MULTI-INPUT multi-output (MIMO) communication is

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST Coverage Performance n Multstream MIMO-ZFBF Heterogeneous Networks Mohammad G. Khoshkholgh, Kang G. Shn, Lfe Fellow, IEEE, Kevan Navae, Senor Member, IEEE, and Vctor C. M. Leung, Fellow, IEEE Abstract We study the coverage performance of multantenna [multple-nput multple-output MIMO] communcatons n heterogeneous networks HetNets. Our man focus s on open-loop and multstream MIMO zero-forcng beamformng at the recever. Network coverage s evaluated adoptng tools from stochastc geometry. Besdes fxed-rate transmsson FRT, we also consder adaptve-rate transmsson ART whle ts coverage performance, despte ts hgh relevance, has so far been overlooked. On the other hand, whle the focus of the exstng lterature has solely been on the evaluaton of coverage probablty per stream, we target coverage probablty per communcaton lnk comprsng multple streams whch s shown to be a more conclusve performance metrc n multstream MIMO systems. Ths, however, renders varous analytcal complextes rooted n statstcal dependence among streams n each lnk. Usng a rgorous analyss, we provde closedform bounds on the coverage performance for FRT and ART. These bounds explctly capture mpacts of varous system parameters ncludng denstes of BSs, SIR thresholds, and multplexng gans. Our analytcal results are further shown to cover popular closed-loop MIMO systems, such as egen-beamformng and spacedvson multple access. The accuracy of our analyss s confrmed by extensve smulatons. The fndngs n ths paper shed lght on several mportant aspects of dense MIMO HetNets: frst, ncreasng the multplexng gans yelds lower coverage performance; second, densfyng network by nstallng an excessve number of low-power femto BSs allows the growth of the multplexng gan of hgh-power, low-densty macro-bss wthout compromsng the coverage performance; and thrd, for dense HetNets, the coverage probablty does not ncrease wth the ncrease of deployment denstes. Index Terms Coverage probablty, densfcaton, heterogeneous cellular networks HetNets, multple-nput multple-output MIMO systems, Posson pont process PPP, stochastc geometry, zero-forcng beamformng ZFBF. Manuscrpt receved Aprl 29, 216; revsed September 13, 216 and November 28, 216; accepted December 27, 216. Date of publcaton January 1, 217; date of current verson August 11, 217. Ths work was supported n part by a UBC Four Year Doctoral Fellowshp, by the Canadan Natural Scences and Engneerng Research under Grant RGPIN and Grant RGPAS , by the Natonal Scence Foundaton under Grant CNS and Grant CNS , and by the Natonal Natural Scence Foundaton of Chna under Grant The revew of ths paper was coordnated by Prof.Y.L.Guan. M. G. Khoshkholgh and V. C. M. Leung are wth the Department of Electrcal and Computer Engneerng, Unversty of Brtsh Columba, Vancouver, BC V6T 1Z4, Canada e-mal: m.g.khoshkholgh@gmal.com; vleung@ece.ubc.ca. K. G. Shn s wth the Department of Electrcal Engneerng and Computer Scence, Unversty of Mchgan, Ann Arbor, MI USA e-mal: kgshn@umch.edu. K. Navae s wth the School of Computng and Communcatons, Lancaster Unversty, Lancaster LA1 4WA, U.K. e-mal: k.navae@lancaster.ac.uk. Color versons of one or more of the fgures n ths paper are avalable onlne at Dgtal Obect Identfer 1.119/TVT I. INTRODUCTION MULTI-INPUT mult-output MIMO communcaton s a promsng technology due to ts potental of achevng hgh spectral effcency and relablty often wthout requrng hgh transmsson power [1]. Supported by decades of thorough nvestgatons, MIMO communcatons have thus far been emboded n multple IEEE standards as well as 3GPP LTE-Advanced [2]. To cope wth the rapd growth of wreless traffc demand [3], MIMO technologes have been re-emergng through copous nnovatve deas. Thus, pervasve explotatons of sophstcated MIMO technologes n conuncton wth unprecedented densfcaton n heterogeneous networks HetNets are envsoned as the man desgn paradgm n next-generaton cellular communcaton systems [4], [5]. There has been extensve research on the applcaton of MIMO n HetNets, manly focusng on solated scenaros e.g., [6]; for example, by evaluatng the performance of femtocells overlayng/underlayng macrocells. Ths lne of research, however, falls short of characterzng the network-wse performance of MIMO n HetNets. Network-wse performance s of utmost mportance when t comes to desgn and mplementaton of large-scale communcaton systems wth mllons of nodes. Ths shortcomng s rooted n the smplfed and often unrealstc assumptons made on the ncorporaton of ntercell nterference ICI n system analyss. As a result, whle n a sngle-cell system, allocatng the system resources s rather straghtforward, the same cannot be drectly appled n the network-wse performance context. For nstance, n a sngle-cell system, decsons such as the number of antennas to be swtched on/off, the number of user equpments UEs to be concurrently served, or choosng between multplexng usng antennas for ncreasng data rate and dversty usng antennas for ncreasng relablty are easy to make [1], [7], whereas n a multcell network, such decsons need sophstcated solutons ncorporatng the ntercell mpact based on network-wse performance metrcs. Whle ncreasng the number of transmtted data streams.e., ncreasng the multplexng gan n a sngle-cell system s locally optmal, t ncreases the ICI, almost wth the same order, whch could offset the effect of the former. It s, therefore, debatable whether strateges yeldng hgher capacty or better coverage from the perspectve of local decsons solated scenaros result n network-wse optmalty. One approach to capture the network-wse effects of adoptng MIMO s to employ analytcal tools from stochastc geometry, see, e.g., [8], [9], and references theren. Such technques IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See standards/publcatons/rghts/ndex.html for more nformaton.

2 682 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 are wdely used n modelng and analyzng ad hoc and sensor networks [1] [12], and recently n cellular communcatons [13]. Some researchers, however, have casted skeptcsm on the accuracy of Posson pont process PPP for modelng the locatons of macro-bss [14]. Ths s because PPP models poston the BSs n the network plane almost ndscrmnately, whereas n practce, macro-bss are often placed far from each other. Ths ssue s nvestgated further n [13], where the PPP assumpton s shown to result n adequately precse characterzaton of macro-bss, and n fact, provdes a rather pessmstc bound on the coverage performance n contrast to other analytc methods such as hexagonal and lattce models, see, e.g., [15] that provde optmstc bounds. The PPP models have also been wdely used for modelng and analyzng HetNets, e.g., [16] [18]. The poneerng work n [16] proposed a flexble approach n modelng K-ter HetNets 1 through K ters of ndependent PPPs. In ths paper, we extend the approach descrbed n [16] to multstream MIMO HetNets and nvestgate ther coverage performance. Our focus s on open-loop MIMO zero-forcng beamformng MIMO-ZFBF, whch s practcally attractve due to ts straghtforward mplementaton, low computatonal complexty, and almost zero feedback overhead. The network-wse performance of MIMO-ZFBF, as well as other pertnent MIMO technques, s nevertheless extensvely studed n the context of ad hoc networks, see, e.g., [19] [24]. The research work of Loue et al. [2] s practcally relevant to ths paper as ther focus s also on open-loop MIMO, such as ZFBF. Several advantages of ZFBF n enhancng the coverage performance of ad hoc networks were hghlghted there, and multstream communcatons were proven to outperform deal sngle-stream ad hoc networks for practcal settngs. In lght of the above fndngs n the context of ad hoc networks, one may argue that the same trends can hold n MIMO HetNets by notcng the convergence, albet partal, of HetNets toward ad hoc networks, for nstance through random nstallaton of remote antenna ports, relays, and small cells. Apart from such analoges, there exst sgnfcant dscrepances between these two networks manly due to the correspondng CA mechansms governng HetNets, as well as centralzed TDMA/FDMA MAC protocols. It s, therefore, necessary to nvestgate whether or not multstream MIMO schemes are of practcal sgnfcance n enhancng the coverage performance of HetNets? It s equally mportant to understand whether n MIMO HetNets, cell densfcaton and hgh multplexng gans should be practced smultaneously n all ters? If not, new technques are needed to evaluate whether for a gven settng excessve densfcaton s preferable to ncreasng multplexng gans? Despte sgnfcant progress n analyzng MIMO communcatons n HetNets, the exstng results are nadequate to comprehensvely address the above concerns and other smlar questons. To address ths nadequacy, we derve closed-form bounds on the coverage performance of MIMO communcatons. The 1 K-ter HetNets consst of K spatally and spectrally coexstng ters, each wth ts own BS. thus-obtaned analytcal results enable thorough nvestgaton of densfcaton and multplexng gans n MIMO HetNets. A. Related Work Chandrasekhar et al. [25] consdered MIMO-based HetNets where a sngle-macrocell system overlad by a number of multantenna femtocells was nvestgated. The system mentoned n [25] adopts spatal-dvson multple access SDMA beamformng and n each cell, a number of UEs, each wth a sngle antenna, are served. For ths confguraton, Chandrasekhar et al. [25] show that the system acheves a hgher area spectral effcency by solely servng one UE per femtocell va conventonal beamformng. The results gven n [25] are extended n [26] to K-ter mult-nput sngle-output MISO HetNets, under the assumpton of the maxmum SIR CA rule. By comparng the coverage probablty, Dhllon et al. [26] showed that SDMA s nferor to the schemes whch support one UE per cell. Ths concluson s also confrmed n [27] for a clustered ad hoc network wth quantzed beamformng. Area spectral effcency of MISO-SDMA systems s studed n [28] and [29] assumng range expanson CA rule, where UEs are assocated wth the BS wth the smallest path loss. In [28] and [29], algorthms for optmzng the system spectral effcency have been provded. A number of approaches have been outlned n [3] pavng the way of effectve constructon of scales n range expanson for MISO-SDMA systems. The bt-error probablty of zero-forcng ZF precodng wth the ad of modelng ICI through a properly ftted Gaussan dstrbuton s derved n [31]. In [32] and [33], the outage performance of dfferent recever technques wth the range expanson method as the assocaton rule has been studed. The postprocessng SIR n MIMO communcatons often nvolves Nakagam-fadng-type fluctuatons. In ths regard, the studes n [34] and [35] are closely related to ths paper. Tanbourg et al. [34] provded results on the coverage probablty of optmal combnng recever under Nakagam fadng channels n ad hoc networks, whch are not drectly extendable to the cellular systems. Furthermore, an analytcal framework s developed n [35] by whch varous functons of nterference processes n Posson network can be characterzed. Schlcher et al. [35] also derved the outage probablty n a system wth Nakagam fadng n ad hoc networks. Open-loop orthogonal space-tme codes are the focus of analyss n [32], where only one multantenna UE s consdered per cell. In [32], two recever technques are consdered based on cancelng and gnorng the ICI. Formulas for the probablty of coverage are provded for both cases n [32]. Focusng on the sngle-ter systems, mnmum mean square estmaton MMSE and partal ZF PZF beamformng schemes are then nvestgated n [33], where both MMSE and PZF are shown to be effectve n cancelng domnant nterferers. B. Man Contrbutons and Organzaton of the Paper Unlke the exstng MIMO HetNets whch manly focus on range expanson see, e.g., [28], [3], [32], and [33], we focus on the CA rule based on the strongest nstantaneous re-

