THE biggest challenge for next generation wireless

Transcription

1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE Interference Management in 5G Revere TDD HetNet With Wirele Bachaul: A Large Sytem Analyi Luca Sanguinetti, Member, IEEE, Ari L. Moutaa, Senior Member, IEEE, and Mérouane Debbah, Fellow, IEEE Abtract Thi wor analyze a heterogeneou networ HetNet, which comprie a macro bae tation BS equipped with a large number of antenna and an overlaid dene tier of mall cell acce point SCA uing a wirele bachaul for data traffic. The tatic and low mobility uer equipment terminal UE are aociated with the SCA while thoe with medium-to-high mobility are erved by the macro BS. A revere time diviion duplexing TDD protocol i ued by the two tier, which allow the BS to locally etimate both the intra-tier and inter-tier channel. Thi nowledge i then ued at the BS either in the uplin UL or in the downlin DL to imultaneouly erve the macro UE MUE and to provide the wirele bachaul to SCA. A concatenated linear precoding technique employing either zero-forcing ZF or regularized ZF i ued at the BS to imultaneouly erve MUE and SCA in DL while nulling interference toward thoe SCA in UL. We evaluate and characterize the performance of the ytem through the power conumption of UL and DL tranmiion under the aumption that target rate mut be atified and imperfect channel tate information i available for MUE. The analyi i conducted in the aymptotic regime where the number of BS antenna and the networ ize MUE and SCA grow large with fixed ratio. Reult from large ytem analyi are ued to provide concie formulae for the aymptotic UL and DL tranmit power and precoding vector under the above aumption. Numerical reult are ued to validate the analyi in different etting and to mae comparion with alternative networ architecture. Index Term HetNet, MIMO, mall cell, maive MIMO, interference management, 5G mobile communication, revere TDD, wirele bachaul, random matrix theory, power conumption minimization, imperfect CSI. Manucript received July 22, 2014; revied December 18, 2014; accepted February 19, Date of publication March 27, 2015; date of current verion May 14, Thi reearch ha been upported by the FP7 Networ of Excellence in Wirele COMmunication NEWCOM# Grant agreement no The wor of L. Sanguinetti i alo funded by the People Programme Marie Curie Action FP7 PIEF-GA Dene4Green. A. L. Moutaa i the holder of the DIGITEO ASAPGONE Chair. The reearch of M. Debbah ha been alo upported by the ERC Starting Grant MORE. L. Sanguinetti i with the Dipartimento di Ingegneria dell Informazione, Univerity of Pia, Pia 56122, Italy, and alo with LANEAS, CentralSupélec, Gif-ur-Yvette 91192, France luca.anguinetti@iet.unipi.it; luca. anguinetti@centraleupelec.fr. A. L. Moutaa i with Department of Phyic, National & Capoditrian Univerity of Athen, Athen 15784, Greece arilm@phy.uoa.gr. M. Debbah i with LANEAS, CentralSupélec, Gif-ur-Yvette 91192, France, and alo with the Mathematical and Algorithmic Science Lab, Huawei R&D, Pari 92100, France merouane.debbah@centraleupelec.fr; merouane.debbah@huawei.com. Color verion of one or more of the figure in thi paper are available online at Digital Object Identifier /JSAC I. INTRODUCTION THE bigget challenge for next generation wirele communication ytem 5G today i to upport the ever-growing demand for higher date rate and to enure a conitent quality of ervice QoS throughout the entire networ [1]. Meeting thee demand require to increae networ capacity by a factor of a thouand over the next year [2]. At the ame time, the power conumption of the information and communication technology indutry and the correponding energyrelated pollution are becoming major ocietal and economical concern [3]. Hence, more cellular networ capacity on the one hand and le energy conumption on the other are eemingly contradictory future requirement on 5G. Since pectral reource are carce, there i a broad conenu that thi can only be achieved with a ubtantial networ denification. In general, there are two different approache for thi, namely, large-cale or maive MIMO ytem [4], [5] and mall-cell networ [6]. The firt approach relie on uing array with a few hundred antenna imultaneouly erving many ten of uer equipment terminal UE in the ame frequency-time reource. The baic premie behind maive MIMO i to reap all the benefit of conventional MIMO, but on a much greater cale [5]. The econd approach relie on a very dene deployment of low-cot and low-power mall-cell acce point SCA poibly equipped with cognitive and cooperative functionalitie. Although promiing, each technology alone i unliely to meet the QoS and capacity requirement for 5G [7]. On the other hand, a promiing olution i a two-tier heterogeneou networ HetNet in which the two above technologie coexit and interplay with each other to improve networ performance [1]. In particular, maive MIMO i ued to enure outdoor coverage and to erve mobile UE allowing for handoff minimization, while SCA act a the main capacity-driver for indoor and outdoor UE with low mobility. While conventional bae tation BS are typically connected through a high capacity wired bachaul networ, the ame i not true for SCA, which are liely to be connected via an unreliable bachaul infratructure whoe feature may trongly vary from cae to cae, with variable characteritic of error rate, delay, capacity and epecially deployment cot. For uch ytem, the bachaul repreent one of the major bottlenec [6]. A more economical and viable alternative i to mae ue of the wirele lin a a bachaul [8]. A. Main Contribution In thi wor, we characterize and analyze the power conumption of an HetNet coniting of a maive MIMO macro IEEE. Peronal ue i permitted, but republication/reditribution require IEEE permiion. See for more information.

