Cell Coverage Optimization for the Multicell Massive MIMO Uplink

Transcription

1 Ce Coverage Optiization for the Mutice Massive MIMO Upink Jin, S., Wang, J., Sun, Q., Matthaiou, M., & Gao, X. 04. Ce Coverage Optiization for the Mutice Massive MIMO Upink. IEEE Transactions on Vehicuar Technoogy. DOI: 0.09/TVT Pubished in: IEEE Transactions on Vehicuar Technoogy Docuent Version: Peer reviewed version Queen's University Befast - Research Porta: Link to pubication record in Queen's University Befast Research Porta Pubisher rights 05 IEEE. Persona use of this ateria is peritted. Perission fro IEEE ust be obtained for a other users, incuding reprinting/ repubishing this ateria for advertising or prootiona purposes, creating new coective works for resae or redistribution to servers or ists, or reuse of any copyrighted coponents of this work in other works Genera rights Copyright for the pubications ade accessibe via the Queen's University Befast Research Porta is retained by the authors and / or other copyright owners and it is a condition of accessing these pubications that users recognise and abide by the ega requireents associated with these rights. Take down poicy The Research Porta is Queen's institutiona repository that provides access to Queen's research output. Every effort has been ade to ensure that content in the Research Porta does not infringe any person's rights, or appicabe UK aws. If you discover content in the Research Porta that you beieve breaches copyright or vioates any aw, pease contact openaccess@qub.ac.uk. Downoad date:07. Oct. 08

2 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy Ce Coverage Optiization for the Mutice Massive MIMO Upink Shi Jin, Meber, IEEE, Jue Wang, Meber, IEEE, Qiang Sun, Michai Matthaiou, Senior Meber, IEEE, and Xiqi Gao, Feow, IEEE Abstract We investigate the ce coverage optiization probe for the assive utipe-input utipe-output MIMO upink. By depoying tit-adjustabe antenna arrays at the base stations, ce coverage optiization can becoe a proising technique which is abe to strike a coproise between covering ce-edge users and piot containation suppression. We foruate a detaied description of this optiization probe by axiizing the ce throughput, which is shown to be ainy deterined by the user distribution within severa key geoetrica regions. Then, the foruated probe is appied to different exape scenarios: for a network with hexagona shaped ces and unifory distributed users, we derive an anaytica ower bound of the ergodic throughput in the objective ce, based on which,itisshown that theoptia choicefor thece coverage shoud ensure that the coverage of different ces does not overap; for a ore generic network with sectora shaped ces and non-unifory distributed users, we propose an anaytica approxiation of the ergodic throughput. After that, a practica coverage optiization agorith is proposed, where the optia soution can be easiy obtained through a sipe one-diensiona ine searching within a confined searching region. Our nuerica resuts show that the proposed coverage optiization ethod is abe to greaty increase the syste throughput in acroces for the assive MIMO upink transission, copared with the traditiona schees where the ce coverage is fixed. Index Ters Ce coverage, assive MIMO, piot containation, upink. I. INTRODUCTION Massive utipe-input utipe-output MIMO systes a.k.a. arge-scae MIMO have drawn considerabe attention in the iterature recenty []. With a arge aount of antennas Manuscript received Deceber 6, 0; revised Juy and October 5, 04. The editor coordinating the review of this paper and approving it for pubication was Y. Gong. S. Jin and X. Gao are with the Nationa Counications Research Laboratory, Southeast University, Nanjing 0096, P. R. China. Eais: {jinshi, xqgao}@seu.edu.cn. J. Wang and Q. Sun are with the Schoo of Eectronic and Inforation Engineering, Nantong University, Nantong 609, China. Eais: {wangjue, sunqiang}@ntu.edu.cn. J. Wang is aso with Singapore University of Technoogy and Design, Singapore 868. M. Matthaiou is with the Schoo of Eectronics, Eectrica Engineering and Coputer Science, Queen s University Befast, Befast, BT 9DT, U.K., and with the Departent of Signas and Systes, Chaers University of Technoogy, SE-4 96, Gothenburg, Sweden. Eai:.atthaiou@qub.ac.uk. This work was supported by Nationa Natura Science Foundation of China under Grants64040, 60, , the Natura Science Foundation of Jiangsu Province under Grant BK00, the Nationa Science and Technoogy Major Project of China under Grant 0ZX , the Progra for Jiangsu Innovation Tea, and the Internationa Science and Technoogy Cooperation Progra of China under Grant 04DFT000. The work of M. Matthaiou has been supported in part by the Swedish Governenta Agency for Innovation Systes VINNOVA within the VINN Exceence Center Chase. depoyedatthebasestationbs,itispossibetoachievevery high spectra, as we as, power efficiency with sipe inear transceivers [], [], e.g., axiu ratio transission MRT and axiu ratio cobining MRC. These attractive features ake assive MIMO a proising technique for the next generation of obie counication systes [4]. According to the aw of arge nubers for independent and identicay distributed i.i.d. Rayeigh fading conditions, the ipact of uncorreated noise and intra-ce interference can be copetey averaged out with assive MIMO, whie the syste perforance is ainy iited by piot containation caused by piot reuse in adjacent ces[5]. Considering assive MIMO systes working in the tie division dupex TDD ode, orthogona piots are sent fro users during the training phase in the upink, whie the BSs perfor channe estiation and use the obtained channe state inforation CSI for both upink reception and downink transission. The nuber of avaiabe orthogona piots is iited by the ength of the channe coherence tie. As the nuber of ces and nuber of users per ce increase, piot reuse is inevitabe; thus, the upink channe estiation in one ce wi be containated by the upink channes of users fro other ces that are using the sae piot sequence. To overcoe this intiatey negative effect, severa works have been docuented. Coordinated channe estiation was proposed in[7], whie piot ength reducing techniques were discussed in [8]. On the other hand, the issue of piot reuse and aocating echanis design was studied in [7], [9], and precoding was investigated in conjunction with piot containation in [5], [0]. Different fro the above entioned approaches, we prefigure that piot containation can be, aternativey, suppressed fro a acroscopic perspective, e.g., the ce coverage. In genera, ce coverage adjustent can be reaized in practice via antenna titing techniques. An eary contribution on the topic of antenna titing can be found in [], which was ater extended to universa obie teecounications systes UMTS [], ong ter evoution LTE systes [], [4] and network MIMO systes [5]. The topic of antenna tit design has been widey studied in recent years [4] [0], aong which sef-optiization of tit ange was investigated in [6] [8], ange signa strength prediction for downtited Note that the treendous CSI feedback overhead akes the frequency division dupex FDD ode chaenging in assive MIMO systes; for this reason, ost reative works on assive MIMO focus on the TDD ode. It shoud be highighted that soe nove ethods have been proposed to ipeent assive MIMO transission in the FDD ode, e.g., see[6] and the references therein. However, a detaied coparison of these different dupex odes is beyond the ain scope of this paper c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

