose performance s SE EE, and EE EE. We can see that the optmzaton amng at maxmzng EE does not provde the mnmal total power consumpton. For the strategy that mnmzes the total power consumpton, the suboptmal method s very close to the optmal soluton. Comparng the suboptmal method wth the tradtonal method, the gan n savng power ncreases wth the crcut power of the actve BS, and decreases wth the growng of the SE. Ths s because the gan comes from closng unnecessary BSs. When the SE s hgh, the suboptmal method has lttle gan because each BS does not have enough subcarrers to serve the users that are close to ts adjacent BSs. In Fg. 2, we compare the EE of the above-mentoned three strateges wth that of the SCN wthout BS closng. A sgnfcant gan n EE s obtaned by closng a large number of BSs that do not serve users. We can also see that n all of the scenaros, a hgh SE requrement leads to a hgh EE. Comparng the suboptmal method wth the tradtonal BS closng method, the gan n savng power s more pronounced than the gan n EE for the low SE regon. Ths s because the optmzaton to mnmze the power consumpton s subject to a gven sum rate requrement but the optmzaton to maxmze the EE s subject to a mnmal sum rate requrement, such that the power consumpton gan s more senstve to SE. In Fg. 3, we show the mpact of farness. We consder P EE tot absolutely farness (β =1/M ) and resource farness (.e., β = r b / M r mb m ), whch mples that cell center users obtan a hgher rate whle cell edge user obtans lower rate. We can see that dfferent knds of farness have mnor mpact when SE s low, because the crcut power s domnant. When SE s hgh, absolutely farness requres more power consumpton than resource farness, because the cell edge users wth absolutely farness needs more transmt power. 5. CONCLUSION We have studed two methods for BS closng, user access and subcarrer allocaton strateges to maxmze EE and to mnmze total power consumpton. We found the optmal soluton for the EE maxmzaton problem, and proposed a suboptmal soluton for the total power mnmzaton problem. Smulaton results show both strateges have sgnfcant gans n savng power and ncreasng EE over tradtonal BS closng scheme especally at low SE regon. The proposed s- trategy toward power mnmzaton consumes much less power than the strategy toward EE maxmzaton. Farness has mnor mpact when SE s low, whle absolutely farness consumes more power than resource farness when SE s hgh.

5 6. REFERENCES [1] G. L, Z. Xu, C. Xong, and C. Yang, Energy-effcent wreless communcatons: tutoral, survey, and open ssues, IEEE Wreless Commun. Mag., vol. 18, no. 6, pp , Dec [14] 3GPP Long Term Evoluton (LTE), Further advancements for e-utra physcal layer aspects (release 9), TSG RAN TR v1.2.0, [2] G. Fettwes and E. Zmmermann, ICT energy consumpton c trends and challenges, Proc. WPMC, [3] G. Auer, V. Gannn, C. Desset, I. Godor, P. Skllermark, M. Olsson, M. A. Imran, D. Sabella, M. J. Gonzalez, O. Blume, and A. Fehske, How much energy s needed to run a wreless network? IEEE Wreless Commun. Mag., vol. 18, no. 5, pp , [4] S. Han, C. Yang, G. Wang, and M. Le, On the energy effcency of base staton sleepng wth multcell cooperatve transmsson, n Proc. IEEE PIMRC, [5] E. Pollaks, R. Cavalcante, and S. Stanczak, Base s- taton selecton for energy effcent network operaton wth the majorzaton-mnmzaton algorthm, n Proc. IEEE SPAWC, [6] E. Oh and B. Krshnamachar, Energy savngs through dynamc base staton swtchng n cellular wreless access networks, n Proc. IEEE GLOBECOM, [7] J. Hoyds, M. Kobayash, and M. Debbah, Green Small-Cell Networks, IEEE Vehcular Tech. Mag., vol. 6, no. 1, pp , Mar [8] M. B. W. E. J. Candes and S. P. Boyd, Enhancng s- parsty by reweghted l1 mnmzaton, J. Fourer Anal. Appl., vol. 14, pp , [9] G. Auer, O. Blume, V. Gannn, I. Gódor, et al., D 2.3: Energy effcency analyss of the reference systems, areas of mprovements and target breakdown, EARTH, Nov [Onlne]. Avalable: delverables.html [10] J. A. Z. Shen and B. Evans, Optmal power allocaton n multuser OFDM systems, n Proc. IEEE GLOBE- COM, [11] D. R. Hunter and K. Lange, A tutoral on MM algorthms, The Amercan Statstcan, vol. 58, pp , [12] C. Isheden and G. P. Fettwes, Energy-effcent multcarrer lnk adaptaton wth sum rate-dependent crcut power, n Proc. IEEE GLOBECOM, [13] A. Goldsmth, Wreless Communcatons. Cambrdge,U.K.: Cambrdge Unv. Press, 2005.