3 KHOSHKHOLGH et al.: COVERAGE PERFORMANCE IN MULTISTREAM MIMO-ZFBF HETEROGENEOUS NETWORKS 683 ceved power as n [16] and [26]. It s mportant to note that the CA rules descrbed n [28], [32], and [33] are equvalent to ther counterpart n sngle-antenna regmes, see, e.g., [13], [18], and [36], and thus overlook the key MIMO characterstcs ncludng multplexng and dversty n the CA stage. Such lmtatons are allevated when the nstantaneous receved power s consdered as the value of SIR explctly and accurately captures the nterplays exstng among dversty, multplexng, and ICI n MIMO communcatons. Extenson of ths rule to multstream MIMO s, however, nontrval, snce UEs should stay assocated wth the same BS on all the streams. In ths paper, we also ntroduce analytcal technques that effectvely deal wth these requrements. In exstng ad hoc networks and MIMO HetNets, only fxedrate transmsson FRT s consdered. Ths s nadequate to analyze HetNets where BSs can adaptvely schedule data among the streams. To the best of our knowledge, the network-wse performance of adaptve-rate transmsson ART s nvestgated n ths paper for the frst tme. To analyze ART, the statstcs of the aggregated scheduled data rate on the streams s requred n whch mathematcal tractablty s a challengng task whch we address n ths paper. Note, also, that whle only the coverage probablty per data stream has been studed n the related lterature, here, we evaluate the coverage probablty per communcaton lnk runnng multple streams. From an analytcal vewpont, the streams SIR n a communcaton lnk are statstcally dependent. Therefore, 1 the exstng results of dealng wth the former metrc are not generally extensble for studyng the performance of FRT and ART; 2 the analytcal evaluaton of the latter metrc s much more complcated than the former, and 3 the former s unable to provde the whole pcture of the performance of MIMO communcatons. Our results ndcate that by varyng system parameters, there are sgnfcant dscrepances between these two metrcs. Fnally, the coverage probablty bounds provded n [22], [26], [28] [3], [32], and [33] do not clearly nterpret the mpact of system parameters on the coverage performance, and also requre calculaton of hgh-order dervatves of the ICI Laplace transform whch adds further analytcal complcatons. One dstnct feature of our approach s the dervaton of an analytcal bound on the coverage probablty that provdes quanttatve nsght n the mpact of key system parameters on the FRT and ART performance. In partcular, our fndngs suggest the followng. 1 As a rule of thumb, ncreasng multplexng gans reduces the coverage performance, partcularly when the network s sparse,.e., low densty of the BSs. 2 For dense networks where BSs are densely populated n the coverage area, there exst scenaros n whch ncreasng the densty of BSs as well as the multplexng gans does not degrade the coverage performance. In fact, f densfcaton s practced n low-power ters, t allows the growth of the multplexng gans of hgh-power lowdensty macro-bss, wthout compromsng the coverage performance. In partcular, ths fndng has a sgnfcant economcal sgnfcance n desgnng cost-effectve Het- Nets n the evoluton phase. 3 The ART coverage performance s much hgher than that of FRT s, whle ts sgnalng overhead s manageable. Ths s an mportant practcal fndng as a sgnfcant coverage performance can be acheved wth a low sgnalng overhead and smple transmtters/recevers, e.g., openloop ZFBF, wthout any need to acqure channel matrces. Ths s mport n ultradense networks whch are vulnerable to feedback overhead, plot contamnaton, and complexty of the MIMO technques. Although our man focus s on the open-loop ZFBF, we wll later extend our analyss to some mportant closed-loop cases such as egen beamformng [.e., maxmum rato transmsson MRT] and MISO-SDMA wth ZFBF at the transmtters, where analytcal results on ther assocated coverage performance are n general unavalable [26]. The rest of ths paper s organzed as follows. The system model and man assumptons are presented n Secton II. Coverage performances of FRT and ART are then analyzed n Secton IV. We then present an extenson of analyss to several mportant MIMO scenaros n Secton V followed by numercal analyss and smulaton results n Secton VI. The paper s concluded n Secton VII. II. SYSTEM MODEL Consder downlnk communcaton n heterogeneous cellular networks HetNets comprsng K 1 ters of randomly located BSs. The BSs of ter Kare spatally dstrbuted accordng to a homogenous PPPΦ, wth spatal densty λ, where λ s the number of BSs per unt area [16]. We further assume that Φ s, Kare mutually ndependent. In ths model, each ter s fully characterzed by the correspondng spatal densty of BSs λ, ther transmsson power P, the SIR threshold β 1, the number of BSs transmt antennas N t, and the number of scheduled streams mn{n t,nr } also referred to as multplexng gan, where N r s the number of antennas n the UEs. Here, the modeled system of multstream data communcaton s consdered as ppes of nformaton [2], [21]. UEs are also randomly scattered across the network and form a PPP Φ U, ndependent of {Φ }s, wth densty λ U.In the system, the tme s slotted and smlar to [25] [27], and [32]. Our focus s on the scenaros n whch at each gven tme slot only one UE s served per actve cell. In cases where more than one UE s assocated wth a gven BS, tme sharng s adopted for schedulng. Our man obectve n ths paper s to evaluate the network coverage performance. Accordng to Slvnayak s theorem [8], [9] and due to the statonarty of the pont processes, the spatal performance of the network can be adequately obtaned from the perspectve of a typcal UE vrtually postoned at the orgn. The measured performance then attans the spatal representaton of the network performance, thus the same performance s expected throughout the network.