3 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy antennas was considered in [9], and throughput optiization was studied for utipe input singe output MISO interference channes [0]. In the iterature, it is usuay required that the three-diensiona radiation pattern in dbi of an antenna eeent is known, and according to [], the radiation pattern can be expressed as [ φ αorn P dbi β tit,φ,θ = in in,sll az] φ db [ θ βtit +in,sll e],sll tot +A ax θ db where β tit is the adjustabe tit ange of the antenna eeent, whie α orn is the fixed orientation ange in the aziuth doain. Moreover, φ and θ are the incident anges in the aziuth and eevation doains, respectivey. For the aziuth and eevation antenna patterns, φ db and θ db are the hafpower beawidths, whie SLL az and SLL e are the side obe eves. At ast, SLL tot is the tota side obe eve, and A ax is the peak antenna gain. Tothebestofourknowedge,thetopicofantennatitdesign in assive MIMO systes reains open for investigation. Recenty, expoiting the eevation anguar diension using active antenna arrays in assive MIMO systes has been proposed in [], where the perforance of a technique tered as fudiension MIMO FD-MIMO, was evauated using a D channe ode, assuing different array topoogies. However, the authors therein assued that the nuber of antennas is not so arge, such that piot containation is not the doinating factor and can be ignored in the syste design. In our work though, we consider an infinitey high nuber of antennas, therefore, piot containation is a doinating design factor in ourcase.intuitivey,ifthecoverageareas ofdifferentcesare stricty not overapping, the sae set of orthogona piots can be reused aong ces whie causing the east containation; yet, squeezing the ce coverage without iit wi ake the coverage of ce-edge users probeatic. Thus, considering the trade-off between interference suppression and the coverage of ce-edge users, an optia ce coverage is expected to exist, whichwiaxiizethecethroughput. Beingawareofthis, this paper akes the foowing contributions: We derive a generic ower bound of the ergodic ce throughput in the assive MIMO upink, where the ce coverage is taken into account as an iportant paraeter. We point out that the syste perforance wi be affected by the average nuber, as we as, the distance distributions of users which are ocated in severa key regions, In this paper, we ignore the detais described by, and focus ony on the concept of ce coverage. Ingenera, iftheantenna isdesigned tohave awideenough -db ain obe width as we as deep enough attenuation outside of the ain obe, the ce coverage can be directy reated with antenna titing, by inspecting whether a user is ocated within the ain obe described by. This sipification adits ore concise atheatica anipuations, as we as, cear physica insights. In this paper, we ony focus on the throughput axiization of the acro ce, whie the users, which are ocated in ce-edge areas and cannot be covered by the acro ce, can be aternativey served by sa ces [] or reays []. The depoyent of sa ces or reays requires new design etrics other than the throughput, such as depoyent cost and icensing, which, is beyond the ain scope of this paper. which are defined by the users ocations described in detai in Definition. In parae, these key regions, and so are the corresponding paraeters, wi be deterined by the ce coverage. Considering hexagona ce shape and unifory distributed users, we first derive exact anaytica expressions for the average nuber of users, as we as, the probabiity density functions PDF of the distance distribution, for each of the above entioned key regions. Using these resuts, the generic ower bound can be speciaized; by axiizing this speciaized expression, we prove that the optia strategy of the ce coverage design in this scenario, is to guarantee that the coverage of different ces does not overap. Considering sectora ce shape and non-unifory distributed users, we derive exact anaytica expressions for the average nuber of users, as we as, the average user distance, for each of the above entioned key regions. Using these resuts, an anaytica approxiation of the syste throughput is proposed, based on which, we are abe to further squeeze the searching region of the optia coverage. It is shown that the syste throughput can be efficienty axiized, through one-diensiona ine search using the proposed approxiation; ost iportanty, the average throughput can be greaty iproved, copared with the setting where the ce coverage is fixed. The reainder of this paper is organized as foows: The syste ode is introduced in Section II, the throughput anaysis, as we as, the definition of the key regions, are then provided in Section III. Ce overage optiization for unifor and non-unifor user distributions is perfored in Section IV and V, respectivey. Our nuerica resuts are shown in Section VI, whie Section VII concudes the paper. II. SYSTEM MODEL We consider a three-ce assive MIMO network upink, 4 where the ce =,, is covered by a BS ocated at height h BS,, whie the BS is being equipped with tit-adjustabe antenna arrays which consist of N antennas. Therefore, there are totay N antennas in the hexagona ce. Further, we assue that there are K singe-antenna users siutaneousy transitting using space-division-utipeaccess SDMA in each ce. During the channe training phase, K orthogonapiotsareassignedtothe K usersineach ce, whie the sae set of piots is being reused aong a threeces.thesysteayoutisiustratedinfig.,wherewe use the shaded parts to denote the coveragearea of every ce, which is adjustabe according to the antenna tit. Moreover, the radius of the coverage area of the -th BS is denoted as r BS,, =,,, whie the coon radius of a ces 4 Note that the ter ce, which we wi be using in this paper, wi refer to a 0 sector. This is done to avoid introducing additiona notation. Nevertheess, our anaysis can be readiy extended to syste ayouts where ore ces are depoyed. With either hexagona or sectora shaped ces that wi be considered in the subsequent anaysis, the three-ce unit represents a baseine topoogy of arger ces. Thus, ater in Fig., we use the widey-used three-sectora hexagona ce as an exape ony for iustration purposes c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