2 1188 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE 2015 tier overlaid with a econd tier of SCA. The UE are endowed with a ingle antenna and have different peed. Thoe aociated with the SCA are primarily tatic or have low mobility while the medium-to-high mobility one are erved by the macro BS. The exce antenna at the BS are ued to erve the macro UE MUE and at the ame time to play the role of wirele bachaul to the SCA. The latter are divided in two group uch that the ditance between SCA belonging to the ame group i maximized and the ariing interference i controlled. A imilar diviion i performed on the MUE on the bai of their proximity to the SCA ee Fig. 1 of Section II. On the other hand, the interference between the macro and econd tier the o-called two-tier interference i handled uing a revere time-diviion-duplexing TDD mode, i.e., the BS i in downlin DL mode when the SCA operate in uplin UL, and vice vera. The TDD protocol reult in a channel reciprocity that enable not only the etimation of large-dimenional channel at the BS, but alo an implicit coordination between the two tier without the need of exchanging channel tate information CSI through the wirele bachaul. A minimum-mean-quare-error MMSE receiver i ued in UL at the BS for interference mitigation. On the other hand, a concatenated linear precoding technique employing either zeroforcing ZF or regularized ZF RZF i ued in DL to atify rate contraint and to null interference toward SCA, thereby providing the tatic mall cell UE SUE a high-quality UL connection with very mall power. The deign and analyi of the networ i performed under the aumption of imperfect CSI for the MUE due to their mobility and i conducted in the aymptotic regime where the number of BS antenna N and the networ ize MUE and SCA grow large with fixed ratio. A we hall ee, the ue of BS antenna for MMSE reception and precoding allow to eep the UL and DL tranmit power of all networ device at a relatively low level for mall to moderate etimation error of MUE channel. However, we how that for a given et of target rate there i a critical value of imperfect CSI beyond which networ operation become infeaible a it i manifeted by the divergence of all power. In thi cae, MUE with high mobility have to lower their own target rate or they have to be erved uing other tranmiion protocol that do not depend on CSI at the tranmitter uch a for example pace-time coding. Thi might alo reult into a ubtantial reduction of the erved rate. In ummary, the main contribution of thi wor account for: i the development of a revere TDD protocol for the coexitence of a maive MIMO macro tier and a dene tier of SCA uing a wirele bachaul for data traffic; ii the aymptotically deign of a concatenated RZF precoding technique for meeting rate contraint under imperfect CSI of MUE; iii the large ytem analyi of the power conumption in the UL and DL of each tier. B. Comparion With Related Literature The ytem under invetigation and the propoed TDD protocol ha been mainly dicued in [9] wherein the author propoe a imilar protocol to exploit the exce antenna at the BS for intra- and inter-tier interference reduction. In contrat to [9], a wirele bachaul i introduced here for the econdary tier and imperfect CSI i aumed for MUE. The wirele bachaul force u to modify the tranmiion protocol in [9] o a to account for revere TDD not only between tier but alo between SCA. Moreover, we are intereted in evaluating the power conumption of the networ rather than the average um rate and conduct the analyi in the large ytem regime. The wirele bachaul ha alo been recently conidered in [8] and [10]. In [8], the author focu on the calability propertie of a wirele bachaul networ modelled a a random multi-antenna extended networ. In [10], a two-tier networ i conidered under the aumption that SCA are full-duplex device equipped with interference cancellation capabilitie. A different line of reearch for wirele bachaul i in the context of mm-wave communication. In [11], for example, the ue of outdoor mm-wave communication for bachaul networing i conidered and a wind way analyi i preented to etablih a notion of beam coherence time. Thi highlight a previouly unexplored tradeoff between array ize and windinduced movement. The impact of imperfect CSI ha been invetigated in [12] wherein the author conider the DL of a multi-cell MIMO ytem erving UE with large diparitie in mobility. The analyi i conducted in the aymptotic regime and how that the mobility of a UE ha a detrimental effect only on it own achievable rate, but ha no direct impact on the other UE. Intead, we conider a two-tier networ and evaluate the impact of imperfect CSI on the power conumption in the UL and DL of each tier, while guaranteeing requeted rate. Moreover, our analyi how that orthogonal tranmiion reource hould be allocated to highly mobile MUE. A imilar reult ha been pointed out in [13] and [14]. The aymptotically optimal deign of linear precoding technique ha received great attention in the lat year. Some reult in thi context can be found in [15] [17]. In contrat to [15], [16], thi wor conider a two tier networ and focue on analyzing the dual problem namely, the power conumption of the overall networ ubject to target rate. On the other hand, the major difference with repect to [17] are the ytem under invetigation and the imperfect CSI aumption at the BS. C. Organization The remainder of thi paper i organized a follow. 1 Next ection introduce the networ architecture along with the tranmiion protocol and channel model. Section III i focued on the UL phae of the BS and aim at computing the power required by all tranmitter taing into account the ariing interference. In Section IV, we conider the DL and deal with the aymptotic analyi and deign of ZF and RZF. In Section V, numerical reult are ued to validate the theoretical analyi and mae comparion among different networ architecture. In Section VI, we dicu a poible olution to overcome the mobility iue along with that of ome other practical apect uch a networ deign, channel correlation at the BS antenna and dynamic UL-DL TDD configuration. Finally, the major concluion and implication of thi wor are drawn in Section VII. 1 The following notation i ued throughout the paper. Matrice and vector are denoted by bold letter. The upercript denote Hermitian operation and S i ued to denote the cardinality of the encloed et S. We let I K denote the K K identity matrix and ue CN, to denote a multi-variate circularlyymmetric complex Gauian ditribution wherea N, tand for a real one. The notation a.. tand for almot urely equivalent.

3 SANGUINETTI et al.: INTERFERENCE MANAGEMENT IN 5G REVERSE TDD HETNETS WITH WIRELESS BACKHAUL 1189 Fig. 1. Networ architecture. The SCA are divided in two different group, namely, S B blue colour and S R red colour. The ame diviion i performed on the MUE on the bai of their minimum ditance from the SCA. II. SYSTEM MODEL We conider a HetNet where a macro tier i augmented with a certain number of low range SCA. Each SCA poee a ingle antenna and devote it available reource to it precheduled SUE. The macro BS employ N tranmit antenna to erve it aociated ingle-antenna MUE. The MUE are aumed to be ditributed within the coverage area, while the SUE are ditributed uniformly over a circle of radiu R around their correponding SCA. A hown in Fig. 1, we aume that the SCA are divided into two group S R red colour and S B blue colour. We denote by M R M B the et collecting MUE that are cloet to SCA in S R S B. For notational convenience, we call R = M R S R and B = M B S B. While conventional ytem have large diparity between pea and average rate, we aim at deigning the ytem o a to guarantee target rate or, equivalently, ignal-to-interferenceplu-noie ratio SINR value. The analyi i conducted in the aymptotic regime in which the number of BS antenna increae a the networ ize become large. A nown problem with the aymptotic analyi i that the target rate are not guaranteed to be achieved when N i finite and relatively mall ee for example [18]. Thi i becaue the approximation error are tranlated into fluctuation in the reulting SINR value. However, thee error vanih rapidly when N tae large yet finite value a it i enviioned for maive MIMO ytem [19], [20]. A. Tranmiion Protocol The operating protocol i etched in Fig. 2. In the frequency-time lot W 1,T 1, the MUE and SCA in R ue the frequency band W 1 for UL tranmiion BS MUE and BS SCA for a time interval of length T 1 wherea the SCA in B tranmit to their aociated SUE in the DL SCA SUE. In W 1,T 2, the revere tae place, i.e., the BS mae ue of W 1 for a time interval of length T 2 to tranmit in the DL to the MUE and SCA in R wherea the SUE aociated to the SCA in B ue W 1 for UL tranmiion. The frequency-time lot W 2,T 1 and W 2,T 2 are ued in the dual way. A een, the exchange of information within each tier tae place in a revere order, i.e., the BS i in the DL mode BS MUE when the SCA operate in the UL SCA SUE, and vice vera. We aume that tranmiion acro tier are perfectly ynchronized the impact of aynchronou tranmiion will be dicued in Section VI and that the channel frequency repone i flat over each frequency band. We alo aume Fig. 2. Illutration of the tranmiion protocol. The exchange of information within each tier tae place in a revere order, i.e., the BS i in the DL mode BS MUE when the SCA operate in the UL SCA SUE, and vice vera. Fig. 3. Illutration of alternative tranmiion model and networ configuration. a HetNet with wired bachaul [9]. b Maive MIMO. All UE are erved by the macro BS. that T 1 + T 2 i upper bounded by the coherence time of the channel. In thee circumtance, UL and DL channel can be conidered a reciprocal and the BS can mae ue of UL etimate for DL tranmiion more detail on thi will be given later on. Remar 1: Oberve that the tranmiion protocol decribed above i mainly driven by the need: i to provide a wirele bachaul to the SCA while erving MUE and SUE; ii to propoe a viable olution to counteract the ariing interference. Thi i achieved by geographically eparating co-channel SUE and by letting the channel reciprocity condition within each tier and between tier hold in order to properly exploit nowledge of the channel for precoding and decoding more detail on the channel acquiition will be given later on when required. Alternative olution can in principle be found. In the imulation, comparion will be made with the two tranmiion protocol hown in Fig. 3. In particular, the one on the left applie to a revere TDD HetNet in which SCA are connected to the BS through a wired bachaul [9]. On the other hand, the protocol on the right i for a maive MIMO ytem in which only the macro-tier i preent [5]. B. Channel Model and Aumption We denote h M R i C N 1 the vector whoe entry h M R i n account for the intantaneou propagation channel between