4 684 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 Let a typcal UE be assocated wth BS x transmttng data streams. Ignorng the mpact of background nose, 2 the receved sgnal y x C N r 1 C s the set of complex numbers s gven as y x = x α 2 Hx s x + x α 2 Hx s x 1 K x Φ /x where x,, s x =[s x,1...s x, ] T C 1, s x,l CN,P / s the transmtted sgnal correspondng to stream l n ter, H x C N r s the fadng channel matrx between BS x and the typcal UE wth entres ndependently drawn from CN, 1,.e., Raylegh fadng assumpton. Transmtted sgnals are ndependent of the channel matrces. In 1, x α s the dstance-dependent path-loss attenuaton, where x s the Eucldan dstance between BS x and the orgn, and α>2sthe path-loss exponent. We defne ˇα = 2/α and assume perfect CSI at the UEs recever CSIR, H x. We focus on the scenaros n whch the channel state nformaton at the transmtter CSIT s unavalable, and hence the BSs of each ter smply turn on transmt antennas where the transmt power P s equally dvded among the transmtted data streams. Such smple precodng schemes are often categorzed as open-loop technques, see, e.g., [2] and [21]. Although the open-loop technques are not necessarly capable of full explotaton of the avalable degrees of freedom DoF, 3 they are practcally appealng. Ths s partly due to the smplcty of the BSs physcal layer confguraton especally lowpower BSs, such as femtocells and dstrbuted antenna ports n whch CSIT s not requred, and partly because of the smple and straghtforward UE structure. Note that avalablty of the CSIT further mposes a hgh sgnalng overhead n ultradense HetNets wth unversal frequency reuse whch s practcally challengng [2], [21], [32]. The practcal mportance of open-loop technques makes t crtcal to nspect the network-wse performance of such technques. In ths paper, we analyze a domnant open-loop technque vz., ZFBF at the recever [2]. In addton to ts practcal smplcty, ZFBF provdes mathematcal tractablty, whch s hard to acheve n most of the MIMO-based technques. Adoptng ZF, a typcal UE utlzes the CSIR, H x, to mtgate the nterstream nterference. The cost s, however, reducng DoF per data stream. Therefore, to decode the l th stream, the typcal UE obtans matrx H x H x 1 H x, where s the conugate transpose, and then multples the conugate of the l th column by the receved sgnal n 1. Let ntendng channel power gans 4 assocated wth the l th data stream, Hx ZF,l, and the ICI caused by x x on data stream l, G ZF, be Ch-squared random varables r.v.s wth DoF of 2N r + 1, and 2S, respectvely. Usng the results gven n [[2], Secton II-A, Eq. 7], 2 In practce, HetNets wth unversal frequency reuse are nterference lmted, and the thermal nose s thus much smaller than the nterference and t s often gnorable. 3 DoF of a MIMO channel s the number of ndependent streams of nformaton that can be relably transmtted smultaneously. 4 Hereby, the term ntendng s used to descrbe the characterstcs of the channel between the typcal UE and ts servng BS. the SIR assocated wth the l th stream s gven as SIR ZF x,l = P x α Hx ZF,l P. 2 K x Φ /x S x α G ZF Note that for each l, Hx ZF,l and G ZF are ndependent r.v.s. Furthermore, Hx ZF,l G ZF and Hx ZF,l GZF x,l are ndependent and dentcally dstrbuted..d. for l l. In 2, for a gven communcaton lnk, SIR ZF x,l are dentcally, but not ndependently, dstrbuted across streams. Fnally, because of path-loss attenuatons the SIR values among the streams n 2 are statstcally dependent. As shown n 2, ncreasng has conflctng mpacts on the SIR. It reduces the per-stream ntended DoF as well as per-stream power whch results n reducton of the receved power of both ntended and nterferng sgnals. Increasng also ncreases the DoF of the ICI fadng channels. To understand the relatonshp between the multplexng gans on the network coverage performance the exact defnton of network coverage performance s provded n Secton III, n the rest of ths paper we nvestgate the statstcs of SIR ZF x,l. III. COVERAGE PROBABILITY IN MULTISTREAM MIMO CELLULAR COMMUNICATIONS In the lterature of multstream MIMO communcatons both n ad hoc see, e.g., [2] [22], [24], and [37] and cellular networks see, e.g., [32], the coverage probablty per stream s consdered as the man performance metrc. Accordngly, f SIR ZF x,l β, the typcal UE s then able to accurately detect the l th stream of data, and thus s n the coverage area. Note that coverage probablty per stream s the probablty of event {SIR ZF x,l β }. To understand t, nvestgaton of the statstcal characterstcs of SIR ZF x,l s only requred. However, there are at least two man ssues related to ths performance metrc. Frst, t s not practcally extendble to cellular systems manly due to the CA mechansm. In fact, the mathematcal presentaton of the multstream MIMO communcatons nvolves dfferent SIR expressons on each ter, see 2. The analytcal model of coverage probablty per stream may rse scenaros that the typcal UE receves data from dfferent BSs on dfferent streams. But n practce, the typcal UE receves streams of data from merely a sngle BS. Second, the coverage performance of the communcaton lnk comprsng of streams cannot be accurately predcted by the performance on a gven stream. Ths s because SIR values among streams are correlated, whch s reported n [38] although for the case of SIMO ad hoc networks, that results n severe reducton of the dversty of multantenna arrays. In our vew ths correlaton can further affect the multplexng gan of the multstream MIMO HetNets too, whose ramfcatons on the coverage performance of the system has to be understood. As a result, the consdered defnton of coverage probablty n the lterature of multstream MIMO s not approprate for cellular systems. To make the analytcal model consstent wth the realty of cellular systems we requre to defne a new, and thus more comprehensve, defnton of the coverage probablty. To ths end, here, we consder the coverage probablty

5 KHOSHKHOLGH et al.: COVERAGE PERFORMANCE IN MULTISTREAM MIMO-ZFBF HETEROGENEOUS NETWORKS 685 per communcaton lnk 5 as the man performance metrc. The exact defnton of ths new metrc s, however, contngent the transmsson strategy that BSs are practcng. A. Transmsson Strateges at the BSs As mentoned earler, the characterstcs of the coverage performance n MIMO HetNets depend on the adopted transmsson strategy at the BSs. BSs adopt ether FRT or ART schemes, whle for the latter, UEs need to feed back the achevable capacty per streams. In the FRT scheme, the transmsson rate on each stream, l, n the typcal UE whch s assocated to BS x s constant and equal to R x,l = log 1 + β nat/s/hz, where β s correspondng SIR threshold. Thus, the total receved data rate s R x = log 1 + β. On the other hand, n the ART scheme the total transmsson rate across streams s equal to R x = log 1 +SIR x,l symbol/s/hz. B. Coverage Probablty n Multstream MIMO Systems We now specfy the CA mechansm n both cases of FRT and ART schemes so that the typcal UE stays assocated wth a sngle BS across all streams. For the case of FRT scheme, the typcal UE s assocate to the Bn whch the weakest 6 SIR across the streams s larger than the correspondng SIR threshold, β. In the other words, for all scheduled streams the correspondng SIR values must satsfy the requred SIR threshold. Accordngly, the typcal UE s consdered n the coverage area f A FRT s nonempty, where { } A FRT = K: max mn SIR x,l β. 3 x Φ,..., For the case of the ART scheme, the typcal UE s consdered n the coverage area f A ART s nonempty, where A FRT = { K: max x Φ log 1 +SIR x,l } log1 + β. 4 Note that to preserve consstency between FRT and ART schemes, we set the requred transmsson rate n the ART scheme equal to log1 + β. The FRT scheme s more sutable for the MIMO transcever structures that the symbol error rate SER s manly nfluenced by the statstcs of the weakest data stream, whle the ART scheme s closely related to the spatally coded multplexng systems [1]. One may thus consder a combnaton of FRT and ART schemes n an adaptve mode selecton scheme n applcatons such as devce-to-devce D2D and two-hop cellular communcatons. For nstance, f the cellular system s lghtly loaded, then by adoptng the ART, t s possble to serve many new devces by the sngle-hop cellular communcatons. On the other hand, when the system s heavly loaded, part of the load 5 In ths paper, we commonly refer to the coverage probablty per lnk as the coverage performance, unless otherwse stated. 6 From practcal vewpont, such requrement s necessary as t allows the ncorporaton of ths fact that all the streams of data are orgnated from a unque BS. can be adaptvely offloaded to proxmty-aware D2D communcatons by swtchng to the FRT scheme. Havng defned the transmsson strateges, CA mechansms, and coverage per lnk, we can now analyze the coverage performance of MIMO HetNets. IV. ANALYZING THE COVERAGE PERFORMANCE A. FRT Scheme Proposton 1: The coverage probablty of the FRT-ZFBF scheme, FRT, s upper-bounded as FRT π Cα ˇα λ P N r S 2β m = K λ P Γ ˇα +m Γ ˇα S Γ1+m ˇα Γ ˇα S S +S S ΓS S 5 where Cα =πγ1 ˇα, and Γ. s the gamma functon. Proof: See Appendx A. The bound presented n Proposton 1 reflects the effect of system parameters ncludng multplexng gans s, deployment denstes λ, and transmsson powers P on the coverage performance. Usng Proposton 1, the coverage performance for ter s upper-bounded as FRT, π λ P C α ˇα β ˇα S ˇα K λ P N r m = ˇα Γ ˇα S +S S ΓS Γ ˇα +m Γ ˇα Γ1+m S S. 6 Based on the bound n 6, we make the followng observatons. 1 In 6, by ncreasng multplexng gans, reduces perstream power n both numerator and denomnator, whch s ndcatve of the ntended sgnals through the term P ˇα, P ˇα, S 2β and ICI va term S K. Note that the BSs n each ter also nterfere wth each other. 2 has an mpact on the level of ICI mposed from ters [through Γ ˇα S +S S 1], and from BSs n ter ΓS S 1], both ncreasng functons of [through Γ ˇα S + Γ. Therefore, the mpact of ICI s ncreased by fxng the multplexng gans n all BSs across all ters and ncreasng the multplexng gan n a partcular cell. Therefore, polces such as ZFBF at the recevers enforcng reluctance toward systematcally dealng wth ICI by cancelng some strong nterferers, for nstance has unexpected mpact on the growth of the ICI due to the home cell multplexng gan. 7 In other words, when dealng wth multstream transmsson, the exact representaton of ICI can be magnfed va the practced multplexng gan at the home cell, rrespectve of the multplexng gans n the adacent cells. By consderng per-stream coverage probablty as the performance metrc see, e.g., [21], [22], and [32], and followng the same lnes of arguments n the proof 7 Analytcal results n ths paper do not necessarly suggest the same for the MMSE-based and closed-loop MIMO technques, as well as technques that force cancellaton of domnant nterferers.