4 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy N r r r r Fig. : Layout of a three-ce assive MIMO syste. which, in this figure, is defined as the distance between the center and the vertex of the hexagon is denoted as r. Now, we ode the N -sized upink channe between the BS in ce, and user k in ce {,,} as h k = P k β tit,φ k,θ k γ k g k where gk CN0 N,I N N is the i.i.d. fast fadingpart of the channe, βtit is the tit ange of BS, which deterines thecorrespondingcoverage,whie φ k and θ k arethe incident anges of user k in ce seen by BS, in the aziuth and eevation doains, respectivey. Moreover, Pk β tit,φ k,θ k is the coefficient of antenna gains, which can be cacuated via, and γk is the correspondingarge-scaefading coefficient caused by path oss, written as γ k = C PL d k α where d k is the distance between the k-th user in ce and the BS in ce, whie α is the pathoss coefficient,and C PL is a constant vaue deterined by the path oss ode that is used. According to [, Eq. ], as N, the asyptotic upink signa-to-interference ratio SIR of user k in ce can be written as SIR upink k R upink su N N = P k β tit,φ k,θ k γ k P k β tit,φ k,θ k γ k where the denoinator corresponds to the inter-ce interference caused by piot containation, assuing the k-th user in ce and share the sae piot sequence. Moreover, for the sake of sipicity, we do not consider any power contro scheein4andthetransitpowerfroausersisassued to be the sae. The su-throughput in bps/hz of a three ces is then written as K = og +SIR upink. 5 =k= k 4 Note that since a piot aocation strategy is not considered in this paper, a coon ter regarding the piot overhead, naey T T piot T, where T is the bock ength and T piot is the training ength, is oitted in 5 and henceforth for brevity. Note that the ce coverage optiization shoud be ipeented in a ong ter basis which ipies that the objective function, i.e. the su-throughput defined in 5, shoud be averaged over a possibe user ocations. On the other hand, the coverage of different ces can be optiized separatey for upink transission, since the BSs act as receivers, thereby causing no interference to each other in this scenario; as such, we can sipy focus on the average throughput of ony one ce denoted as ce hereafter, without oss of generaity, and the optiization probe can be described as [ K ] axe og +SIR upink k 6 k= s.t. r in r BS, r ax where r in and r ax are respectivey the iniu and axiu coverage of one BS. Assuption : The foowing assuptions are ade to sipify the anaysis. Note that the assuptions stated herein appy ony to soe specia scenarios in our subsequent anaysis. Uness otherwise specified, in the foowing sections, resuts without aking these assuptions are sti generic and can be appied to practica scenarios. We assue that the BS hight h BS, is sa copared with the ce radius. As such, the distance fro the k-th user in ce to BS, i.e., d k, is cacuated using ony the coordinates in the horizonta pane, whie h BS, is ignored in the cacuation. 5 Siiar to [7, Exape ], here we assue, for the sake of sipicity, that the tit-adjustabe antenna array has unifor gain over the span of its ain obe, i.e., for the users satisfying that d k r BS,, we et Pk β tit,φ k,θ k =. 7 On the other hand, for the users ocated outside of the -db ain obe, according to, the antenna gain is constant and can be written as P k β tit,φ k,θ k = SLL tot +A ax C. 8 SincethevaueofC PL inwinotaffecttheanaysis, hereafter we sipy set C PL = for the ease of description. III. THROUGHPUT ANALYSIS In this section, we anayze the ergodic throughput in ce, i.e., the objective in 6, aiing at representing it in ters of the user ocation distributions. This wi be the basis of our subsequent coverage anaysis. To proceed, we first introduce the foowing definition: 5 As wi be shown ater, ce coverage optiization deonstrates high superiority ainy in the scenarios where ost users are ocated in the ceedge region. As such, considering a typica ce configuration where the height ofthebsisapproxiatey 0,whietheceradiusis500,theerrorcaused by this sipification wi be sa enough to be ignored c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

5 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 4 BS BS Fig. : Iustration of the key regions in Definition. A A A A throughput of ce can be ower bounded by R su, R LB where su, K A og + +K og Ā + K K Ā C D +K A D Ñ KC K Ā C D +K A D Ñ 8 D E [γ k] k KĀ 9 Definition : We herein define the foowing key regions iustrated in Fig. : A : The region contains the users in ce, which are ocated within the coverage area of the BS in ce. Ā : The region contains the users in ce, which are ocated out of the coverage area of the BS in ce. A : The region contains the users in ce, which are ocated within the coverage area of the BS in ce. Ā : The region contains the users in ce, which are ocated out of the coverage area of the BS in ce. Hereafter, we use K A to denote the user set ocated within region A, whie A foows the definitions in Definition. The nuber of users in region A, i.e., the cardinaity of K A, wi be denoted as K A. Note that we have K A +K Ā = K 9 K A +K Ā = K. 0 Moreover,fork K Ā,thecorrespondingantennagainsP k we drop the paraeters of Pk β tit,φ k,θ k hereafter for brevity is C, according to ite in Assuption. Foowing the sae ine of reasoning, it aso hods that P k dbi = C, k K Ā. Now, for k K A or k K Ā, the SIR defined in 4 can be respectivey rewritten as where and SIR upink N k = D +D, for k K A SIR upink k = N D +D, for k KĀ N P kγ k 4 N Cγ k 5 D Pr{k K Ā }Cγ k 6 D Pr{k K A }Pkγ k. 7 With these definitions, we propose a ower bound for the objective function in 6 in the foowing theore: Theore : For the assive MIMO upink, the ergodic as D E[P k γ k ] k K A 0 Ñ E[P k γ k ] k KA Ñ E[γ k ] k KĀ. Proof: The ergodic throughput in ce can be rewritten [ K R su, E og k= +SIR upink k [ ] = K A E og +SIRk A ] +K E Ā [og +SIR k Ā ] 4 where E [ ] eans taking expectation with respect to the ocations of the users within both ces and. Note that for SIR k A and SIR k Ā, their denoinators are the sae as defined in and, whie the noinators are different, as defined in 4 and5, respectivey. We aso appy 7 bynotingthattheprobabiityin6and7canbecacuated as the ratio of nuber of users within the corresponding region overthetotanuberofusersk.finay,weusethefoowing Jensen s ower bounding technique: E [og + X ] og Y + E [ ]. 5 Y X Then, the theore is directy obtained. Reark : Note thattheore is given in a generic for, where we do not use any of the sipifications decared in Assuption. In Theore, the assive MIMO upink throughput is directy reated to ong-ter statistic paraeters, such as the average nuber of users in every key region, as we as, the distribution of the distance fro users to the BS, which are deterined by the user ocation distribution and can be easiy obtained at the BS by ong-ter easuring and estiation. In the foowing, we wi appy Theore to different typica ce shapes and user distributions, to obtain soe anaytica resuts for specific scenarios. IV. COVERAGE OPTIMIZATION FOR UNIFORM DISTRIBUTION OF USERS In this section, we speciaize the statistica expectation ters in 8 for a typica network structure with hexagona shaped ces and unifory distributed users, as described in c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