4 1190 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE 2015 the ith MUE in M R and the nth antenna at the BS. For mathematical convenience, we aume that the BS antenna are uncorrelated ee Section VI-C for a dicuion on thi aumption. In thee circumtance, the channel vector h M R i can be modelled a [16], [21]: h M R i = Nlx i z i 1 where x i denote the poition of MUE i in M R computed with repect to the BS, z i CN0, I N N 1 account for the mall-cale fading channel and lx i :R 2 R + i the average channel gain due to pathlo at ditance x i. Since the forthcoming analyi doe not depend on a particular choice of lx i a long a it i a decreaing function of the ditance x i and i bounded from below, we eep it generic [22]. Accordingly, we let H MR =[h M R 1 h M R 2 h M R M R ] CN MR be the matrix collecting the channel of all MUE in M R.Theame model i adopted for the SCA and SUE. In particular, we let H SR C N S R and H SB C N S B be the matrice collecting the channel gain from the BS antenna and the SCA in S R and S B, repectively. In all ubequent dicuion, we aume that only an etimate ĤMR of H MR i available. In particular, we model each vector ĥm R i of ĤMR a [16] ĥ M R i = Nlx i 1 τ 2i z i + τ i v i = Nlx i ẑ i 2 where v i CN0, 1/N I N account for the independent channel etimation error. The parameter τ i [0, 1] reflect the accuracy or quality of the channel etimate, i.e., τ i =0correpond to perfect CSI, wherea for τ i =1the CSI i completely uncorrelated to the true channel. Oberve that imperfect CSI arie naturally for MUE a a conequence of mobility [12], [16]. Since SCA occupy fixed poition in the networ, then the propagation channel remain contant for a ufficiently large number of phae to be accurately etimated. For thi reaon, in all ubequent dicuion we aume that H S R and H S B are perfectly nown at the BS i.e., τ i =0if i S R or S B. The ame aumption i made for the SUE channel. III. LARGE SYSTEM ANALYSIS OF THE MACRO-TIER INTERFERENCE IN UL We tart dealing with the cae in which the BS i in UL mode. Without lo of generality, the frequency-time lot W 1,T 1 of Fig. 2 i conidered. 2 A een, two intance of interference appear. One come from UL ignal of MUE and SCA in R and affect the receiving SUE in B wherea the other account for the interference that the BS experience from the DL mode of SCA in S B. The former interference i limited due to the geographical eparation of co-channel SUE. Although inherently mitigated by the geographical eparation of R and B, thi interference can be a limiting factor due to the potentially large number of tranmitting MUE ee alo the analyi in Section VI-B and the lac of patial degree of freedom at the SUE. Therefore, it cannot be neglected but it mut be taen into account while deigning the tranmit power of MUE in UL and SCA in DL. With regard to the latter interference, it eaily follow that the large number of antenna provide an effective mean to mitigate it detrimental effect and at the ame time to imultaneouly erve all tranmitter in R. For thi purpoe, we aume that an MMSE receiver i employed at the BS. For notational convenience, we denote K = R the total number of tranmitter MUE and SCA in R and call S = S B the number of SCA in S B.Wealolet c = K N and c S = S N. 3 We denote H=[h 1, h 2,...,h K ]=[H MR, H SR ] C N K the matrix collecting the intantaneou UL channel of MUE and SCA in R and denote {p R,ul } the correponding UL tranmit power. Denoting G =[g 1, g 2,...,g K ] C N K the MMSE matrix, the UL achievable rate for device in R i [21] R R,ul =log 2 1+SINR R,ul 5 with SINR R,ul given by 6, hown at the bottom of the page, where σ 2 account for thermal noie and p S B,dl i the DL tranmit power of SCA in S B. A mentioned earlier, we aume that the MMSE receiver operate under the aumption of imperfect nowledge of H MR. Thi amount to etting G a in 4 hown at the bottom of the page, [21] where ĥ i the th column of Ĥ given by Ĥ =[ĤMR H SR ]. Oberve that {p R,ul } and {p S B,dl } are aumed to be perfectly nown at the BS. Thi information can be eaily acquired through ignalling [23]. 2 The ame analyi can be performed for W 2,T 1. G = K i=1 SINR R,ul = p R,ul i i=1,i ĥ ĥ + S p R,ul i p S B,dl h S B h S B =1 p R,ul g h i 2 + S =1 g h 2 p S B,dl + Nσ 2 I N 1 Ĥ 4 g hs B σ 2 g 2

5 SANGUINETTI et al.: INTERFERENCE MANAGEMENT IN 5G REVERSE TDD HETNETS WITH WIRELESS BACKHAUL 1191 Remar 2: It i worth oberving that in the frequency-time lot W 1,T 1 under conideration H SR can be eaily acquired at the BS uing UL pilot from SCA in S R. On the other hand, the etimation of H SB mut be performed in a different way ince the UL mode BS SCA for S B tae place over the frequency band W 2. A poible olution might conit in uing pilot that the SCA in S B end in DL SCA SUE to their aociated SUE. An alternative approach might be to periodically witch the operation of frequency band W 1 and W 2 [24]. The aim of thi ection i to compute the UL and DL tranmit power {p R,ul } and {p S B,dl } required to meet target requirement {r R,ul } and {r S B,dl } under imperfect CSI of MUE. For notational convenience, the upercript ul and dl are dropped in the equel. We tart auming that the downlin power {p S B } are fixed and given. Let γ =2 rr 1 be the target SINR value for uer in R. Then, the following lemma can be proved. Lemma 1: If the MMSE receiver in 4 i employed at the BS with correponding SINR expreion given in 6, then in the limit N,K,S with c + c S 0, 1 we have that p R p R a.. 0 with p R = 1 γ ξδ lx 1 τ 2 7 with τ =0if S R. The quantitie ξ and δ are computed a the unique olution to 8 and 9, hown at the bottom of the page. Proof: The proof relie on uing the ame random matrix theory reult of [16] to obtain the determinitic equivalent of the SINR in 5 for a given et of {p S B }. Thi reult i then ued to compute the determinitic equivalent of the power {p R } that are required in the aymptotic regime to achieve the SINR contraint {γ }. The etch of the proof i given in the Appendix. The evaluation of {p S B } require the computation of the DL SINR of the th SUE in S B, which i given by SINR S B = σ 2 + K p S B h 2 =1 p R h, 2 10 where h i the channel propagation coefficient from it erving SCA wherea h, i the channel coefficient of the th interfering UL tranmiion in R. 3 Oberve that if K i large, then the interference term in 10 can be reaonably aumed to be determinitic and equal to it mean ee Section VI-B for more detail on thi. More pecifically, under the aumption that all power p R are finite and the cell ize i fixed, uing the law of large number yield 1 p R K h, 2 1 p R K K lx, 11 =1 =1 where x, denote the ditance of SUE from tranmitter in R. In contrat, the power of the ueful ignal in 10 i a random quantity that depend on the fluctuation of h 2.To tae thi randomne into account, we ue the ergodic mutual information a a metric. 4 Uing 11, we find the following aymptotic reult: { E h log 2 1+SINR S B where E 1 z = z wherea dt e t } SINR S B = K e 1/SINRS B E 1 log2 1/SINR S B 12 t i the exponential integral of order 1 σ 2 + K p S B lx =1 p R lx, 13 with p R being obtained from 7. Impoing 12 equal to r S B and inverting the exponential integral provide the target SINR γ. Setting SINR S B = γ and uing 7, the DL power of SCA atifying the target contraint i obtained a p S B = γ σ γ lx, lx ξδ 1 τ 2 14 lx =1 with τ =0if S R and γ =2 rr 1. Plugging the above reult into 8 and 9, it follow that the computation of the power {p R } and {ps B } reduce to the eay ta of finding ξ and δ a the unique olution of 8 and 9 that depend only on ytem parameter uch a imperfect CSI factor {τ },SINR contraint {γ } and number of MUE and SCA. 3 In writing 10, we have not neglected the interference coming from the other SCA in S B a they are aumed to be relatively paced apart. 4 Oberve that an alternative route might be that of uing the outage capacity criterion. [ ξ = 1 σ N δ = 1 N i=1 γ i δ 1 N γ i δ1 τi 2+γ 1 i N i=1 i=1 τ 2 i 1 τ 2 i γ i 1 τi 2 δ + 1 δ1 τi 2+ γ i δ 2 N + 1 N i=1 S =1 S =1 γ i γ i 1 τi 22 δ τi 2+ γ i δ 2 N ] p S B lx ξ 1+p S B lx ξ p S B lx ξ 1+p S B 2 + ξσ 2 lx ξ S = p S B lx ξ 1+p S B 2 + ξσ 2 lx ξ