6 686 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 of Proposton 1, one can also show that the coverage probablty per stream l s gven as 8 FRT,,l π λ P Cα ˇα β ˇα N r m = K λ Γˇα+m ΓˇαΓ1+m ˇα P Γˇα+S S ΓS 7 In the upper-bound, the effect of the ICI mposed from ter s shown to be represented solely through Γˇα+S ΓS whch s ndependent of. Snce Γ ˇα S +S ΓS Γˇα+S ΓS, multplexng gan could reduce the negatve effect of hgher multplexng gan S, on the lnk performance compared to the gven stream performance due to the dependence of SIR values among the streams. A drect concluson s that performance of a gven stream of a communcaton lnk does not necessarly represent the entre pcture of the communcaton lnk performance. 3 The multplexng gan affects the ntended sgnal strength n 6 va S ˇα N r r = Γ ˇα +r Γ ˇα Γ1+r S that s dependent on N r + 1 whch s the avalable DoF for transmttng each stream of data. Comparng 6 wth 7, one can see that by consderng the per-stream coverage as the performance metrc, ths effect s overlooked. For β = β and = S,, 5 s reduced to πs ˇα r N ΓS S Γ ˇα S FRT + m S Cα Γ ˇα S + S Γ ˇα m = S Γ1 + m 8 that demonstrates scale nvarance,.e., the coverage probablty does not change wth the changes n the densty of the deployment of BSs. B. ART Scheme Here, we focus on the ART scheme. Accordng to Campbell Mecke s theorem [8], [9], the correspondng coverage probablty s ART 2πλ r P { S } log 1 +SIR x,l log1 + β dr. Analyzng 9 s, however, challengng due to the complexty of obtanng probablty dstrbuton functon of S log1 +SIR x,l. Utlzng Markov s nequalty results n the followng bound see Appendx B ART α 2 λ log1+β K λ ˇα P Γˇα+N t +1 ΓN t +1 ˇα P Γˇα+S S ΓS Such an expresson for the coverage probablty per stream does not exst n the lterature except for hgh SNR regmes as n [29]. However, the upper-bound n 1 s loose. Therefore, n Proposton 2, we derve a tghter upper-bound usng a heurstc approxmaton and based on the FRT coverage bound, FRT. Proposton 2: The coverage probablty of the ART-ZFBF scheme, ART, s approxmated9 as ART.5 FRT +.5 π Cα λ l ˇα ˇα P N r β m = K λ P S l Γ ˇα l +m Γ ˇα l Γ1+m ˇα Γ ˇα l +S S ΓS where FRT s gven n Proposton 1. Proof: See Appendx C. 1 l +1 l l 11 The mpacts of multplexng gans s, deployment denstes λ, and transmsson powers P on the coverage performance are evdent n 11. Smlar to the FRT scheme, for β = β and = S,, 11 demonstrates scale nvarance. Note that snce A FRT A ART there holds ART czf FRT.In Secton VI, we wll present numercal results of comparng the outage probablty of the FRT and ART schemes. V. EXTENSIONS OF THE ANALYSIS As mentoned earler, the man focus of ths paper s on the evaluaton of coverage performance n the open-loop ZFBF systems. However, the analyss s general enough to predct the coverage performance of other practcally relevant HetNets. In ths secton, we provde varous examples of showng how the derved analytcal results n Secton IV can be employed to predct the coverage probablty of other HetNets. For smplcty, here, we only consder the FRT scheme. A. Sngle-Input Sngle-Output SISO Systems The results presented n Secton IV can be ft to the SISO systems by smply settng = N t = N r = 1. Proposton 1 suggests that c SISO = π C α K λ P ˇα β ˇα K λ P ˇα, where Cα = CαΓ1 +ˇα. Note that c SISO s equvalent to the coverage probablty derved n [16] for the sngle-antenna systems. B. Sngle-Input Multple-Output SIMO Systems For the SIMO systems, we set = 1, and Proposton 1 reduces to SIMO = c SISOΩ, where Ω= N r 1 Γˇα+r r= ΓˇαΓ1+r. Applyng Kershaw s nequalty [37], thus N r 1 r= ˇα 1 r.5 + ˇα +.25 Ω N r 1 ˇα 1, r= r +.5ˇα N or r 1 ˇα 1 N x.5 + ˇα +.25 dx Ω r 1 x +.5ˇαˇα 1 α dx. Therefore, N r + ˇα +.25 ˇα 1 SIMO c SISO α 2 N r +.5ˇαˇα 1. Ths last expresson ndcates that czf SIMO c SISO N r ˇα, whch s an ncreasng functon of N r.in Fg. 1, czf SIMO c SISO s plotted versus α, and N r. Increasng the number 9 The symbol n 11 s ntroduced to reflect that the RHs approxmately an upper-bound. 2

7 KHOSHKHOLGH et al.: COVERAGE PERFORMANCE IN MULTISTREAM MIMO-ZFBF HETEROGENEOUS NETWORKS 687 Fg. 1. c SIMO c SISO versus α and N r. of receve antennas s shown to make a greater performance gan for small values of α. The mpact of a large path-loss exponent can also be compensated by ncreasng the number of receve antennas. C. MISO Systems So far, we have assumed that the CSIT s not provded. However, some cases wth CSIT known at the BSs can also be covered by our analyss. Let us consder a MISO system, where N r = 1, and = 1, and assume that CSIT s avalable to the BSs utlzed for egen beamformng,.e., MRT [7]. In such a system, the SIR at the typcal UE served by x s gven as SIR MRT x = where H MRT x K P x α Hx MRT x Φ /x P x α G MRT 12 x and G MRT x are Ch-squared wth 2N t DoF, and exponental r.v.s, respectvely. Usng Proposton 1, the coverage probablty s thus gven as c MRT MISO = π λ P Cα By applyng Kershaw s nequalty c MRT MISO c SISO λ P α 2Γα On the other hand, cmrt MISO SIMO N r, therefore cmrt MISO 1. SIMO ˇα N t 1 β m = K λ P ˇα ˇα N t 1 β m = λ λ λ P β ˇα N t P ˇα β P β ˇα. K λ N t ˇα N r P β K λ P β ˇα Γˇα+m ΓˇαΓ1+m Γˇα+m ΓˇαΓ1+m. 13. In practce, N t Fg. 2. Coverage probablty of ZFBF and MISO-SDMA systems versus S 1, where λ 1 = 1 4, λ 2 = 5 1 3, α = 4, N r = N t 1 = N t 2 = 16, P 1 = 5 W, P 1 = 1 W, β 1 = 1 db, and β 2 = 5. D. MISO-SDMA Systems Another example scenaro n whch the BSs have access to the CSIT s the MISO-SDMA system. Let N r = 1 and = 1,. We further assume that each cell of ter serves U N t UEs, adoptng ZFBF at the transmtter see [29] and [26] for more nformaton. Assumng a fxed transmt power, the SIR of the typcal UE that s assocated wth BS x s gven as SIR MRT x = K P U x α Hx SDMA P 14 x Φ /x U x α G SDMA x where Hx SDMA and G SDMA x are both Ch-squared r.v.s wth 2N t U + 1 and DoF of 2U, respectvely [25], [26]. Usng Proposton 1, we then obtan see also [39] c SDMA MISO = π Cα ˇα λ P N t U U β m = K λ P U ˇα Γˇα+U ΓU Γˇα+m ΓˇαΓ1+m 15 Remark 1: For the cases of SISO, SIMO, MISO-MRT, and MISO-SDMA, the above-obtaned bounds are accurate when β > 1. To the best of our knowledge, there are no closedform expressons of the coverage probablty. Fg. 2 shows that for U 2 = S 2 = 1 both ZF-FRT and SDMA perform smlarly. Furthermore, by ncreasng S 1, equvalently U 1, the coverage probablty n both systems s slghtly reduced. Nevertheless, for the settng, where U 2 = S 2 = 3, the coverage probablty s reduced n both systems whle the SDMA system overperforms the ZF-FRT system. The multstream ZF- FRT system and the multuser SDMA system are fundamentally dfferent as n the former all the transmtted streams to a user are requred to be successfully receved to consder that user n the coverage. Therefore, by fxng the densty of the BSs the lkelhood of successful recepton of all streams mght be generally lower. Nevertheless, n the multuser SDMA each UE s only.

8 688 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 responsble for detectng ts own sngle stream data. Of course, the lkelhood of successful recepton for each ndvdual stream mght also reduce by ncreasng the number of UEs due to reducton of DoF and ICI ncrease, however, the reducton s less than that of the ZF-FRT scheme. In terms of the complexty, multuser SDMA for each UE requres perfect channel drecton nformaton to be able to construct the precodng matrx, whereas the ZF-FRT scheme does not requre any feedback. E. Orthogonal Space-Tme Block Codes OSTBCs Systems Recognzng the statstcal resemblances of the SIR expressons among ZFBF and OSTBCs systems see, e.g., [2], the analyss of ths paper can readly be extended to the case of OSTBC systems. To do so, we need to assume that fadng matrces, the postons of BSs and UEs, and ther assocatons reman unchanged durng the space-tme block codes. Analyzng schemes, such as maxmum raton combnng at the recever whle the transmtters do not have CSIT, are more complex due to the nterstream nterference at the recever sde [4]. VI. NUMERICAL ANALYSIS AND SIMULATION RESULTS We now provde numercal and smulaton results. K = 2s assumed for easer presentaton of the results. We frst focus on provdng numercal analyss of coverage performance of FRT and ART schemes, amng to shed lght on how multplexng gans affect the strength of ntendng sgnals and nterference. We then provde techncal nterpretatons of the observed trends. The second part of ths secton provdes varous smulaton results to corroborate our analyss and nvestgate the mpacts of densfcaton and MIMO communcatons on the coverage performance. We also nvestgate the cases n whch densfcaton and MIMO communcatons are benefcal to the network s coverage performance. A. Numercal Analyss To capture the mpact of multplexng gans on the coverage probablty, we smply assume β = β, λ = λ, and P = P. 1 FRT Scheme: We start wth the FRT scheme. Proposton 1 provdes an upper-bound of the coverage probablty. Here, we consder the coverage probablty for ter n 6. Examnaton of 6 reveals two mpacts of multplexng gans: 1 the DoF of ntendng and nterferng sgnals and 2 the transmsson power per stream on both attendng and nterferng sgnals. To dstngush them, we frst exclude the mpact of multplexng gans on the transmsson power per stream t s equvalent to sayng that the transmsson power at BSs of ter proportonally ncreases wth S. We then defne f 1 S 1 = Δ 1 N r S 1 Γ ˇα S +r 1 1 S1 S1 ˇα r 1 = and f Γ ˇα S Γ1+r 1 2 S 1,S 2 = Δ 1 Γ ˇα S +S 2 S1 1 ΓS 2 + Γ ˇα S +S 1 S1 1 ΓS 1. It s easy to observe that functons f 1 S 1 and f 2 S 1,S 2 represent the effect of multplexng gans S 1, and S 2 n the numerator and the denomnator of 6, whle the mpact of power per stream s excluded. Moreover, we ntroduce functons f1 S 1 and f2 S 1,S 2, respectvely, as f1 S 1 = Δ S1 ˇα f 1 S 1 and f2 S 1,S 2 = Δ S2 ˇα Γ ˇα S +S 2 S1 1 ΓS 2 + S1 ˇα Γ ˇα S +S 1 1 S1 ΓS 1 so that the mpacts of multplexng gans on the transmt powers at the BSs are also captured. As t s seen from 6, FRT,1 f 1 S 1 f2 S 1,S 2. Functons f 1S 1 and f1 S 1 can be nterpreted as tangble ntended-dof per communcaton lnk, and effectve ntended-power per communcaton lnk, respectvely. Smlarly, to capture the mpact of multplexng gans on the coverage performance per stream n 7, we defne g 1 S 1 = Δ N r S 1 Γˇα+r 1 r 1 = ΓˇαΓ1+r 1 and g 2S 1,S 2 = Δ Γˇα+S 2 ΓS 2 + Γˇα+S 1 ΓS 1, whle the effect of multplexng gans on the power per stream s excluded. To ncorporate ths, we further defne g1 S 1 = Δ S1 ˇα g 1 S 1 and g2 S 1,S 2 = Δ S2 ˇα Γˇα+S 2 ΓS 2 + S1 ˇα Γˇα+S 1 ΓS 1. It s then easy to verfy from 7 that FRT,1,l g1 S 1 g2 S 1,S 2. On the other hand, to nspect the mpact of multplexng gans n the terms of sgnal detecton versus DoF behavor, we also defne h 1 S 1 E[mn l=1,...,s1 χ 2 2N r S 1 +1 ] as an approxmaton of the expected ntended-dof per communcaton lnk, where χ 2 2m stands for Ch-squared r.v. wth DoF m and s obtaned from h 1 S = S = S = = = g e g g N r S +1 ΓN r S e y S! ΓN r S y N r S S 1 ΓN r S dy dg e g N r S S 1 g l g N r S +1 e g l! ΓN r S dg l= e Sg k +...+k N r S =S 1 gn r S +1+ N r S l = lk l N dg r S l= k l!l! k l S! ΓN r S k +...+k N r S =S 1 e Sg g N r S +1+ N r S l = N r S k +...+k N r S =S 1 l= k l!l! k l lk l dg S! ΓN r S N r S N r S l= lk l! S N r S +2+ N r S l = lk l N r S l= k l!l! k l Ths way, k 1 S 1 N r S s actually the expected ntended-dof per stream. Contrastng h 1 S 1 k 1 S 1 aganst functons f 1 S 1, f 2 S 1,S 2 g 1 S 1, and g 2 S 1,S 2 reveals how much of the expected DoF s actually helpful n mprovng the ablty of the recevers n detectng sgnals. Fnally, we defne h 1 S 1=S1 ˇα h 1 S 1 and g1 S 1=S1 ˇα g 1 S 1 as the overall.