6 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 5 Assuption. After that, the optia r BS, is found for this scenario. Assuption Unifor Distribution of Users: The shape of the ces and the user ocations satisfy The ces are assued to be hexagona shaped. A users are assued to be unifory distributed in their corresponding ces. As such, due to the syetry of this syste ayout, the optia coverage areas i.e., r BS,, =,, of a three BSs wi be the sae. Thus, hereafter in this section, we drop the subscript in r BS,, and sipy use r BS to denote the paraeter to be optiized. A. Paraeter Specification for Throughput Anaysis We first speciaize the paraeters that are needed in cacuating 8, in the scenario described by Assuption. At first, we evauate the average nuber, as we as, the PDF of their distances to BS, of the users distributed in every key region defined in Definition. The resuts proposed in this subsection wi serve as a necessary basis of the subsequent rate anaysis. Proposition : With Assuption, the average nuber of users ocated in every key region defined in Definition can berespectiveyevauatedas6and7atthebottoofthis page, and K Ā = K K A 8 K Ā = K K A. 9 Proof: Under the assuption that the users are unifory distributed in the ces, the nuber of users in a region A is proportiona to the area of A, thus it can be obtained as K A = in K,K AA 0 A ce where A is the area of a region, whie A ce is the area of each rhobus ce, which is A ce = ce. Using 0 and, 6 and 7 are obtained using sipe but tedious geoetrica anipuation ethods, whie 8 and 9 are obtained by 9 and 0. Proposition provides exact anaytica expressions for the average nuber of unifory distributed users, for each of the key regions defined in Definition. Then, regarding the distributions of d k and d k, the foowing two eas are respectivey derived: Lea : The PDF of the rando distance between the vertex of one rhobus and a unifory distributed node in an adjacent rhobus, sharing the sae side but being with different orientation, is written as 0, x < f d k x = r 4x arccos x, r x r πx x arccos x, r < x πx x arccos x, < x r 0, x > r. Proof: We use the area-ratio approach used in [5], where the CDF of the distance between one fixed point and a unifory distributed point in a ce, can be written in the for of the ratio of two corresponding areas. The area of the rhobus ce was deterined in. On the other hand, the area of A can be deterined separatey as in at the botto of this page. Thus, the CDF of d k can be obtained by notingthat AA A ce,asdescribedin4seebottoofthenext page, and the corresponding PDF is derived by differentiating 4 with respect to x. Lea : The PDF of the rando distance between a unifory distributed node in a rhobus and its vertex, is K A = K K A = K K πr BS 6 arccos r r BS BS +r rbs 4 r, π, r BS r r < r BS r K, r BS > r 0, r BS K r BS arccos r r r BS BS 4 r, r+ π arccos r r BS BS r π 6 arccos r r BS BS + rbs, r BS 4 r r K r r < r BS r, r < r BS < rbs r K, r BS > r 6 7 AA = πd 4 πr 6 d d arccos d d 4 r arccos d + 4 π d d arccos d + d r d 4 r r, r < d d, < d r., c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

7 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 6 written as f d k x = 4πx, x < 4π x 8 xarccos x, x r 0, x > r. 5 Proof: The proof foows the sae ine of reasoning as that in the proof of Lea. Havingtheresutsin Proposition,LeaandLea in hand, we are now ready to proceed with deriving anaytica expressions for the expectation ters 9. These resuts are provided in the foowing proposition: Proposition : In the typica scenario under Assuption and Assuption, the expectation ters 9 can be anayticay evauated as 6 and 7 at the botto of this page, where G i x,i =,, are respectivey defined as G x C α,rx α 4 nc α,n,rx α n+ n=0 8 G x 4 nc α,n,rx α n+ 9 n=0 G x C α,r where x α + C α,n,rx α n+ n=0 40 C α,r π 4 α n n n r n C α,n,r 4 n n+ α n+. 4 On the other hand, Ñ and Ñ are respectivey written as Ñ = A ce AA H x r BS r in, / H x r in +H x rbs /, / H x +H x r /, r in r BS < r BS r x > r 4 Ñ = A ce A Ā / H x r BS +H x r /, r BS < H x r rbs, r BS r 0, x > r 44 where H x and H x are defined as H x C α,rx +α 45 H x 4 C α,rx +α + 4 n C α,n,rx n+α+. 46 n=0 Proof: See Appendix I. The paraeters derived in Proposition are in a copicated for, and so is the corresponding throughput ower bound in Theore ; however, the bound expression consists of ony eeentary functions. Thus, it wi be convenient to cacuate nuericay in practice in a far ore efficient anner co- F d k x = x arccos 0, x < r x 4 r, r x r x 4 r r + AA r BS =r A ce, r < x x + AA rbs = A ce, < x r, x > r x r πx π x arccos x + r πx 6 x arccos x + r 4 D = A ce A Ā D = A ce AA G x r / +G x r +G x r, r BS < r G x r rbs +G x r +G x r, r r BS r G x r BS +G x r, r < r BS G x r r BS, < rbs r 0, r BS > r 0, r BS < r G x rbs /r, r r BS r G x r / +G x rbs r, r < r BS G x r / +G x r +G x rbs, < rbs r G x r / +G x +G x r, r BS > r r c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