6 1192 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE 2015 From the above reult, it follow that the imperfect CSI coefficient {τ } impact both ξ and δ in 8 and 9. In particular, from 7 it follow that ξδ 1 can be thought of a the fractional UL power increae of all tranmitter MUE and SCA in R. Interetingly, thi happen even though only the MUE channel are etimated erroneouly while perfect CSI i aumed for SCA. To gain ome inight on the maximum tolerable level of imperfect CSI, we now loo for which value of {τ } and {γ } the power diverge. Thi amount to olving 9 for δ 0 ince ξ can be hown to remain finite even when all power diverge. In doing o, it turn out that 9 ha finite poitive olution only if 1 2 τ γ N 1 τ 2 1 c c S. 15 M R If thi condition i not met, then all power diverge. If τ = τ for any M R one get that τ ha to be maller than τ max MMSE given by 1/2 τ max MMSE = 1+ γ M c 16 1 c c S where γ M tand for γ M = 1 γ 17 K M R average SINR requirement of all device in M R. IV. LARGE SYSTEM ANALYSIS OF THE MACRO-TIER INTERFERENCE IN DL We now conider the cae in which the BS i in DL mode. Without lo of generality, the frequency-time lot W 1,T 2 of Fig. 2 i conidered. A for the UL, two intance of interference arie. The interference experienced by MUE and SCA from UL tranmiion in S B can be reaonably neglected ince the number of tranmitting SUE i relatively mall one per SCA and geographically far away from the MUE and SCA in R. On the other hand, the interference from BS to the SCA in UL mut be properly mitigated to avoid a evere degradation of the networ performance. For thi purpoe, we aume that the BS mae ue of linear precoding and acrifice ome of it degree of freedom or exce antenna to imultaneouly erve all receiver in R and at the ame time to null the interference toward S B.WeletV =[v 1, v 2,...,v K ] C N K be the precoding matrix and denote p R,dl the DL tranmit power aigned to the th device in R. The total DL tranmit power at the BS i [25] P R,dl = =1 p R,dl v 2 18 wherea the achievable DL rate for a generic receiver in R i R R,dl =log SINR R,dl with p R,dl SINR R,dl h v 2 =. 19 h v i 2 + σ 2 We impoe R R,dl with γ =2 rr,dl i=1,i p R,dl i = r R,dl or, equivalently, SINR R,dl = γ 1. Than to the reciprocity of UL and DL channel, the BS can exploit UL etimate for DL tranmiion. A for the UL, we aume that perfect nowledge of H S B and H S R i available while imperfect CSI i aumed for H M R. For notational convenience, the upercript dl i dropped in the equel. The complete elimination of the macro-tier interference at SCA in S B can be achieved by contraining the precoding matrix V to lie in the null pace of H S B. Under the aumption of perfect nowledge of H S B, thi i achieved etting V = T S B F where F =[f 1, f 2,...,f K ] C N K i a deign matrix and T S B C N N i obtained a T S B = I N H S B H S B H S B 1 H S B. 20 Let U = T SB H C N K be the compoite channel and denote Û it correponding etimate defined a Û = TSB Ĥ under the aumption given above where Ĥ =[ĤMR H SR ]. The matrix Û i ued in the equel to deign F according to the RZF and ZF criteria. A. Regularized Zero Forcing We tart auming that F tae the following form: F = ÛΛ 1 Û + NρI N 1 Û 21 where Λ =diag{lx 1,lx 2,...,lx K } and ρ>0 i a deign parameter. A in [16], ρ i multiplied by N to enure that ρ converge to a contant a N,K,S. We refer to the concatenated matrix V RZF = T S B F a RZF and denote P R RZF = K =1 p R T SB 2 f 22 it correponding tranmit power. Oberve that in the deign of F in 21 we exploit nowledge of the average channel attenuation {lx i } through Λ. Thi information can be eaily oberved and etimated accurately at the BS becaue it change lowly with time relative to the mall-cale fading even for MUE with medium-to-high mobility. Thi choice i inpired to [17] wherein it i proved that in the downlin of a ingletier MIMO ytem with perfect CSI, uch a ind of RZF i aymptotically equivalent to the optimal linear precoder when the ame rate contraint are impoed for all UE. Due to the imperfect CSI and the projection into the null pace of SCA in S B, the reult in [17] do not apply to networ under invetigation. However, the ue of {lx i } i intrumental to get a cloed form expreion for the optimal ρ in 21.

7 SANGUINETTI et al.: INTERFERENCE MANAGEMENT IN 5G REVERSE TDD HETNETS WITH WIRELESS BACKHAUL 1193 For convenience, we let A = 1 K M R γ 1 τ 2 lx + 1 K S R γ lx 23 and and denote B = 1 2 τ γ K 1 τ 2 M R 24 γ = 1 γ 25 K =1 the average SINR requirement of all device in R. Lemma 2: If RZF i ued and N,K,S with c + c S 0, 1, then P R RZF P R a.. RZF 0 where P R RZF i given by P R RZF = cσ 2 A ρ γ 26 cb where the optimal ρ i computed a Alo, p R p R ρ = 1 c S γ a.. p R = γ R P RZF lx γ 2 0 with c 1+ γ τ 2 +τ 2 1+ γ2 + σ2 lx 1 + γ2 1 τ 2 28 with τ =0if S R. A it i een, ρ doe not depend on {τ } and it i baically in the ame form of the perfect CSI cae in [17] with the exception of the term 1 c S that account for the interference nulling toward the SCA. Indeed, if no SCA are active in the networ, then c S =0and ρ tae the ame form in [17]. Since P R RZF mut be poitive and finite, from Lemma 2 it i een that the following condition mut be atified: 1 K 2 τ γ 1 τ 2 M R < ρ γ 29 c from which etting τ = τ for any M R one get τ<τ max RZF = 1+ c γ M 1/2 ρ 30 γ where γ M i given by 17. B. Zero Forcing Setting Λ = I K into 21 yield F =ÛÛ + NρI N 1 Û from which uing the Woodbury matrix identity and impoing ρ =0the ZF precoder V ZF = T SB ÛÛ Û 1 eaily follow or, equivalenty, V ZF = T S B Ĥ Ĥ T S B Ĥ Fig. 4. A naphot of the UE ditribution in the imulated networ wherein the number of SCA i 16 and the number of MUE i 128. The latter are ditributed uch that 8 of them are in the proximity of the coverage are of a given SCA. A ingle SUE i active for each SCA. Lemma 3: If ZF i ued and K, N with c + c S 0, 1, then P R ZF P R a.. ZF 0 with P R ZF = cσ 2 A 1 c S cb a.. Alo, p R p R 0 with p R = γ 1 τ 2 σ 2 + τ 2 lx P R ZF 33 with τ =0if S R. Proof: The proof follow the ame tep of that for Lemma 2 and thu i omitted for pace limitation. From 32, it i een that the following condition mut be atified: 1 c S cb +1> 0 or, equivalently, 1 2 τ γ K 1 τ 2 < 1 c c S. 34 M R c If τ = τ for any, then we have that 1/2 τ<τ max ZF = 1+ γ M c c c S From 30, it i een that τ max max RZF i alway larger than τ ZF, meaning that RZF i more robut than ZF to imperfect CSI of MUE. Oberve that the ame condition a in 35 mut be fulfilled in the UL ee 16 in Section III. V. N UMERICAL RESULTS Monte-Carlo imulation are now ued to how that the above aymptotic characterization provide an effective mean to evaluate the performance of a networ with finite ize. The