9 KHOSHKHOLGH et al.: COVERAGE PERFORMANCE IN MULTISTREAM MIMO-ZFBF HETEROGENEOUS NETWORKS 689 Fg. 3. f 1 S 1, g 1 S 1, h 1 S 1,andk 1 S 1 versus S 1 for K = 2, N r = 2, and α = 3.5. representatons of the multplexng gans on the expected DoF per lnk and per stream, respectvely. Fg. 3 plots f 1 S 1 and g 1 S 1 versus S 1.Bothf 1 S 1 and g 1 S 1 are shown to be monotoncally decreasng functons of S 1, and hence ncreasng the multplexng gan S 1 results n a lower coverage probablty from both lnk and stream perspectves. Furthermore, f 1 S 1 s shown to be smaller than g 1 S 1, so per-lnk coverage probablty s much smaller than the that of per stream. Therefore, per-lnk and per-stream coverage probabltes react dfferently to changes n the multplexng gan. We further study the mpact of transmsson power n Fg. 3, where f 1 S 1 and g 1 S 1 are presented for varous multplexng gans. Fg. 3 shows smlar patterns. The man dfference s that by ncreasng S 1, f 1 S 1 and g 1 S 1 declne more quckly than f 1 S 1 and g 1 S 1. Moreover, we observe that values of functons f 1 S 1 and g 1 S 1 are n general much smaller than that of h 1 S 1 and k 1 S 1, respectvely. Consequently, the expected DoF can be consdered as optmstc measures of the recever s capablty n terms of sgnal detecton. Fg. 4 demonstrates f 2 S 1,S 2 and g 2 S 1,S 2. Both functons are shown to exhbt the same pattern by varyng S 1 and S 2, where generally f 2 S 1,S 2 g 2 S 1,S 2. Therefore, by reducng the multplexng gan S 1, the negatve mpact of ICI on the performance of a communcaton lnk s reduced, compared to the performance of a gven stream. We also observe that by ncreasng S 2, both functons are ncreased. By ncorporatng the mpact of power, however, the observed behavor s dramatcally changed, as shown n Fg. 4, where f 2 S 1,S 2 and g 2 S 1,S 2 are gven versus S 1. One can see that 1 there are meanngful dscrepances between functons f 2 S 1,S 2 and g 2 S 1,S 2 not only from ther correspondng values but also from ther behavors wth respect to S 1 ; 2 whle f 2 S 1,S 2 and g 2 S 1,S 2 are monotoncally ncreasng functons of S 1 left plot, f 2 S 1,S 2 demonstrated decreasng and mldly ncreasng patterns dependng on S 1. Functon g 2 S 1,S 2 s also slghtly ncreased by ncreasng S 1. Fg. 4. f 2 S 1,S 2, g 2 S 1,S 2, f2 S 1,S 2,andg2 S 1,S 2 versus S 1 for K = 2, N r = 2, and α = 3.5. Fg. 5. Coverage probablty of the ART and FRT schemes versus S, where λ = λ, P = P,andβ = β,. Combnng the fndngs of Fgs. 3 and 4, we conclude that ncreasng the multplexng gans reduces the coverage probablty. Furthermore, the man reason for hgher multplex gans resultng n a smaller coverage probablty s due to the mparng mpact of multplexng gans on the effectve ntended-power per communcaton lnk, notcng the flat response of functon f 2 S 1,S 2 to S 1 n Fg. 4 as well as a sharp drop of functon f 1 S 1 to S 1 n Fg. 3. To confrm ths concluson, we set S 1 = S 2 = S, and llustrate per-lnk coverage probablty 6 and per-stream coverage probablty 7 versus parameter n Fg. 5. Both nterpretatons of the coverage probabltes are shown to be monotoncally decreasng the functons of S. Accordng to Fg. 5, ncreasng the multplexng gan from S = 1 to S = 2 reduces the coverage probablty per lnk by more than

10 681 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 3%, wth an almost 15% reducton n the coverage probablty per stream. For N r =, S π 1 ΓS FRT Cαβ ˇα S ˇα. 16 Γˇα/S + S Usng Kershaw s nequalty see, e.g., [37], we wrte Γ ˇα S + S ΓS > = S + ˇα S ˇα/S 2 S + ˇα S 1 2 ˇα S ˇα/S. 17 C π 1 αβ ˇα Substtutng 17 nto 16 yelds FRT S ˇα 1 S ˇα/S 1 ˇα 2S whch s a decreasng functon of S. Thus, ncreasng the multplexng gan S reduces the coverage probablty. Note that the above numercal and analytcal results are based on the upper-bound gven n Proposton 1. The smulaton results presented n Secton VI-B confrm the accuracy of Proposton 1, and thus the conclusons drawn here reman vald. 2 ART Scheme: We consder the ART scheme for whch the correspondng coverage probablty s approxmated n Proposton 2. Accordng to Proposton 2, ts coverage probablty s proportonally related to the coverage probablty of FRT. Thus, the above-mentoned numercal analyss would stay vald n the case of ART. Note that comparng wth the bound for the coverage probablty of the FRT scheme gven n 5, understandng the mpact of the multplexng gans even n the smplfed scenaro of ths secton s not straghtforward. Therefore, we rely on a numercal analyss by comparng the approxmaton n 11 wth the bound gven n Proposton 1. In Fg. 5, 5 and 11 are plotted for a system wth K = 2, and S 1 = S 2 = S. The ART scheme s shown to perform sgnfcantly better than FRT. For nstance, when S = 4, and α = 4.5, adoptng the ART scheme makes a more than 45% coverage performance mprovement over the system wth FRT. The modest cost of ths mprovement s the extra sgnalng overhead caused by the UEs feedng back to the BSs the achevable data rates for each stream. Fg. 5 also suggests that compared to the FRT scheme, n the ART scheme the coverage performance dmnshes faster by ncreasng the multplexng gan. For nstance, by ncreasng the multplexng gan from S = 1toS = 2, the coverage performance of FRT ART s reduced by 3% 1%. Fg. 5 further ndcates that the coverage performance of ART s more senstve to the varaton of the path-loss exponent than that of FRT. Therefore, the FRT scheme demonstrates a level of robustness aganst changes e.g., from outdoor to ndoor n the wreless envronment. B. Smulaton Results In our smulaton, we set K = 2 and randomly locate BSs of each ter n a dsk of radus 1 unts accordng to the correspondng deployng densty. All BSs are always actve and the smulaton s run for 4 snapshots. In each snapshot, we Fg. 6. Coverage probablty of the FRT and ART schemes versus β 2, where λ 1 = 1 4, λ 2 = 5 1 4, α = 4, N r = 1, P 1 = 5 W, P 1 = 1 W, and β 1 = 5. randomly generate MIMO channels based on the correspondng multplexng gans at the BSs. 1 Accuracy of the Bounds: Fg. 6 plots the coverage probabltes under FRT and ART schemes versus β 2.Asshownfor β 2 1, whch s the case of our model, the analytcal bounds closely follow the smulaton results. Ths fndng s mportant especally for the case of ART as the proposed bound n 11 s heurstc. For the case of β 2 < 1, however, the analyss s not representatve. Therefore, Fg. 6 confrms the results reported n [16] and [26]. We further observe that by ncreasng β 2,the coverage probablty s reduced n all graphs and ART outperforms FRT. In both schemes, by ncreasng the multplexng gan, S 1, the correspondng coverage probabltes are shown to be reduced. Fg. 7 compares the analyss and smulaton results versus β 1, showng the same patterns observed n Fg. 6. However, comparson of Fgs. 6 and 7 shows that ncreasng β 1 makes less mpact on the reducton of the coverage probablty n both schemes. From the comparson of Fgs. 7 and 6, we also fnd that ncreasng β 2 wdens the gap between FRT and ART whle the growth of β 1 narrows the gap. The observed dscrepances are due to the dfferences between the transmsson power and denstes of the BSs n dfferent ters. We also evaluate the accuracy of our analyss aganst the densty of BSs deployment n Fgs. 8 and 9. In the former the latter, we fx λ 1 = 1 4 λ 2 = 1 4 and change λ 2 λ 1. Both fgures confrm that the proposed approxmatons for both FRT and ART closely follow the correspondng coverage probablty. Ths also confrms our concluson on the mpact of the multplexng gans on the coverage performance of FRT and ART n the prevous sectons. 2 Impact of Multplexng Gans and Densfcatons: Fgs. 8 and 9 also hghlght the followng mportant trends. 1 ART provdes better coverage performance than FRT by almost 2 25%, whch s smaller than our prevously expected value n Secton IV-B. Ths s because n