8 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 7 pared to tie-consuing Monte-Caro siuations. Nuerica resuts, which we wi show ater, deonstrate that this ower bound is capabe of capturing the exact changing trend of the ergodic su rate versus r BS. As such, it is usefu in the subsequent coverage optiization anaysis. B. Coverage Optiization Based on Theore and Proposition, we obtain the foowing coroary on the coverage optiization in the considered network with unifor distribution of users: Coroary : With the paraeters derived in Proposition, the optia r BS that axiizes the ergodic throughput ower bound proposed in Theore, is written as r opt BS =. 47 Proof: See Appendix II. Coroary indicates that for the considered network ayout with Assuption and Assuption, where the positions of a users are unifory distributed in hexagona shaped ces, the benefit gained fro enarging the coverage area of the BS which eans that ore edge users wi be covered, wi be ess than the rate oss caused by piot containation, which aso stes fro the coverage area enargeent. Thus, one guideine for ce panning in assive MIMO systes in this scenario, wi be that the coverage areas of different ces shoud not overap with each other. Note that the scenario considered in this section, is a sipified idea ode which is not appicabe for practica designs. Nevertheess, using this ode, we can theoreticay showcase the fundaenta tradeoff between serving ce-edge users and piot containation suppression. For ore practica scenarios with non-unit antenna gains and non-unifor user distributions, it can be anticipated that r opt BS ay be shifted fro. In the foowing, we wi show for ore generic networks, where the users are non-unifory distributed, that coverage optiization wi bring significant throughput gains. V. COVERAGE OPTIMIZATION FOR NON-UNIFORM DISTRIBUTION OF USERS It is not surprising that unifor user distribution eads to the concusion that non-overapping coverage shoud be optia. However, when the users are not unifory distributed, the optia coverage shoud be carefuy re-cacuated. In this section, we extend the anaysis to ore genera networks with non-unifor user distribution. For the ease of description of this scenario, we aso change the ce-shape assuption to be sectora shaped, which, is aso typica and widey adopted in the corresponding iterature [6]. The scenario considered in this section is suarized in the foowing assuption: Assuption Non-Unifor Distribution of Users: The ce shape and the user ocations distribution are respectivey deterined as: The ces are assued to be sectora shaped. The users are non-unifory distributed in each ce; aso, the user ocations s distributions are different aong a three ces. This wi be described by different nuber N BS r ce ce r N BS inner-ce region ce-edge region Fig. : Iustration of the inner-ce and ce-edge regions. of inner-ce and ce-edge users, as introduced in the foowing. Fortheeaseofanaysis,wefurtherdivideaceintotwo areas described in Fig. : the inner-ce area where d < r and the ce-edge area where r < d < r. For ce, the nuber of users in these twoareasaredenotedask inner andk edge,respectivey. As such, we have K = K inner +K edge. 48 Moreover, we assue that the users are unifory distributed in these two areas, respectivey. It is noted that with Assuption., overapping occurs ony aong the ce-edge regions in different ces, whie overapping wi not happen for the inner-ce regions. Thus, this definition of ce-edge and inner-ce areas is eaningfu and sufficienty reaistic in practice. A. Paraeter Specification for Throughput Anaysis Foowing the sae ethodoogy as in Section IV, we first derive exact anaytica expressions for the average nuber of users, as we as, the average distance to BS, for the users distributed in the key regions defined in Definition. These resuts serve as necessary basis for the foowing rate anaysis. Proposition : With Assuption, the average nuber of users ocated in every key region defined in Definition can be respectivey evauated as K A = K inner K A = K edge π +K edge α 49 α arccos α + 50 α α + α α + +arccos 4 α 4 α 4 α where we define α rbs, r 5 for brevity. Moreover, we have K Ā = K K A 5 K Ā = K K A. 5 Proof: Denoting the area of the inner-ce region as A inner, and the area of the ce-edge region as A edge, we can c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

9 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 8 respectivey evauate the as A inner = π r 54 A edge = π r. 55 On the other hand, using sipe geoetry, we can get AA = πα r 56 AA 57 = r α arccos α + α + α α α + +arccos 4 α 4 α 4 α 58 Then, the nuber of users in each region can be respectivey cacuated as K A = K inner +K edge AA A inner 59 A edge K A = K edge AA. 60 A edge Foowing the sae ine of reasoning as that used in proving Proposition, and using sipe geoetry, the proposition can be proved. In the foowing proposition, we derive the average distance fro the users distributed in every key region to BS. Proposition 4: With Assuption, and for the users distributed in every key region defined in Definition, their average distance to BS can be respectivey evauated as d = K inner K A + r K inner K A α α 6 r d = α r 6 where d E[d k ] for a k K A, is the average distance fro the users ocated in region A to BS, whie d, d and d are siiary defined. For the two ters d and d, their expressions becoe extreey copicated in this generic scenario, thus are oitted here; nevertheess, we wi give a brief description on the corresponding cacuation of these two ters, in the proof of this proposition. Proof: See Appendix III. The resuts fro Proposition and Proposition 4 are now directy appied to the rate anaysis. Note that the assuption of non-unifor distribution of users akes the optiization of r BS, uch ore copicated than that in the uniforydistributed scenario. For this reason, instead of using the ower bounding technique in Theore, we hereafter ake use of an approxiation of R su,, which is given in the foowing proposition: Proposition 5: For the assive MIMO upink, the ergodic su rate of the users in ce can be approxiated by 6 at the botto of this page, where the average nuber of users K A, K, K Ā A and K Ā are defined in Proposition, whie the average distances d, d, d and d can be obtained via Proposition 4. Proof: The proposition is obtained by sipy repacing the rando distance ters in the SIR ter in 4, with their statistica expectations. Itisnotedthat6isagenericresut,whichisnotrestricted to particuar ce shapes. 6 Further appying Proposition and Proposition to 6, the derived resut sti consists of ony eeentary functions, thus can be convenienty cacuated in practice. Most iportanty, our nuerica resuts in Section VI wi show that using the rate approxiation in Proposition 5 for ce optiization can provide significant throughput gains. B. Coverage Optiization The rate approxiation proposed in Proposition 5 is sti too copicated for the derivation of the exact optia soution of r BS,. However,as aforeentioned,it consists of ony eeentaryfunctions,thustheoptia r BS, canbeconvenienty obtained through one-diensiona ine searching. Moreover, withthehepof6,thesearchingrangeoftheoptia r BS, can be further squeezed, thereby aking the ipeentation of ce coverage optiization ore feasibe in practice. As a starting point and, without oss of generaity, we can ake the foowinggeneric assuption that d k is distributed in a range bounded as: 7 d,in d k d,ax. 64 Siiary, for d k we assue 0 d k d,ax The paraeters in 6 can be cacuated with Assuption. However, 6 itsef is generic. 7 The assuption that in, d,in < d,ax is reasonabe in practice. For exape, in the network described in Fig., where hexagon shaped ces are assued, we have d,in = and d,ax = r; whie in Fig., where sector shaped ces are considered, we have d,in = r and d,ax = r. R su, Rsu, approx K A og + d K α A d α α og +KĀ +K Ā C d + C d α K A d α α +K Ā C d c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