8 1194 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE 2015 TABLE I GENERAL SYSTEM PARAMETERS particular, we aume τ = τ and let τ 2 = τ 2 + ς 2 where τ 2 i baically modelled a a contant term that baically account for pilot contamination, noiy meaurement and other ource of etimation error while ς account for etimation error induced by mobility. Following [12], [16], we et τ 2 = 0.08 while we compute ς 2 a follow [21] ς 2 =1 J0 2π 2 v λ ζ 37 Fig. 5. Average UL tranmit power for MUE and SCA a a function of MUE rate for different networ architecture when τ 2 =0.1 and the wirele bachaul traffic i fixed to 3 bit//hz. reult are obtained for 1000 different channel realization and UE ditribution. We aume that the BS i equipped with N = 128 antenna and cover a quare area centered at the BS with ide length 500 m over which 16 SCA are ditributed on a regular grid with an inter-ite ditance of 125 m. We aume that 128 MUE are active in the cell and that a ingle SUE i uniformly ditributed within a dic of radiu 35 m around each SCA. The SUE are aociated with the cloet SCA while the MUE are aociated with the BS. Accordingly, the two et R and B count 64 MUE and 8 SCA with 8 MUE in the proximity of each SCA. A random naphot of the networ i depicted in Fig. 4. We aume that the UL and DL wirele and r S B,ul are equal and fixed to 3 bit//hz. The pathlo function lx i [22] 1 lx =2L x 1+ x β x β 36 bachaul rate of SCA r S B,dl where β>2 i the pathlo exponent, x >0 i ome cut-off parameter and L x i a contant that regulate the attenuation at ditance x. We aume that β =3.5 and L x = 86.5 db. The latter i uch that for f c =2.4 GHz the attenuation at x i the ame a that in the cellular model analyzed in [26]. Although in TDD ytem the effective value of {τ } are expected to be different between UL and DL ince the channel are etimated in the UL and then ued in DL, the ame value of {τ } are ued for both lin in all ubequent imulation. In where J 0 denote the 0-th order Beel function of the firt ind, v i the velocity in m/ of MUE, λ i the carrier wavelength in meter and ζ i the UL or DL lot duration in econd. Since λ =0.125 m, etting ζ =1m and v =15or 50 m/h yield τ 2 =0.1 and 0.3, repectively. The parameter etting i ummarized in Table I for implicity. Comparion are made with the two alternative protocol and networ configuration mentioned in Remar 1. In particular, we conider a HetNet in which the SCA ue a wired bachaul infratructure for data traffic and a maive MIMO ytem in which all UE MUE and SUE are erved by the macro BS. Oberve that marer ymbol correpond to Monte Carlo imulation while olid line are baed on the analytic reult. Fig. 5 depict the average tranmit power for MUE and SCA over the cell a a function of the requeted rate of MUE when τ 2 =0.1. Depite the fact that the power of SCA in 7 doe not depend explicitly on the MUE rate r R,ul for M R, a mild dependence on MUE requirement i hown in the reult of Fig. 5. Thi i due to the fact that increaed target rate for the MUE reult to increaed overall interference in the ytem. A imilar behaviour i oberved in Fig. 6 for the DL power of SCA. From the reult of Fig. 5, it alo follow that the average UL power of MUE in the propoed HetNet i eentially the ame of a HetNet with wired bachaul even though a wirele bachaul traffic of 3 bit//hz i provided. In addition, it how that the uplin tranmit power of SCA are quite cloe to thoe of SUE in the Maive MIMO cae. On the contrary, Fig. 6 how a ignificant power reduction for SCA in DL mode. Thi i becaue the reception of aociated SUE i properly hielded from nearby MUE in the propoed networ architecture. Fig. 7 and 8 provide inight on the effect of channel uncertainty on power conumption. Here again the target rate for the SCA are fixed to 3 bit//hz. Clearly, τ 2 =0correpond to the perfect CSI cae. It can be een that for τ 2 =0.3 correponding to a velocity of 50 m/h the ytem become infeaible if the MUE target rate go beyond a certain level given approximately by 1.5 bit//hz a obtained through 16. A een, the power rapidly increae within a relatively narrow

9 SANGUINETTI et al.: INTERFERENCE MANAGEMENT IN 5G REVERSE TDD HETNETS WITH WIRELESS BACKHAUL 1195 Fig. 6. Average DL tranmit power for SCA toward their repective SUE a a function of MUE rate for the HetNet and HetNet with wired Bachaul architecture when τ 2 =0.1 and the wirele bachaul traffic i fixed to 3 bit//hz. Fig. 8. Average DL tranmit power for SCA in the propoed HetNet architecture a a function of MUE rate for different value of τ 2. The wirele bachaul traffic i et to 3 bit//hz. Fig. 7. Average UL tranmit power for MUE and SCA for the propoed HetNet architecture a a function of MUE rate for different value of τ 2.The wirele bachaul traffic i et to 3 bit//hz. window beyond thoe rate value, thereby allowing the ytem to operate at relatively low power up to cloe the critical point. Fig. 9 and 10 illutrate the average DL tranmit power of the BS when RZF and ZF are employed with τ 2 =0.1. A expected, RZF provide a ubtantial power reduction with repect to ZF. In particular, we oberve that for a target rate of 2 bit//hz only 0.1 W are required at the BS to erve in DL all MUE and SCA. Compared to a maive MIMO ytem, a marginal increae of power i required by the propoed HetNet. However, thi i achieved with the benefit of a ubtantial power aving at the SUE. Indeed, numerical reult reveal that for a target ergodic rate of 3 bit//hz, the required power for a SUE i 0.85 mw in the HetNet cae while it i 0.22 W for a maive MIMO ytem. Oberve that thi power aving at SUE i of paramount importance a it allow to prolong the lifetime of batterie. Compared to an HetNet with wired bachaul, the propoed architecture achieve a ubtantial power aving epecially for large target rate. A for the UL, thi i becaue the interference from SUE i properly hielded. Fig. 11 report the average DL tranmit power at the BS of RZF and ZF when τ 2 =0, 0.1 and 0.3. A een, for τ 2 = 0.3 the power required by both precoding technique diverge when the MUE target rate increae. A expected, RZF i more robut than ZF to imperfect CSI and can handle rate up to 1.75 bit//hz. To facilitate comparion and highlight the potential gain of the propoed HetNet, in Table II we report the UL and DL power conumption in the networ. In particular, we conider the cae of a MUE target rate of 1.5 bit//hz and a velocity of 15 m/h i.e., τ 2 =0.1. From the imulation above, it follow that the average UL power of each MUE i 83 mwatt. Taing into account that the bandwidth i 10 MHz and the number of MUE for each frequency band i 64, thi correpond to an aggregate area throughput of 3.84 Gb//m 2. An additional throughput of 0.96 Gbit//m 2 come from the 8 SUE tranmitting to the BS through the SCA at target rate of 3 bit//hz. Thi occur at the cot of 0.25 Watt for each SCA while the power conumed by a SUE i relatively mall and given by 0.85 mwatt. In the DL, the ame throughput a for the UL i achieved conuming only 55 mwatt at the BS and 0.75 Watt at the SCA. Putting everything together, it follow that a total aggregate area throughput of 4.8 Gb//m 2 i achieved with a total power conumption of only 5.52 Watt in the UL and 6.05 Watt in the DL, thereby howing the potential gain of the propoed HetNet. Note that the total power conumption of the maive MIMO networ i 8.32 Watt in the UL while it i only Watt in the DL. A mentioned above, however, thi i achieved at the price of a large increae of the tranmit power at SUE up to 0.22 W compared to the propoed HetNet only 0.85 mwatt.

10 1196 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE 2015 TABLE II POWER CONSUMPTION IN WATT OF THE DIFFERENT ARCHITECTURES FOR A MUE TARGET RATE OF 1.5 bit//hz WITH τ 2 =0.1 Fig. 9. Average DL tranmit power at the BS when RZF i employed with τ 2 =0.1 and wirele bachaul 3 bit//hz. Comparion are made with a HetNet with wired bachaul and a ingle-tier maive MIMO ytem operating according to the tranmiion protocol of Fig. 3. Fig. 10. Average DL tranmit power at the BS when ZF i employed with τ 2 = 0.1 and wirele bachaul 3 bit//hz. Comparion are made with a HetNet with wired bachaul and a ingle-tier maive MIMO ytem operating according to the tranmiion protocol of Fig. 3. VI. DISCUSSIONS AND PERSPECTIVES In thi ection, we dicu the impact of mobility along with ome other practical apect of the propoed HetNet. Fig. 11. Average DL tranmit power at the BS when RZF and ZF are employed with different value of τ 2 and wirele bachaul 3 bit//hz. A. Impact of Mobility In [12], the author how that if the networ um rate i conidered then low and high mobility MUE can coexit and be erved imultaneouly. Thi i becaue the imperfect CSI of each given MUE ha detrimental effect only on it own achievable rate while it ha no impact on the performance of the other. Thi i in harp contrat to the reult obtained in thi wor where we have hown that the UL and DL tranmit power for meeting target rate depend heavily on the mobility of each MUE. In particular, a ingle MUE with high mobility and rate requirement might largely increae the required power. Thi call for alternative olution. The implet one would be to lower the target rate and thu the correponding SINR for the MUE with large channel etimation error uch that, for example, in UL the condition for δ 0 in 15 i atified. An alternative olution for DL mode might conit in dividing the MUE in two et A M and A H with A M A H = characterized by medium and high mobility, repectively. The MUE in A M are erved imultaneouly while thoe in A H are erved one at a time uing pacetime coding STC technique that do not require any CSI at the BS. Conider for example the frequency-time lot W 1,T 2 for which M R = A M A H.LetK = A M + S R, K STC = A H and S = S B. The BS would firt imultaneouly tranmit to the K MUE and SCA in R = A M S R while removing the interference toward to the S SCA in S B. Then, it would erve the K STC MUE in A H one at a time while nulling the interference to S B. In thee circumtance, the ignal tranmitted to MUE in A H tae the form x = T S B with