11 KHOSHKHOLGH et al.: COVERAGE PERFORMANCE IN MULTISTREAM MIMO-ZFBF HETEROGENEOUS NETWORKS 6811 Fg. 7. Coverage probablty of FRT and ART schemes versus β 1,where λ 1 = 1 4, λ 2 = 5 1 4, α = 4, N r = 1, P 1 = 5 W, P 1 = 1 W, and β 2 = 5. Fg. 8. Coverage probablty of the FRT and ART schemes versus λ 2,where λ 1 = 1 4, α = 4, N r = 1, P 1 = 5 W, P 1 = 1W, β 1 = 2, and β 2 = 5. Secton IV-B, transmsson powers, deployng denstes, and SIR thresholds are assumed to be the same n both ters. One may conclude that the advantage of ART over FRT s fully explotable n a homogenous network deployment,.e., P = P, = S, λ = λ, and β = β. 2 Multplexng gans S 1 and S 2 make the followng dfferent mpacts on the coverage performance. a Accordng to Fg. 8, whle the densty of hgh-power BSsnter1,λ 1, s fxed, f S 1 = S 2, ncreasng λ 2 lowers the coverage probablty. On the contrary, Fg. 9 ndcates that when the densty of lowpower BSs n ter 2, λ 2, s fxed by ncreasng λ 1, a hgher coverage performance results for S 1 = S 2. Fg. 9. Coverage probablty of FRT and ART schemes versus λ 1,where λ 2 = 1 4, α = 4, N r = 1, P 1 = 5 W, P 1 = 1W, β 1 = 2, and β 2 = 5. In fact, for cases wth the same multplexng gan across the ters, the coverage probablty could decrease/ncrease dependng upon the densfed ter. Therefore, n such cases t s more effcent to densfy the ter wth the hgher transmsson power. b Fg. 8 shows that for fxed λ 1, ncreasng λ 2 s benefcal and results n a hgher coverage performance, where S 1 = 6, and S 2 = 2. Fg. 9, on the other hand, llustrates that for S 1 = 6 and S 2 = 2 and when λ 2 s fxed, ncreasng λ 1 lowers the coverage probablty. Consequently, n cases wth dfferent multplexng gans, the results suggest that t s better to densfy the ter wth low-power and/or low multplexng gan. c For hgh values of λ 2, Fg. 8 also shows that both cases of S 1 = 6, S 2 = 2 and S 1 = S 2 = 2 perform the same. For hgh values of λ 1,Fg.9,however, shows a large gap between the coverage probablty of system S 1 = 6, S 2 = 2 and that of system S 1 = S 2 = 2. In other words, for a network wth ultradense low-power ter, the multplexng gan of hgh-power ter can be ncreased wthout compromsng the coverage performance. In summary, ncreasng the densty of low-power BSs ter 2 should be nterpreted as a green lght for ncreasng the multplexng gan of ter 1 wthout hurtng the coverage performance. Moreover, densfcaton n ter 1 results n a hgher performance provded that smlar multplexng gans are set across all ters. 3 The results n Fgs. 8 and 9 also ndcate that ncreasng the densty of low-power BSs of ter 2 makes greater mpact on the coverage probablty than t does n ter 1. For nstance, a ten-fold densfcaton of ter 2 ter 1 changes the coverage performance by more than 25% 1%. Ths s a very mportant

12 6812 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 Fg. 1. Coverage probablty of the FRT and ART schemes versus N r.aλ 2 = 1 2.bλ 2 = 1 4. In both plots, λ 1 = 5 1 5, α = 4, P 1 = 5 W, P 1 = 2 W, β 1 = 2, and β 2 = 5. Fg. 11. Coverage probablty of the FRT and ART schemes versus N r.aλ 1 = 1 2.bλ 1 = 1 4. In both plots, λ 2 = 5 1 5, α = 4, P 1 = 5 W, P 1 = 2 W, β 1 = 2, and β 2 = 5. practcal nsght because nstallng more low-power BSs s cheaper than ncreasng the densty of hghpower BSs of ter 1. 4 The above results also confrm that for large values of λ 1 and λ 2, the coverage probablty s stable and does not react to densfcaton. Ths s also referred to as scale nvarancy, see [16]. Ths ndcates that we could ncrease the capacty by nstallng more BSs wthout hurtng the coverage. As a result, wthout sacrfcng the coverage performance, we can ncrease the densty of BSs n ter 2 to smultaneously ncrease the multplexng gan of ter 1. 3 Impact of Number of Receve Antennas: In Fgs. 1 and 11, we study the mpact of the number of receve antennas N r on the coverage performance. We frst revew the results of Fg. 1, where a sparse ter 1 wth the densty of BSs, λ 1 = 5 1 5,s consdered. Two scenaros are consdered wth respectve to the densty of BSs n ter 2: 1 dense, the results of whch are shown n the left plot, and 2 sparse, the results of whch are gven n the rght panel. In both cases, we nvestgate three cases: 1 S 1 = S 2 = 1, 2 S 1 = N r, S 2 = 1, and 3 S 1 = S 2 = N r. In both dense and sparse scenaros, the case of S 1 = S 2 = N r performs very poorly and ncreasng the number of antennas worsens performance. In ths case, ART slghtly outperforms FRT. Moreover, for small values of N r, the sparse scenaro yelds a better performance than that of the dense scenaro. For large values of N r, however, both scenaros perform almost the same. Note that ncreasng N r mproves the coverage probablty n both dense and sparse cases for S 1 = S 2 = 1. Besdes, comparson of the left and rght fgures shows that the densty of ter 2 has a mnor mpact on the coverage performance. It s also seen that the ART scheme does not make a maor mprovement over FRT n ths case. The case of S 1 = N r, S 2 = 1 behaves dstnctvely aganst ncreasng N r. Recall that the frst ter s sparse. In the scenaro that ter 2 s also sparse [see Fg. 1b] ncreasng N r and thus the multplexng gan of ter 1 has a modest mpact on the coverage performance, and the ART scheme slghtly mprove the coverage performance compared to the FRT scheme. Nevertheless, for a dense ter 2, as the left plot ndcates, the case of S 1 = N r and S 2 = 1 performs almost the same as the case of S 1 = S 2 = 1. Smlarly, ART does not make any mprovement over FRT. Furthermore, ncreasng N r and thus S 1, S 2 = 1 mproves the coverage probablty. Now, let us look at Fg. 11 n whch we have fxed the densty of ter 2 to λ 2 = and nvestgate the coverage performance aganst N r for both scenaros where ter 1 s sparse

13 KHOSHKHOLGH et al.: COVERAGE PERFORMANCE IN MULTISTREAM MIMO-ZFBF HETEROGENEOUS NETWORKS 6813 Fg. 12. a Coverage probablty of the FRT scheme versus λ 2 = 1 4. b Coverage probablty of the ART scheme versus λ 2 = 1 4. In both plots, coverage probablty of the FRT and ART schemes versus λ 2,whereλ 1 = 1 4, α = 4, N r = 1, P 1 = 5 W, P 1 = 1 W, β 1 = 2, and β 2 = 5. the rght fgure and dense the left fgure. We agan consder three cases: 1 S 1 = S 2 = 1, 2 S 1 = N r, and S 2 = 1, and 3 S 1 = S 2 = N r. In both dense and sparse scenaros, the case of S 1 = S 2 = N r performs very poorly and ncreasng the number of antennas worsens performance. In ths case, ART outperforms FRT. Note that comparson of both fgures shows that the densty of ter 1 does not have any specfc mpact on the coverage. As shown n Fg. 1, the case of S 1 = S 2 = 1 reacts postvely to the ncrease of N r. In ths case, both FRT and ART perform smlarly. Fnally, we consder the case of S 1 = N r and S 2 = 1. Both fgures show that the coverage performance s better than the case of S 1 = S 2 = N r but much smaller than the case of S 1 = S 2 = 1. Furthermore, ncreasng N r reduces the coverage probablty where the resultng reducton n the case of sparse scenaro, rght plot, s not as bad as the case of dense scenaro, left plot. Comparng these fndngs wth ts counterpart n Fg. 1, we observe that ths case s n fact reacted postvely to the growth of N r, especally n the dense scenaro. Thus, f we were to apply densfcaton n conuncton wth hgh multplexng gans, we would suggest to keep the densty of the hgh-power ter low and the densty of low-power ter hgh. Ths allows us to ncrease the multplexng gan of the hgh-power ter up to the number of the UE s antennas, provded that the multplexng gan of low-power ter s kept as small as possble. 4 Impact of Path-Loss Model: The analytcal results of ths paper s based on the generc path-loss model, L 1 = x α. Here, to nvestgate the mpact of path-loss model, we compare the coverage probablty n a system wth path-loss model L 1 and two other alternatve path-loss models n the lterature vz., L 2 = max{1, x } α, and L 3 =1 + x α. The coverage performance of FRT and ART schemes s presented n Fg. 12a, and b, respectvely. As t s seen, regardless of multplexng gans, for both FRT and ART schemes the systems wth L 1 and L 2 path-loss models follow smlar trends and acheve almost the same coverage probablty. For very dense system confguratons, however, the coverage probablty n a system wth L 2 path-loss model s slghtly declned. It s also seen that densfcaton n a system wth L 3 path-loss model results n ncreasng the coverage probablty untl a certan pont after whch the coverage probablty s reduces A smlar result s also spotted for double-slop path-loss model n [41] for SISO systems. Fnally, t s mportant to note that n dense deployment and for S 1 = S 2 = 2, and S 1 = 6 and S 2 = 2, the coverage performance of FRT and ART schemes s very close regardless the path-loss model. VII. CONCLUSION In ths paper, we have evaluated the coverage performance of multantenna MIMO ZFBF communcatons n HetNets. Our man goal was to understand the coverage performance per each communcaton lnk n multstream communcatons. By employng the stochastc geometry, we studed the networkwse coverage performance. The analyss has covered both cases of FRT and ART. We have derved a set of closedform approxmatons for the coverage performance for both FRT and ART, accuraces of whch were also examned and confrmed aganst smulatons. Our proposed bounds captured the mpact of varous system parameters on the coverage probablty. The man fndngs of our analyss and smulatons were as follows: 1 the larger the multplexng gans, the lower the coverage probablty; 2 densfcaton of the network s better to be practced n low-power ters as t paves the way for ncreasng the multplexng gans of the hgh-power, low-densty macro- BSs wthout compromsng the coverage performance; 3 when dealng wth multstream MIMO communcatons, the tangble DoFs n detectng the ntended sgnals are much smaller than those of the wreless medum; 4 the senstvty of the tangble DoFs of the ntended sgnals aganst the multplexng gans was the man culprt