10 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 9 Agorith Practica ce coverage optiization. Set K A = 0,d A = 0. Set t = 0,T stat = T 0, where T 0 is a predefined tie interva for updating the ce coverage;. Whenauserkgetsaccessed,etK A = K A +,d A = d A +d k if k K A d k is the distance fro user k to the objective BS;. When t = T stat, cacuate the average distance d A = da K A. Then, use Proposition 5 and Coroary to deterine the optia coverage; 4. CoparethevauesofK A withthatintheprioroop. If the change is significant e.g., greater than α th % where α th is a predefined threshod, reduce T 0 ; siiary, if the change is non-significant, aintain or enarge the vaue of T 0 in Step and start the new oop. Cuuative probabiity ce ce Monte-Caro Anayt. resut Ce radius r Fig. 4: CDF of d k and d k in a network with hexagona shaped ces and unifory distributed users. Then, the foowing coroary can be obtained: Coroary : The optia r BS,, which axiizes the ergodic upink su rate approxiation 6, wi be within the interva in, d,in r opt BS, d,ax. 66 Proof: Fro 6, it is cear that when r BS, > d,ax, the ters K A, KA, as we as, d and d wi be fixed. As such, if r BS, keeps enarging, the ony ter which wi be affected in 6 wi be the interference ter caused by piot containation, i.e., D K A d α α +K Ā C d in the denoinator. Assuch, R su, wibedecreasingwithrespectto r BS,. On the other hand, when r BS, < in, the interference, d,in ter D in 6 wi be fixed; as such, it is easy to shown that R su, wi be increasing with respect to r BS, in this regie. As a concusion of this section, Proposition 5 provides an effective objective function whie Coroary further squeezes the searching range within which this objective function can be axiized. With these resuts in hand, the optia r BS, can be easiy found by sipe one-diensiona ine searching techniques. Based on Proposition 5 and Coroary, we propose a ce coverage optiization schee which can be easiy ipeented in practice, as described in Agorith. Our nuerica resuts wi show that the proposed schee significanty iproves the syste throughput, copared with fixed ce coverage. VI. NUMERICAL RESULTS As a necessary basis of the subsequent siuations, we first need to nuericay vaidate the resuts derived in Leas,, as we as, the resuts in Propositions,, and 4. At first, the CDFs of d k and d k are shown in Fig. 4, where the ce radius is set to be r = 500, and the curves are respectivey obtained by both Monte-Caro siuations and the anaytica expressions in Leas and. An exact atch between the Monte-Caro and the anaytica resuts can be observed. Recaing the proofs of Lea, Lea and Proposition, the average nubers of users described in 6 and 7, can be directy reated to the PDFs described in and 5. As a consequence, Fig. 4 aso does prove the accuracy of Proposition. Nuber of users Monte-Caro Anayt. resut A r BS, Fig. 5: The average nuber of users vs. r BS, in a network with sectora shaped ces and non-unifory distributed users. Then, we vaidate Proposition 4 by depicting the average nuber of users in regions A and A, versus the vaue of r BS, in Fig. 5. We set r = 500 and K = 00 in the siuation. Again, a perfect atch between the Monte-Caro and anaytica resuts is shown. Moreover,as r BS, increases, the average nubersof users in regions A and A are both increasing, which indicates that whie serving ore users in ce, BS wi face ore interference fro ce. As a consequence, an optiu coverage which is abe to strike a coproise between these contradicting effects does exist, as wi be shown ater. InFig.6,wecoparetheMonte-Caroresutwiththeower A c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

11 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 0 Ergodic throughput in ce bps/hz Monte-Caro Lower bound Approx. Average throughput in ce bps/hz Monte-Caro Approx. r BS, = r r BS Fig.6:Ergodicthroughputince vs. r BS inanetworkwith hexagona shaped ces and unifory distributed users α inner Fig. 7: Throughput in ce vs. α inner in a network with sectora shaped ces and non-unifory distributed users. bound Theore and the approxiation Proposition 5 of the ergodic throughput in ce, vs. the coverage area of the BSs, i.e., r BS. In the siuation, we set r = 500, K = 0. Assuing unit power gains within the BS coverage area and 0dB outside that coverage, the Monte-Caro resut is cacuated directy using the SIR definition in 4, averaged over 500 ties of rando generations of the users positions. Itisshownthattheowerbound,asweas,theapproxiation are abe to refect the sae changing trend as the Monte- Caro resut, thus are quaified to be used in the coverage optiization design. Note that the tightness of the ower bound is different at different vaues of r BS ; this is because the bounding technique in 5 has been respectivey appied to two weighted ters as shown in 4; with different vaue of r BS, the weight of these two ters, naey K A and K A, wi be different, thus eading to different tightness of the cobined ower bound. Nevertheess, it is shown that a curvesachievetheiraxiuatthesaevaueofr BS,which is about 4 as shown in the figure. This resut, which is in fact r, coincides perfecty with our anaysis and the resuts drawn in Coroary. In Fig. 7, the achievabe upink throughput in ce is depicted versus α inner, where α inner Kinner 67 K is the paraeter indicating the user distribution in ce. When α inner =, it eans that a users in ce are ocated in the inner-ce regions, thereby causing the east piot containation to the users in ce ; on the other hand, when α inner = 0, a users in ce are ocated in the ceedge region, and the syste perforance wi be severey degraded by piot containation. In the siuation, we assue that the users in ce are unifory distributed, i.e., α inner = Ainner A ce.inthefigure,differentresutsareshownwhen the ce coverage is fixed to be r BS, = r, for =,,, as we as, the setting where the ce coverage is adjustabe accordingtothechangingoftheuserdistributions,i.e., α inner. Moreover, for the coverage-adjustabe setting, we copare the Monte-Caro resutwhere the searching is carried out directy using and the one-diensiona ine searching using the approxiation proposed in Proposition 5. It is shown that6 in Proposition 5 is a very effective etric, which eads to neary the sae goba optiu achieved by tedious Monte- Caro siuation. Most iportanty, the graph deonstrates that coverage optiization resuts in significant gains in the syste throughput, copared with the conventiona setting where the coverage is fixed. Specificay, when the vaue of α inner is sa, i.e., ore interfering users are ocated in the ce-edge regions of the adjacent ces, the gains brought by ce coverage optiization becoe substantia. As anticipated, when α inner grows arge, the benefits of coverage optiization are decreasing, since piot containation vanishes. We now show the optia ce coverage for different user distribution conditions, deterined by both α inner and α inner in Fig. 8. The resuts indicate that when the nuber of ce-edge users increases in adjacent ces, i.e., when α inner decreases, the optia coverage of ce shoud be reduced. On the other hand, with increasing α inner, i.e., ore innerce users in ce, the optia coverage of ce aso decreases. Note that the optia coverage is aways ess than r = 500, which confirs our concusion drawn fro Coroary. Essentiay, it indicates that if the throughput is axiized for the acro ces, the ce-edge users, which are ocated in the center region of the three-ce unit shown in Fig., wi not be covered by any of these ces. As such, sa ce stations are necessary to be paced in this area to provide seaess coverage of the entire network. At ast, we appy the ce coverage optiization Agorith to a practica network, where a typica 9-ce network is considered, as shown in Fig. 9. In the figure, we use back dots to denote the positions of the BSs, each consisting of three 0 sectora antenna arrays ipeented with arge but finite nuber of antennas, i.e., fro 00 to 500. In c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