11 SANGUINETTI et al.: INTERFERENCE MANAGEMENT IN 5G REVERSE TDD HETNETS WITH WIRELESS BACKHAUL 1197 being uch that E{ } = pa H,dl /N I N correponding to uniform STC. A a conequence, the determinitic equivalent of the DL SINR of MUE in A H i found to be: SINR A H,dl 1 c S pah,dl lx a.. σ from which uing dominated convergence argument and continuou mapping theorem it follow that p A H,dl p A H,dl a.. 0 with p A H,dl = 1 γ σ 2 1 c S lx. Let T STC be the time required to erve the K STC MUE in A H and call T LP = T 2 T STC where LP tand for linear precoding and T 2 i defined in Fig. 2. Accordingly, the average pectral efficiency R AVG in bit//hz of the networ over T 2 = T LP + T STC i R AVG = T LP T 2 log 2 1+γ + T STC T 2 K STC =1 K+K STC =K+1 log 2 1+γ and the correponding energy conumption i obtained a E T2 = cσ 2 K+K AT LP 1 c S cb +1 + T STC 1 γ σ 2 STC 1 c S lx. =K+1 A een, the rate of MUE erved by STC i reduced by a factor 1/K STC compared to the other one if T STC T LP.Onthe other hand, if T STC K STC T LP then the pectral efficiencie are comparable, but the energy conumption increae ubtantially. B. Tradeoff Between Proximity Effect and Denity of Uer A cloe inpection of 13 reveal that the interference term I K = K =1 pr lx for SUE in S B increae with K.Thi mean that, although patially eparated, the interference from UL ignal in R might be large due to the poibly large value of K. For example, for the etting of Table II the average interference level normalized to the noie power i numerically found to be Although pretty ignificant, thi interfence level doe not prevent the networ to properly operate ince SUE experience on average good SINR due to their proximity to the SCA. Clearly, thi i a conequence of the pecific networ under conideration and, in particular, it largely depend on the SCA radiu R, the inter-sca-location ditance Δ and the MUE denity. All thee parameter play a ey role in determining the SINR of SUE. Unfortunately, a theoretical analyi revealing the interplay among all of them i a challenging problem. To partially addre thi iue, we reort to a ind of wort cae cenario in which the MUE tranmit with contant power, i.e., p R = p, and are uniformly ditributed with denity α in an infinite cell with the only exception of a circle of radiu d =Δ/2 Raround the SUE. 5 5 From Fig. 4, it follow that d i actually the minimum ditance x between any SUE-MUE pair ince it correpond to the extreme cae of the SUE being at ditance R from the SCA and the MUE being at the cloet point to it. Under the above aumption, we have that detail are omitted for pace limitation: E{I K }= 4παpL x x β β 2 d β 2 F 1, 1 2 β ;2 2 x β β, 39 d where F i the hypergeometric function [27]. Plugging the ytem parameter of Table I into the above equation and etting p =83mWatt a pecified in Table II yield E{I K }/σ , which i of the ame order of the one evaluated numerically and given by Thi validate the above analyi and mae 39 accurate enough although derived under implifying aumption. Interetingly, if d x then 39 reduce to E{I K } 4παpL x β 2 from which the value d β 2 of d required to eep the interference level at a precribed value for a given MUE denity can be eaily obtained. Moreover, oberving that ld x β /d β for d x we obtain E{I K } 2π β 2 αd2 pld, which ha the following very intuitive explanation: The average interference i up to a proportionality factor 2π/β 2 only due to the αd 2 MUE located at a ditance of order d from the SUE. Thi provide a imple way to evaluate the tradeoff between the denity of uer and the minimum eparation between MUE and SUE. Oberve that the above analyi i valid only when the MUE are uniformly ditributed. If thi aumption doe not hold true, the problem i much more involved ince the location itelf of SCA hould be alo optimized taing into account the patially varying MUE denitie. However, uch a cae i beyond the cope of thi wor and left for future reearch. C. Impact of Correlation at BS Antenna If the BS antenna are correlated, then the channel vector of the ith device in A i modelled a h A i = Nlx i Θ 1/2 i w i where Θ i denote the ith channel correlation at the BS [16]. A for poition x i, the matrice Θ i are uually aumed to change lowly compared to the channel coherence time and thu are uppoed to be perfectly nown at the BS [16], [28]. A a conequence, ĥa i can be reaonably modelled a ĥa i = Nlxi Θ 1/2 i ẑ i with ẑ i till given by 2. Aume that RZF i employed. Then, V RZF = T SB F with 1 F = N Θ 1/2 i ẑ i ẑ 1/2 i Θ i + NρI N Û 40 i=1 Θ 1/2 where Û = TSB Ĥ and i = T SB Θ 1/2 i. Following the ame tep in [16], [28], one can in principle compute the determinitic equivalent of {p R R } and P RZF for Θ i I N. Although poible not hown for pace limitation, thi end up to compute the fixed point of a et of equation and to evaluate the invere of K K matrix. All thi i not only much more involved than the cae Θ i = I N but it i alo le intrumental to get inight into the tructure of the aymptotic tranmit power and into the interplay among the different parameter uch a imperfect CSI factor {τ }, SINR contraint {γ } and number of MUE and SCA. In addition, the optimal regularization parameter ρ can only be found through a numerical optimization procedure. x β