14 6814 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 of reducng the coverage probablty wth multplexng gans; and 5 ncreasng the multplexng gan n a cell whle all other multplexng gans are kept ntact may result n unexpected amplfcaton of ICI. APPENDIX A PROOF OF PROPOSITION 1 The followng lemmas are used n provng Proposton 1. Lemma 1: For an r.v., H, dstrbuted accordng to χ 2 2M wth CCDF F H z =e z M 1 m = z m m!, the nverse Laplace transform of F H z s L FH zt = M 1 m = 1 m! δm t 1, where δ m t s the mth dervatve of Drac s Delta functon. Furthermore, there holds L F H z t t dt = M 1 Γˇα+m ˇα m = ΓˇαΓm +1. Proof: The proof follows the same lne of argument as n the proof of [42, Corollary 1].The only dfference s that n [42] the fadng dstrbuton s Nakagam-m fadng wth power 1 and the CCDF s F H z =e Mz M 1 m = M m z m m!. Lemma 2: Consder a shot nose process, I = K I, where I = x Φ P x α H x, and H x s are..d. r.v.s dstrbuted accordng to χ 2 2M. Assume H s dstrbuted accordng to χ 2 2M and s ndependent of H x s. Then, for a gven real parameter Δ P {H ΔI} = L FH te t ˇα Δ ˇα C α ˇα λ P Γˇα + M ΓM K dt where Cα =πγ1 ˇα and L FH t Z s the nverse Laplace transform of CCDF of r.v. H as gven n Lemma 1. Proof: Due to ndependence of processes Φ s, we get P {H ΔI} = E = L FH te tδ K I dt L FH t K L I tδ dt 18 where L I t s the Laplace transform of r.v. I and L I tδ = Ee tδ P x α H x x Φ = E Φ x Φ E H x e tδp x α H x [1 1+tΔP x α M ]x dx = e 2π λ = e π λ tδp ˇα ΨM,α 19 where ΨM,α= [1 1 + w α/2 M ]dw. Applyng [43, Eq. 8] for the Laplace transform of the shot nose process, I, we obtan L I tδ = e C αλ tδp ˇα E[H ˇα ] = e C αλ tδp ˇα Γˇα + M ΓM 2 notcng that for Ch-squared r.v.s wth M DoF E[H ˇα ]= Γˇα+M ΓM. Substtutng 2 nto 18 completes the proof. Note that by comparng 2 and 19, t can be shown that ΨM,α= C α Γˇα+M π ΓM. Proof of Proposton 1: The coverage probablty s defned as the probablty of the outcome n 3. Accordng to [16, Lemma 1], and assumng β 1, we have FRT = P max x Φ K mn SIR ZF l=1,..., x,l β = E 1 mn SIR ZF x l=1,...,,l β. 21 x Φ Equaton 21 s further smplfed as 21 a = { } 2πλ r P mn SIR ZF x,...,,l β dr b = 2πλ r E {Φ } P { SIR ZF x,l β {Φ } } dr 22 where r = x, and a s due to Slvnyak Mecke s and Campbell Mecke s theorems [8], and n b we use the fact that condtoned on processes Φ s, the SIR expressons n 2 across streams are n statstcally ndependent. For a gven r,p { SIR ZF P HZF r,l = r,l β {Φ } } s equal to β P r α e t β P r α K x Φ /x t K P S x α G ZF x Φ /x E G ZF {Φ }, P S x α G ZF dt 23 where we use 18 n Lemma 2. Snce Hx ZF,l are dentcal r.v.s, we dsmss ndex l from L FH t ZF. Substtutng 23 nto 22 followed by some straghtforward manpulatons, we get 22 = 2πλ r E {Φ } = E G ZF e t S β P r α = 2πλ r dr E {Φ } E G ZF e β P r α 2πλ r dr E {Φ } e β P r α P S x α G ZF dt dr P S x α G ZF t l P S x α G ZF t l K t K x Φ /x K x Φ /x t l dt l x Φ /x E G ZF x t l dt l

15 KHOSHKHOLGH et al.: COVERAGE PERFORMANCE IN MULTISTREAM MIMO-ZFBF HETEROGENEOUS NETWORKS 6815 as G ZF are..d. across streams. Consequently FRT S β P r α E G ZFe x = 2πλ r dr E {Φ } P S x α 2πλ r dr S β P r α e a = P S x α l = 1 l = 1 2πλ r dr r 2 C S α β ˇα K P P λ = 1 e = 2πλ =... G ZF t l... G ZF t l E Φ K ˇα S S EG ZF l = 1 r 2 C S α β ˇα K P P λ = 1 r e ˇα π C λ P α β K λ K x Φ /x t l dt l x Φ /x E G ZF x t l dt l t l dt l ˇα S EG ZF... [ S P S ˇα EG ZF G ZF,l t l l = 1 S GZF t l dt l ˇα G ZF,l t l ˇα t l dt l ] ˇα,l t l dr 24 where n a we apply 2 n Lemma 2. Drect evaluaton of 24 s complex, and hence we use the arthmetc geometrc nequalty for dervng an upper-bound. Thus, FRT = K ˇα π Cα λ P... β λ P S ˇα EG ZF ˇα π P C α β K =1 λ λ S ˇα = K =1 λ 1 [ S ˇα S ] ˇα GZF S,l t l... S t l dt l L F t H ZF l dt l ˇα S t l ˇα P S S EG ZF GZF,l ˇα π C α P ˇα S t P β ˇα ˇα S E G ZF λ S ˇα G ZF ˇα S t dt S. 25 where the last step s due to the fact that r.v.s G ZF are..d. across streams. Snce H ZF s a Ch-squared r.v. wth 2N r + 1 DoF usng the results of Lemma 1 and Lemma 2 n 25 completes the proof. APPENDIX B MARKOV S BOUND Accordng to Markov s bound, we have λ ART 2π log1 + β 1 +SIR ZF x,l dr λ a = 2π log1 + β 1 e z SIR ZF x λ b = 2π log1 + β z K Ee 1 Ee z P c = r dz dr P S x α x Φ /x S r α λ 2π log1 + β H ZF x E log e z r E z r G ZF x 1 P 1 + z r α N r +1 d = λ 2π log1 + β 1 z e z ˇα C α K λ P ˇα 1 z dz dr 1 r EL I z z Γˇα + S S ˇα ΓS K dz dr r 1 N P r z r α dr dz 26 where n step a we notce that the SIR expressons are dentcal among the streams and apply formula log1 + a = e w w 1 e aw dw [44]; n step b, we apply a smple change of varable; step c s due to ndependence of pont processes and the fact that r.v. Hx ZF s Ch-squared wth 2N r + 1 DoF; fnally, n step d, we substtute L I t from Lemma 2 n Appendx A. By ntroducng varable w =z P / ˇα x 2, 26 s further reduced to 26 = ˇα λ P π log1 + β w α 2 N t dw +1 z ˇα 1 e z ˇα C α λ P ˇα K Γˇα + S S ˇα ΓS dz.