12 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy 0 opt r BS, α inner α inner Fig. 8: Optia ce coverage vs. α inner and α inner in a network with sectora shaped ces and non-unifory distributed users. coordinate y coordinate x Fig. 9: Layout of the 9-ce network with randoy ocated users. every sector, 0 users are non-unifory ocated and the users beong to different sectors are described respectivey using circe, triange and x-ark in the figure. The user ocation distribution is deterined by the nuber of inner-ce and ceedge users as described in Fig., which, are independenty and randoy generated aong different sectors as we as different siuation trias. In Fig. 0, we evauate the average throughput of the centra ce aong a 9 ces using Monte-Caro siuation. The throughput is potted versus increasing nuber of antennas. As a benchark, a reference coverage deterination ethod abeed as no overap in the figure, which sipy deterines the coverage of every sector to avoid overapping, is Average throughput per ce bps/hz Agorith No overap Nuber of antennas per sector Fig. 0: Average throughput per ce vs. nuber of antennas per sector. aso iustrated. It is shown that the proposed ce coverage optiization agorith significanty increases the throughput. As anticipated, the throughput increent gets arger as the nuber of antenna increases, for the reason that our agorith is designed based on the asyptotic rate approxiation with an infinite nuber of antennas. As a ast coent, we ephasize the ipact of nuber of antennas on our proposed agorith. With the assuption of an infinite nuber of antennas, interference ony coes fro piot containation caused by the users who are using the sae piot in adjacent ces or sectors. On the other hand, with finite nuber of antennas, interference aso coes fro the other users in the sae ce, and a users in adjacent cesassuing a frequency reuse factor. Since our agorith is based on the asyptotic assuption, the finiteantenna interference is ignored in the design. However, we note that with arge but finite nuber of antennas such as as shown in Fig. 0, the utua interference between two independent wireess inks is anyways very sa abeit notzero,which,onyhodsforthe extreecase. Inthisfinite antenna regie, considering ony the piot-containating user, other than a users in adjacent ces, is a reasonabe choice when perforing ce coverage optiization. Athough the achievabe throughput is uch ess than that of the infiniteantenna case, the resut in Fig. 0 ceary shows that significant gains can sti be reaized by the proposed agorith with arge but finite nuber of antennas. VII. CONCLUSIONS In this paper, ce coverage optiization was investigated in the assive MIMO upink. We first foruated a detaied description of this iportant optiization probe, where it was pointed out that the syste throughput wi be deterined by the user distributions in soe key geoetrica regions. The foruated probe was then appied to different practica scenarios. For a network with hexagona shaped ces and unifory distributed users, an anaytica ower bound of the c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

13 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy ergodic su rate in the objective ce was derived, based on which it was proved that the optia choice for the ce coverage shoud ensure that the coverage of different ces does not overap. For a ore generic network with sectora shaped ces and non-unifory distributed users, we proposed an anaytica approxiation of the ergodic su rate; after that, the optia soution can be easiy obtained through a sipe one-diensiona ine searching within a bounded searching region. Our nuerica resuts showcased that the proposed coverage optiization ethod can substantiay increase the syste throughput for the assive MIMO upink transission, copared with the traditiona schee where the ce coverage is fixed. APPENDIX I PROOF OF THEOREM Starting with evauating D, we have dā,ax r D = PLxf Ā xdx = d Ā,in r BS x xdx αfā 68 where d Ā,in and d Ā,ax are the iniu and axiu distances between the users in the region Ā and BS, respectivey; PLx is the function of path oss defined in, whie f Ā x f d k x for k KĀ = Pr d k = x k KĀ 69 Pr d k = x,k KĀ f d = = k x Pr k K A / Ā 70 Ā Ace is the PDF of d k conditioned on that the objective user is ocatedintheregie Ā.To continueevauating68, weake use of Lea, and introduce the infinite series expansion of arccosx such that arccosx = π n nx n+ n=0 4 n n+, for theeaseofanaysis.then,theindefiniteintegraof x f α Ā x can be derived as 0, x < r G x, xdx = r x r x αfā G x, r < x 7 G x, < x r 0, x > r where G i x,i =,, were defined in Then, 6 can be directy obtained by appying 7 to 68. Note that D can be obtained on a siiar note. Then, we seek to evauate Ñ and Ñ. We first evauate the foowing indefinite integra as H x, x < x α f d xdx = 7 H x, x r 0, x > r where H x and H x were defined in 45 and 46. Then, the foowing proof foows the sae ine of reasoning as that used before, which eads us to 4 and 44. APPENDIX II PROOF OF COROLLARY First, consider the regie where r BS, then 8 can be sipified as 7 at the botto of this page, where C = C G x r / + G x r + G x r is a constant which is independent of r BS. Then, we investigate the onotonicity of 7 by taking the derivative with respect to r BS. By doing so, it can be shown that in the regie r BS, RLB su, is onotonousy increasing. Siiary, in the regie where r BS >, RLB su, is decreasing. The derivation is trivia thus is oitted here. APPENDIX III PROOF OF PROPOSITION 4 In order to evauate d, we first define the foowing user sets: we use k K to denote the users ocated within the inner-ce region, whie using k K to denote the users ocated in the region A A edge. Then, d can be written that [ ] d E[d k] = Pr{k K k K A }E +Pr{k K k K A }E d k [ ] d k. 74 For user k who is ocated in region A, it is easy to show that Pr{k K k K A } = K inner K A 75 Pr{k K k K A } = K inner K A. 76 Ontheotherhand,thePDFof d k and d k can be obtained using the[ ethod ] introduced [ in] the proof of Leas and. Then, E d k and E d k can be respectivey evauated as [ ] E d k = r 77 [ ] E d k = α r. 78 R LB su, = K A og + +K A C ce AA H x og rbs Ā + r in A C ce H x AĀ C / 7 r in +H x r / c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.