12 1198 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE 2015 the BS mut be deigned o a to alo mitigate interference toward the SUE in S B.IfSCA SUE i horter than BS MUE, the SCA in S B are affected by the interference due to UL tranmiion in M R and S R. The effect of thi interference would be the ame of that evaluated in Section III. In ummary, the propoed networ architecture and tranmiion protocol allow dynamic TDD tranmiion within the mall-cell tier from SCA to SUE while a full duplex BS would be required to handle aynchronou tranmiion at the macro-tier level. Fig. 12. Average DL tranmit power at the BS when RZF i employed with different value of τ 2 and wirele bachaul 3 bit//hz. Comparion are made with the cae in which BS antenna are correlated. Fig. 12 report the DL tranmit power when the BS i equipped with RZF and antenna are correlated. Following [28], the entrie of Θ for =1, 2,...,K are computed a [Θ ] i,l = 1 θ +Δ ϕ /2 e iπ coϕ ϕ 41 Δ ϕ θ Δ ϕ /2 where Δ ϕ i the angular pread and θ i the directional of departure of the th ignal. We et Δ ϕ = π/12 and aume that θ are uniformly ditributed in [0, 2π. Only a marginal difference i oberved in term of required power between the two cae. Moreover, imperfect CSI ha the ame impact in both cae. A imilar behaviour i obtained for larger value of Δ ϕ up to Δ ϕ = π/6. D. Dynamic UL-DL TDD The tranmiion protocol of Fig. 2 relie on the aumption that tranmiion acro tier are perfectly ynchronized. However, the ynchronou operation with a common UL and DL configuration in multiple cell may not match the intantaneou traffic ituation in a particular cell. The amount of traffic for DL and UL may vary ignificantly with time and between cell. Thi call for the adoption of a dynamic UL-DL configuration [24]. Henceforth, we dicu ome practical implication of dynamic TDD for the propoed networ architecture. Conider for example the frequency band W 1 in Fig. 2 and aume that the SCA in S R are not aligned with the UL and DL tranmiion of MUE in M R. If for example the UL phae BS SCA i horter than BS MUE, then the ubequent DL phae BS SCA would partially overlap with BS MUE. A imilar ituation would occur if the SCA are in the UL for a longer time interval. In both cae, the adoption of a dynamic TDD protocol at the SCA would require a full duplex BS. On the other hand, if the SCA in S B are not aligned with the MUE in M R, the following two ituation might occur. If SCA SUE i longer than BS MUE, then the linear precoder at VII. CONCLUSION Thi wor ha focued on the power conumption in the UL and DL of a HetNet in which a maive MIMO macro tier erving medium-to-high mobility UE i overlaid with a dene tier of SCA uing a wirele bachaul for traffic. A revere inter-tier and intra-tier TDD protocol ha been propoed to let the BS imultaneouly handle the traffic of macro UE and SCA without cauing much interference to the overlaid tier. Linear proceing ha been ued at the BS for data recovery and tranmiion while atifying rate requirement and mitigating interference. In particular, we have conidered an MMSE receiver and a concatenated linear precoding technique baed on ZF and RZF. The analyi ha been conducted in the aymptotic regime where the number of BS antenna and networ ize grow large with fixed ratio. Reult from random matrix theory have been ued to derive cloed-form expreion for the tranmit power and beamforming vector a well a to invetigate the impact of imperfect CSI on the power conumption. It turn out that for a given et of target rate there i a critical value of imperfect CSI beyond which the power of all tranmitter rapidly increae and eventually diverge. However, analytical and numerical reult have hown that when uch critical value are not met the propoed architecture allow to achieve an aggregate area throughput on the order of 4.8 Gb//m 2 in UL and DL on a 10 MHz band with a very limited amount of power on the order of 6 Watt in both UL and DL. An important follow-up of thi wor could be the development of cheduling algorithm for erving MUE characterized by very high mobility without lowering the erved rate. The extenion of the analyi to the DL of a multi-cell networ in which multiple BS with limited cooperation are active i alo very much intereting [29]. Thi could be addreed uing the reult in [30] and [31]. The large ytem analyi ued throughout thi wor could in principle be alo ued for other macro-diverity tudie uch a thoe in [32]. An intereting problem i alo to develop networ architecture able to exploit the gain of maive MIMO when the macro tier level operate according to a frequency diviion duplexing FDD ytem. APPENDIX 1 Proof of Lemma 1: The proof build upon applying the aymptotic reult hown in Appendix II of [16] under the aumption that the correlation matrix of h i given by lx I N. More preciely, the determinitic equivalent of g h follow directly from [16] by taing into account that G in 4

13 SANGUINETTI et al.: INTERFERENCE MANAGEMENT IN 5G REVERSE TDD HETNETS WITH WIRELESS BACKHAUL 1199 SINR R P R + ξ2 ξ 1 N i=1 RZF = cμ 1 + μ 2 lx i p R i =1 [ τi τ 2lx p R ] 1 τi ξlx i p R i 1 γ K 1 τ 2 lx μ 2 P R RZF S + 1 lx p S B N =1 1+ξlx p S B 2 + σ 2 1 τ 2 + τ μ 2 + σ2 1 + μ 2 lx a include the power p R,ul. Omitting the mathematical detail for pace limitation, we have that g h 1 τ 2 ξlx a ξlx p R,ul where ξ i given by 8. The aymptotic expreion of g g i found to be [16] g g + lx ξ a ξlx p R,ul and i obtained by imply noting that g g = ĥ g where denote the derivative with repect to σ 2. To compute the determinitic equivalent of g h i 2, we apply the Woodbury identity twice and ue the ame argument a in [16] to obtain τi τi 2 lx ilx ξ ξlx i p R i 2 1+ξlx p R The determinitic equivalent of g hs B 2 follow from the above reult by recalling that τ i =0for SCA channel. Plugging everything together lead to 45, hown at the top of the page, from which impoing SINR R = γ the reult follow uing imple calculu. 2 Proof of Lemma 2: The proof follow the ame tep of [16] with the only exception that the projection matrix T SB mut be included in the analyi. Note that ÛΛ 1 Û = K =1 TS Bẑ ẑ TSB uch that 1 F = N T S Bẑ ẑ TS B + NρI N T SB Ĥ 47 =1 which i exactly in the ame form of the RZF precoder ued in [16] when all the UE have the ame correlation matrix given by T SB uing the notation of [16] thi amount to etting Θ = T SB. From the reult of Theorem 2 in [16], it follow that if T SB ha uniformly bounded pectral norm on N i.e., lim up N,K,S TSB < then SINR R P R RZF p R 1 τ 2 lx μ 2 1 τ 2 + τ μ2 + σ2 1+μ 2 lx a.. 0 with τ =0if M R and μ being the olution of μ = 1 1 N tr T S B T S c B 1+μ + ρi N Applying the Woodbury identity to T S B c 1+μ + ρi N with T S B given in 20 and oberving that trh SB H S B H SB 1 H S B =S, then 48 become 1 c μ =1 c S 1+μ + ρ. 49 The determinitic equivalent of P R RZF i found to be [16] P R RZF = cμ μ 2 p lx 50 K =1 with μ = μ1+μ2 c+ρ1+μ. Aume now that the power p R 2 i choen uch that SINR R i equal to a pecified γ in the large ytem limit. Then, one get p R = γ R P RZF 1 τ 2 + τ μ2 + σ2 lx 1 + μ2 lx μ 2 1 τ 2 51 with τ =0if S R, which ued in 50 yield 46. Solving 46 with repect to P R RZF and taing the derivative with repect to ρ yield omitting the computation for implicity P R RZF = ρ 2c 2 Aσ 2 γ μ μ c + ρ 1 + μ 2 c γ + B1 + μ 2 2. From the above reult, it turn out that the minimum power i achieved when μ = γ. Plugging thi reult into 49 yield 27 from which the reult in Lemma 2 follow from 46 and 51. REFERENCES [1] J. Andrew et al., What will 5G be? IEEE J. Sel. Area Commun., vol. 32, no. 6, pp , Jun [2] The 1000x Data Challenge, Qualcomm, Tech. Rep. [Online]. Available: [3] Smart 2020: Enabling the low carbon economy in the information age, The Climate Group and Global e-sutainability Initiative GeSI, Bruel, Belgium, Tech. Rep., [Online]. Available: mart2020.org [4] T. Marzetta, Noncooperative cellular wirele with unlimited number of bae tation antenna, IEEE Tran. Wirele Commun., vol. 9, no. 11, pp , Nov [5] E. Laron, O. Edfor, F. Tufveon, and T. Marzetta, Maive MIMO for next generation wirele ytem, IEEE Commun. Mag., vol. 52, no. 2, pp , Feb [6] J. Hoydi, M. Kobayahi, and M. Debbah, Green mall-cell networ, IEEE Veh. Technol. Mag., vol. 6, no. 1, pp , Mar [7] V. Jungnicel et al., The role of mall cell, coordinated multipoint, and maive MIMO in 5G, IEEE Commun. Mag., vol. 52, no. 5, pp , May 2014.