16 6816 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 Usng the same notaton as n the proof of Lemma 2, we can wrte ΨN t 1 + 1,α= w α 2 N t dw +1 = Cα π Usng ths, 26 s then reduced to ART α 2 We wrte 1 ART.5P max K x Φ = 1 +.5P max K x Φ = 1 λ P log1+β K λ Γˇα + N t + 1 ΓN t S. + 1 ˇα Γˇα+N t +1 ΓN t +1 ˇα P Γˇα+S S ΓS APPENDIX C PROOF OF PROPOSITION mn log 1 +SIR x,l log1 + β,..., max log 1 +SIR x,l log1 + β,..., 28 where the frst term s prevously obtaned n Proposton 1 and s equal to FRT. We then derve a bound of the second term as { } 2πλ x 1 P max SIR ZF x l=1,...,,l <β dx = 2πλ r E {Φ } 1 1 P{SIR ZF x β {Φ }} dr 29 n whch we use the monotoncty of log functon, and notng that condtoned to the PPP sets, {Φ }, the SIR values are statstcally ndependent r.v.s across the streams. We also represent the multplcaton of probabltes assocated wth the streams through a summaton. Snce SIRs are dentcal r.v.s among the 1 Let us consder m dentcal but dependent r.v.s Z 1,Z 2,...,Z M. To evaluate P{ m Z m >R}, we frst notce that M mn m Z m m Z m M max m Z m. Therefore, P{mn Z m >R/M} P{ m Z m >R} P{max Z m >R/M}. Usng ths, we then approxmate P{ m Z m >R} through the mean of the upper-bound and lower bound. streams, we have 29 = 2πλ l l =1 P S { SIR ZF x,l l 1 l +1 r E {Φ } } β {Φ } dr. 3 Applyng the same lne of argument as n the proof of Proposton 1, 3 s reduced further to πλ P ˇα S S Cα β l... l K l =1 λ l ˇα λ P S ˇα EG ZF t l dt l π l 1 l +1 Cα ˇα P N r β m = K λ P 1 l +1 [ l l Γ ˇα l +m Γ ˇα l Γ1+m ˇα Γ ˇα l +S S ΓS ] ˇα =1 GZF,l t l l l. 31 Substtutng 31 and 5 nto 28 results n 11, completng the proof. REFERENCES [1] D. Tse and P. Vswanath, Fundamentals of Wreless Communcaton. Cambrdge, U.K.: Cambrdge Unv., Sep. 24. [2] Q.L et al., MIMO technques n WMAX and LTE: A feature overvew, IEEE Commun. Mag., vol. 48, no. 5, pp , May 21. [3] Csco, Vsual networkng ndex, Whte Paper, Feb [Onlne]. Avalable: [4] J. G. Andrews et al., What wll 5G be? IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp , Jun [5] J. G. Andrews et al., Femtocells: Past, present, and future, IEEE J. Sel. Areas Commun., vol. 3, no. 3, pp , Apr [6] D. Gesbert et al., Mult-cell MIMO cooperatve networks: A new look at nterference, IEEE J. Sel. Areas Commun.,vol.28,no.9,pp , Dec. 21. [7] A. J. Goldsmth, Wreless Communcatons. Cambrdge, U.K.: Cambrdge Unv., 25. [8] J.F.C.Kngman,Posson Processes. London, U.K.: Oxford Unv., [9] M. Haengg and R. K. Gant, Interference n large wreless networks, Found. Trends Netw., vol. 3, no. 2, pp , 28. [Onlne]. Avalable: mhaengg/pubs/now.pdf [1] E. S. Sousa and J. A. Slvester, Optmum transmsson ranges n a drectsequence spread-spectrum multhop packet rado network, IEEE J. Sel. Areas Commun., vol. 8, no. 5, pp , Jan [11] F. Baccell et al., Stochastc analyss of spatal and opportunstc ALOHA, IEEE J. Sel. Areas Commun., vol. 27, no. 7, pp , Sep. 29. [12] S. P. Weber et al., Transmsson capacty of wreless ad hoc networks wth successve nterference cancellaton, IEEE Trans. Inf. Theory, vol. 53, no. 8, pp , Aug. 27. [13] J. G. Andrews et al., A tractable approach to coverage and rate n cellular networks, IEEE Trans. Commun., vol. 59, no. 11, pp , Nov. 211.

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Hamd, Capacty of MRC on correlated Rcan fadng channels, IEEE Trans. Commun., vol. 56, no. 5, pp , May 28. Mohammad G. Khoshkholgh receved the B.Sc. degree n electrcal engneerng from Isfahan Unversty, Isfahan, Iran, n 26, and the M.Sc. degree n electrcal engneerng from the Tarbat Modares Unversty, Tehran, Iran, n 28. He was wth the Wreless Innovaton Laboratory, Tarbat Modares Unversty, from 28 to 212. From February 212 to February 214, he was wth Smula Research Laboratory, Fornebu, Norway, workng on developng communcaton solutons for smart grd systems. He s currently wth the Unversty of Brtsh Columba, Vancouver, BC, Canada. Hs research nterests manly nclude the modelng and analyzng wreless communcatons, rado resource allocatons, and spectrum sharng. Mr. Khoshkholgh was the recpent of the Vaner Canada Graduate Scholarshps. Kang G. Shn LF 12 s the Kevn and Nancy O Connor Professor of computer scence wth the Department of Electrcal Engneerng and Computer Scence, Unversty of Mchgan, Ann Arbor, MI, USA. He has supervsed the completon of 74 Ph.D degrees and authored/coauthored more than 8 techncal artcles more than 3 of these are n archval ournals, a textbook, and more than 2 patents or nventon dsclosures. He was a co-founder of a couple of startups and also lcensed some of hs technologes to ndustry. Hs current research focuses on QoS-senstve computng and networkng as well as on embedded real-tme and cyber-physcal systems. Mr. Shn was the recpent of numerous best paper awards, ncludng the Best Paper Awards from the 211 ACM Internatonal Conference on Moble Computng and Networkng, the 211 IEEE Internatonal Conference on Autonomc Computng, the 21 and 2 USENIX Annual Techncal Conferences, as well as the 23 IEEE Communcatons Socety Wllam R. Bennett Prze Paper Award and the 1987 Outstandng IEEE Transactons of Automatc Control Paper Award. He has also receved several nsttutonal awards, ncludng the Research Excellence Award n 1989, Outstandng Achevement Award n 1999, Dstngushed Faculty Achevement Award n 21, and Stephen Attwood Award n 24 from the Unversty of Mchgan the hghest honor bestowed to Mchgan Engneerng faculty; a Dstngushed Alumn Award of the College of Engneerng, Seoul Natonal Unversty n 22; 23 IEEE RTC Techncal Achevement Award; and 26 Ho-Am Prze n Engneerng the hghest honor bestowed to Korean-orgn engneers.

18 6818 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 8, AUGUST 217 Kevan Navae SM 1 receved the B.Sc. degree from the Sharf Unversty of Technology, Tehran, n 1995, Iran, the M.Sc. degree from the Unversty of Tehran, Tehran, Iran, n 1997, and the Ph.D. degree from Tarbat Modares Unversty, Tehran, Iran, n 24, all n electrcal engneerng. From March to November 24, he was wth the School of Mathematcs and Statstcs, Carleton Unversty, Ottawa, ON, Canada, as a Postdoctoral Research Fellow. From December 24 to September 26, he was wth the Broadband Communcaton and Wreless System BCWS Centre, Carleton Unversty, where he was the Proect Manager of BCWS partcpaton n European Unon 6th Framework Integrated Proect, the Wreless World Intatve New Rado on beyond 3G wreless systems. From September 26 to July 211, he was wth the Department of Electrcal and Computer Engneerng, Tarbat Modares Unversty. Snce July 211, he has been wth the School of Electrcal and Computer Engneerng, Unversty of Leeds, Leeds, U.K. Hs research nterests nclude the feld of rado resource allocaton for wreless communcaton systems, dynamc spectrum allocaton, cogntve rado networks, and cooperatve communcatons. Dr. Navae s on the edtoral board of the European Transactons on Telecommuncatons. He has been on the techncal program commttee of dfferent IEEE conferences, ncludng IEEE Global Telecommuncatons Conference, IEEE Internatonal Conference on Communcatons, IEEE Vehcular Technology Conference VTC, and IEEE Wreless Communcaton Networkng Conference, and chared some of ther symposa. He has also served as the Co-Char of the Wreless Network Track, IEEE VTC 212, Yokohama, Japan, and the IEEE 8th Internatonal Workshop on Wreless Network Measurements WNMee 212, Paderborn, Germany. He was the recpent of the 211 IEEE Iran Secton Young Investgator Award. Vctor C. M. Leung S 75 M 89 SM 97 F 3 receved the B.A.Sc. Hons. and Ph.D. degrees n electrcal engneerng from the Unversty of Brtsh Columba UBC, Vancouver, BC, Canada, n 1977 and 1981, respectvely. From 1981 to 1987, he was a Senor Member of Techncal Staff and a Satellte System Specalst wth MPR Teltech Ltd., Burnaby, BC, Canada. In 1988, he was a Lecturer wth the Department of Electroncs, Chnese Unversty of Hong Kong. He returned to UBC as a Faculty Member n 1989 and currently holds the postons of a Professor and the TELUS Moblty Research Char n advanced telecommuncatons engneerng wth the Department of Electrcal and Computer Engneerng. He has coauthored more than 7 techncal papers n nternatonal ournals and conference proceedngs and 29 book chapters and coedted 8 book ttles. Hs research nterests nclude the areas of wreless networks and moble systems. Dr. Leung s a Fellow of the Royal Socety of Canada, the Engneerng Insttute of Canada, and the Canadan Academy of Engneerng and s a Regstered Professonal Engneer n the Provnce of Brtsh Columba, Canada and was the recpent of the Natural Scences and Engneerng Research Councl Postgraduate Scholarshp for the Ph.D. degree, the APEBC Gold Medal as the Head of the graduatng class n the Faculty of Appled Scence, the IEEE Vancouver Secton Centennal Award, and the 212 UBC Kllam Research Prze. Several of hs papers had been selected for best paper awards. He was a Dstngushed Lecturer of the IEEE Communcatons Socety. He s a member of the edtoral boards of IEEE WIRELESS COMMUNICATIONS LETTERS, Computer Communcatons, and several other ournals and has prevously served on the edtoral boards of the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS Wreless Communcatons Seres, the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, the IEEE TRANSAC- TIONS ON COMPUTERS, andjournal of Communcatons and Networks. Hehas guest-edted several ournal specal ssues and contrbuted to the organzng commttees and techncal program commttees of numerous conferences and workshops.