14 This artice has been accepted for pubication in a future issue of this journa, but has not been fuy edited. Content ay change prior to fina pubication. Citation inforation: DOI 0.09/TVT , IEEE Transactions on Vehicuar Technoogy According to 74, 77 and 78, 6 can be obtained. On a siiar note, we obtain 6. The aforeentioned derivation of d and d requires ony sipe geoetrica cacuation in sectora areas. However, for the two regions defined in ce, i.e., A and Ā, the corresponding cacuation becoes ore copicated. In the foowing, we give a brief introduction to the derivation, whie the detaied resuts wi be oitted here, for the reason that they are in very tedious fors whie itte insight can be provided. At first, with the network ayout described by Fig., the area of the region A defined in Definition, can be derived as AA = rbs, θ r BS, +r h +r rbs, φ +r h 79 where r BS, +r θ arccos r BS, 4r rbs, φ arccos 80 8 h r BS, sinθ. 8 On the other hand, the area of the overapping region described in Fig. can be cacuated as π A overap r. 8 Assuing that r BS, fas into the ce-edge region, the CDF of d k, which is the rando distance fro the user distributed in region A to BS, can be written as F d k x = AA rbs,=x A overap. 84 Taking the derivative of 84 with respect to x, we get the PDF of d k. After that, the anaytica expression of d can be cacuated as d = rbs, r xf d k xdx. 85 At ast, the ter d depends on both the inner-ce and ce-edge regions, which akes a direct cacuation even ore chaenging. As such, we ake the foowing sipification in the derivation: in the considered network ayout, it is reasonabe to assue that the average distances to BS fro the users within either the inner-ce regions, or the ceedge regions, are pre-known syste paraeters, and we denote theasd,edge andd,inner respectiveyinthefoowing.then, the average distance to BS, fro a users in ce, can be obtained as d,ce K K edge d,edge +Kinner d,inner. 86 On the other hand, d,ce can be aternativey evauated as d,ce = K A K d +K Ā d. 87 As such, once d is obtained through85, we can obtain d straightforwardy using 87. REFERENCES [] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, Scaing up MIMO: Oppertunities and chaenges with very arge arrays, IEEE Signa Process. Mag., vo. 0, no., pp , Jan. 0. [] T. L. Marzetta, Noncooperative ceuar wireess with uniited nubers of base station antennas, IEEE Trans. Wireess Coun., vo. 9, no., pp , Nov. 00. 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Andrews, Fundaenta iits of cooperation, IEEE Trans. Inf. Theory, vo. 59, no. 9, pp. 5 56, Sep. 0. Shi Jin S 06-M 07 received the B.S. degree in counications engineering fro Guiin University of Eectronic Technoogy, Guiin, China, in 996, the M.S. degree fro Nanjing University of Posts and Teecounications, Nanjing, China, in 00, and the Ph.D. degree in counications and inforation systes fro the Southeast University, Nanjing, in 007. Fro June 007 to October 009, he was a Research Feow with the Adastra Park Research Capus, University Coege London, London, U.K. He is currenty with the facuty of the Nationa Mobie Counications Research Laboratory, Southeast University. His research interests incude space tie wireess counications, rando atrix theory, and inforation theory. He serves as an Associate Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, IEEE COMMUNICA- TIONS LETTERS, and IET COMMUNICATIONS. Dr. Jin and his co-authors have been awarded the 0 IEEE Counications Society Stephen O. Rice Prize Paper Award in the fied of counication theory and a 00 Young Author Best Paper Award by the IEEE Signa Processing Society. Michai Matthaiou S 05 M 08 SM was born in Thessaoniki, Greece in 98. He obtained the Dipoa degree 5 years in Eectrica and Coputer Engineering fro the Aristote University of Thessaoniki, Greece in 004. He then received the M.Sc. with distinction in Counication Systes and Signa Processing fro the University of Bristo, U.K. and Ph.D. degrees fro the University of Edinburgh, U.K. in 005 and 008, respectivey. Fro Septeber 008 through May 00, he was with the Institute for Circuit Theory and Signa Processing, Munich University of Technoogy TUM, Gerany working as a Postdoctora Research Associate. He is currenty a Senior Lecturer at Queen s University Befast, U.K. and aso hods an adjunct Assistant Professor position at Chaers University of Technoogy, Sweden. His research interests span signa processing for wireess counications, assive MIMO, hardwareconstrained counications, and perforance anaysis of fading channes. Dr. Matthaiou is the recipient of the 0 IEEE CoSoc Best Young Researcher Award for the Europe, Midde East and Africa Region and a co-recipient of the 006 IEEE Counications Chapter Project Prize for the best M.Sc. dissertation in the area of counications. He was corecipient of the Best Paper Award at the 04 IEEE Internationa Conference on Counications ICC and was an Exepary Reviewer for IEEE COMMUNICATIONS LETTERS for 00. He has been a eber of Technica Progra Coittees for severa IEEE conferences such as ICC, GLOBECOM, VTC etc. He currenty serves as an Associate Editor for the IEEE TRANSACTIONS ON COMMUNICATIONS, IEEE COMMUNICATIONS LETTERS and was the Lead Guest Editor of the specia issue on Large-scae utipe antenna wireess systes of the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. He is an associate eber of the IEEE Signa Processing Society SPCOM and SAM technica coittees. JueWangS 0-M 4received the B.S.degree in counications engineering fro Nanjing University, Nanjing, China, in 006, the M.S. degree and Ph. D. degree fro the Nationa Counications Research Laboratory, Southeast University, Nanjing, China, respectivey in 009 and 04. In 04, he joined the Schoo of Eectronic and Inforation Engineering, Nantong University. Meanwhie, he is with Singapore University of Technoogy and Design SUTD as a post-doctora research feow. His research interests incude MIMO wireess counications, utiuser transission, MIMO channe odeing, assive MIMO systes and physica ayer security. Qiang Sun S 0 received the Ph.D. degree in Counication and Inforation Syste fro Southeast University, Nanjing, China, in 04. He joined the Schoo of Eectronic and Inforation Engineering, Nantong University, Nantong, China, in Apri 006. Now he is a ecturer of inforation systes and counications. His current research interests incude assive MIMO and sa ce networks. Xiqi Gao SM 07 F 4 received the Ph.D. degree in eectrica engineering fro Southeast University, Nanjing, China, in 997. He joined the Departent of Radio Engineering, Southeast University, in Apri 99. Since May 00, he has been a professor of inforation systes and counications. Fro Septeber 999 to August 000, he was a visiting schoar at Massachusetts Institute of Technoogy, Cabridge, and Boston University, Boston, MA. Fro August 007 to Juy 008, he visited the Darstadt University of Technoogy, Darstadt, Gerany, as a Hubodt schoar. His current research interests incude broadband uticarrier counications, MIMO wireess counications, channe estiation and turbo equaization, and utirate signa processing for wireess counications. He serves as an Associate Editor for the IEEE TRANSACTIONS ON SIGNAL PROCESSING and the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. Dr. Gao received the Science and Technoogy Awards of the State Education Ministry of China in 998, 006 and 009, the Nationa Technoogica Invention Award of China in 0, and the 0 IEEE Counications Society Stephen O. Rice Prize Paper Award in the fied of counications theory c 0 IEEE. Persona use is peritted, but repubication/redistribution requires IEEE perission. See for ore inforation.