14 1200 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 6, JUNE 2015 [8] H. S. Dhillon and G. Caire, Wirele bachaul networ: Capacity bound, calability analyi and deign guideline, CoRR, vol. ab/ , [Online]. Available: [9] J. Hoydi, K. Hoeini, S. ten Brin, and M. Debbah, Maing mart ue of exce antenna: Maive MIMO, mall cell, and TDD, Bell Lab Tech. J., vol. 18, no. 2, pp. 5 21, Sep [10] B. Li and P. Liang, Small cell in-band wirele bachaul in maive MIMO ytem: A cooperation of next-generation technique, CoRR, vol. ab/ , [11] S. Hur et al., Millimeter wave beamforming for wirele bachaul and acce in mall cell networ, IEEE Tran. Commun., vol. 61, no. 10, pp , Oct [12] A. Muller, E. Bjornon, R. Couillet, and M. Debbah, Analyi and management of heterogeneou uer mobility in large-cale downlin ytem, in Proc. Ailomar Conf. Signal, Syt. Comput., Nov. 2013, pp [13] H. Shirani-Mehr, G. Caire, and M. Neely, MIMO downlin cheduling with non-perfect channel tate nowledge, IEEE Tran. Commun., vol. 58, no. 7, pp , Jul [14] P. de Kerret and D. Gebert, Degree of freedom of the networ MIMO channel with ditributed CSI, IEEE Tran. Inf. Theory, vol. 58, no. 11, pp , Nov [15] R. Zahour and S. Hanly, Bae tation cooperation on the downlin: Large ytem analyi, IEEE Tran. Inf. Theory, vol. 58, no. 4, pp , Apr [16] S. Wagner, R. Couillet, M. Debbah, and D. T. M. Sloc, Large ytem analyi of linear precoding in correlated MISO broadcat channel under limited feedbac, IEEE Tran. Inf. Theory, vol.58,no.7,pp , Jul [17] L. Sanguinetti, E. Björnon, M. Debbah, and A. Moutaa, Optimal linear pre-coding in multi-uer MIMO ytem: A large ytem analyi, in Proc. IEEE GLOBECOM, Dec. 2014, pp [18] A. T. H. Agharimoghaddam and N. Rajatheva, Decentralizing the optimal multi-cell beamforming via large ytem analyi, in Proc. IEEE Int. Conf. Commun., Sydney, Autralia, Jun. 2014, pp [19] J. Hoydi, S. ten Brin, and M. Debbah, Maive MIMO in the UL/DL of cellular networ: How many antenna do we need? IEEE J. Sel. Area Commun., vol. 31, no. 2, pp , Feb [20] H. Huh, G. Caire, H. Papadopoulo, and S. Ramprahad, Achieving maive MIMO pectral efficiency with a not-o-large number of antenna, IEEE Tran. Wirele Commun., vol. 11, no. 9, pp , Sep [21] D. Te and P. Viwanath, Fundamental of Wirele Communication. New Yor, NY, USA: Cambridge Univ. Pre, [22] L. Sanguinetti, A. Moutaa, E. Bjornon, and M. Debbah, Large ytem analyi of the energy conumption ditribution in multi-uer MIMO ytem with mobility, IEEE Tran. Wirele Communication, vol. 14, no. 3, pp , Mar [23] E. Björnon, L. Sanguinetti, J. Hoydi, and M. Debbah, Optimal deign of energy-efficient multi-uer MIMO ytem: I maive MIMO the anwer? IEEE Tran. Wirele Commun., to be publihed. [Online]. Available: [24] Z. Shen, A. Khoryaev, E. Erion, and X. Pan, Dynamic uplindownlin configuration and interference management in TD-LTE, IEEE Commun. Mag., vol. 50, no. 11, pp , Nov [25] E. Björnon and E. Jorwiec, Optimal reource allocation in coordinated multi-cell ytem, Found. Trend Commun. Inf. Theory, vol. 9, no. 2 3, pp , [26] G. Calcev et al., A wideband patial channel model for ytem-wide imulation, IEEE Tran. Veh. Technol., vol. 56, no. 2, pp , Mar [27] I. S. Gradhteyn and I. M. Ryzhi, Table of Integral, Serie and Product. New Yor, NY, USA: Academic Pre, [28] A. Adhiary, J. Nam, J.-Y. Ahn, and G. Caire, Joint patial diviion and multiplexing-the large-cale array regime, IEEE Tran. Inf. Theory, vol. 59, no. 10, pp , Oct [29] S. Lahminaryana, M. Aaad, and M. Debbah, Coordinated multi-cell beamforming for maive MIMO: A Random Matrix Approach IEEE Tran. Inf. Theory., to be publihed. [30] J. Zhang, C.-K. Wen, S. Jin, X. Gao, and K.-K. Wong, Large ytem analyi of cooperative multi-cell downlin tranmiion via regularized channel inverion with imperfect CSIT, IEEE Tran. Wirele Commun., vol. 12, no. 10, pp , Oct [31] L. Sanguinetti, R. Couillet and M. Debbah, Large ytem analyi of bae tation cooperation in the downlin, ubmitted to Proc. IEEE GLOBECOM, San Diego, CA, USA, Dec [32] D. A. Banayaa, P. J. Smith, and P. A. Martin, Performance analyi of macrodiverity MIMO ytem with MMSE and ZF receiver in flat rayleigh fading, IEEE Tran. Wirele Commun., vol. 12, no. 5, pp , May Luca Sanguinetti S 04 M 06 received the Laurea Telecommunication Engineer degree cum laude and the Ph.D. degree in information engineering from the Univerity of Pia, Italy, in 2002 and 2005, repectively. Since 2005, he ha been with the Dipartimento di Ingegneria dell Informazione, Univerity of Pia. In 2004, he wa a viiting Ph.D. tudent at the German Aeropace Center DLR, Oberpfaffenhofen, Germany. During the period June 2007 June 2008, he wa a Potdoctoral Aociate in the Department of Electrical Engineering, Princeton Univerity. During the period June 2010 September 2010, he wa elected for a reearch aitanthip at the Techniche Univeritat Munchen. From July 2013 to July 2015, he wa with the Alcatel-Lucent Chair on Flexible Radio, Supélec, Gif-ur-Yvette, France. He i an Aitant Profeor at the Dipartimento di Ingegneria dell Informazione, Univerity of Pia. He i currently erving a an Aociate Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICA- TIONS and IEEE JOURNAL OF SELECTED AREAS OF COMMUNICATIONS erie on Green Communication and Networing. Hi expertie and general interet pan the area of communication and ignal proceing, etimation and game theory and random matrix theory for wirele communication. He wa the co-recipient of two bet paper award: WCNC13 and WCNC14. He i alo the recipient of the FP7 Marie Curie IEF 2013 Dene deployment for green cellular networ. Ari L. Moutaa SM 04 hold a B.S. degree in phyic from Caltech and M.S. and Ph.D. degree in theoretical condened matter phyic from Harvard Univerity, repectively. He joined Bell Lab, Lucent Technologie, NJ, USA, in 1998, firt in the Phyical Science Diviion and then alo in the Wirele Advanced Technology Laboratory. He i currently a faculty member of the Phyic Department, National Capoditrian Univerity of Athen, Greece. During , he held a DIGITEO Senior Chair in Oray, France. Dr. Moutaa erved a Aociate Editor for the IEEE TRANSACTIONS ON INFORMATION THEORY between 2009 and Hi main reearch interet lie in the area of multiple antenna ytem and the application of game theory and tatitical phyic to communication and networ. Mérouane Debbah S 01 A 03 M 04 SM 08 F 15 received the M.Sc. and Ph.D. degree from Ecole Normale Supérieure de Cachan, France. He wored for Motorola Lab, Saclay, France, from 1999 to 2002 and the Vienna Reearch Center for telecommunication, Vienna, Autria, until From 2003 to 2007, he joined the Mobile Communication Department, Intitut Eurecom, Sophia Antipoli, France, a an Aitant Profeor. Since 2007, he i a Full Profeor at Supelec, Gif ur Yvette, France. From 2007 to 2014, he wa Director of the Alcatel-Lucent Chair on Flexible Radio. Since 2014, he i Vice-Preident of the Huawei France R&D center and Director of the Mathematical and Algorithmic Science Lab. Hi reearch interet are in information theory, ignal proceing and wirele communication. He i an Aociate Editor in Chief of the Journal Random Matrix: Theory and Application and wa an Aociate and Senior Area Editor for IEEE TRANSACTIONS ON SIGNAL PROCESSING repectively in and He i a recipient of the ERC grant Advanced Mathematical Tool for Complex Networ Engineering MORE. He i a WWRF fellow and a member of the academic enate of Pari-Saclay. He i the recipient of the Mario Boella award in 2005, the 2007 IEEE GLOBECOM bet paper award, the Wi-Opt 2009 bet paper award, the 2010 Newcom++ bet paper award, the WUN CogCom Bet Paper 2012 and 2013 Award, the 2014 WCNC bet paper award a well a the Valuetool 2007, Valuetool 2008, CrownCom2009, Valuetool 2012 and SAM 2014 bet tudent paper award. In 2011, he received the IEEE Glavieux Prize Award and in 2012, the Qualcomm Innovation Prize Award.