Position Aided Beam Alignment for Millimeter Wave Backhaul Systems with Large Phased Arrays

Transcription

1 Extndd vrsion of an invitd papr at IEEE CAMSAP Position Aidd Bam Alignmnt for Millimtr Wav Backhaul Systms ith Larg Phasd Arrays Gorg C. Alxandropoulos Mathmatical and Algorithmic Scincs Lab, Paris Rsarch Cntr, Huai Tchnologis Franc SASU, 20 Quai du Point du Jour, Boulogn-Billancourt, Franc mail: arxiv: v3 [cs.it] 12 Oct 2017 Abstract Wirlss backhaul communication has bn rcntly ralizd ith larg antnnas oprating in th millimtr av (mmwav) frquncy band and implmnting highly dirctional bamforming. In this papr, focus on th alignmnt problm of narro bams btn fixd position ntork nods in mmwav backhaul systms that ar subjct to small displacmnts du to ind flo or ground vibration. W considr nods quippd ith antnna arrays that ar capabl of prforming only analog procssing and communicat through irlss channls including a lin-of-sight componnt. Aiming at minimizing th tim ndd to achiv bam alignmnt, prsnt an fficint mthod that capitalizs on th xchang of position information btn th nods to dsign thir bamforming and combining vctors. Som numrical rsults on th outag probability ith th proposd bam alignmnt mthod offr usful prliminary insights on th impact of som systm and opration paramtrs. I. INTRODUCTION Millimtr av (mmwav) communication [1] is a promising tchnology for addrssing th high throughput rquirmnt for th fifth gnration (5G) mobil ntorks [2], [3]. Shortrang mmwav communication at th unlicnsd band of 60 GHz is alrady standardizd in IEEE ad [4] and initial thortical invstigations on mmwav cllular systms [1], [5] hav idntifid thir potntials and ky challngs. Th mmwav frquncis hav bn also rcntly considrd for th irlss backhaul communication of small clls [6], [7], hich ar xpctd to b dnsly dployd as an fficint mans for incrasing th gographic spctrum rusability [8]. Rliabl mmwav backhauling dpnds on vry dirctional communication, hich ar implmntd in practic ithr ith antnnas having larg aprturs or ith larg phasd antnna arrays [6]. By xploiting th fact that th avlngth at vry high frquncis is vry small, larg phasd antnnas can b chaply packd into small form factors and, thus, hav bn ffctivly usd in ralizing highly dirctional BamForming (BF) supporting long outdoor links. To achiv th full bnfit from BF in a communication link btn multi-antnna nods, th ntir channl stat information nds to b availabl at both communication nds. Hovr, this information is hard to acquir in mmwav systms du to th lo cohrnc tim, th Radio Frquncy (RF) hardar limitations, and th small Signal-to-Nois Ratio (SNR) bfor BF. Although rcnt thortical orks [5], [9] [11] capitalizd on th spatial sparsity of mmwav channls [12] to stimat portions or th ntir channl gain matrix, th prsntd approachs rquird lngthy training phass to stimat th channl in multipl dirctions using complx comprssd snsing algorithms. Anothr family of approachs (.g., [13] [18]) for fficint BF is basd on bam sitching btn th communicating nods in ordr to find pair(s) of bams from thir availabl codbooks mting a prdfind prformanc thrshold. Whn such bam pair(s) is(ar) found, bam alignmnt is considrd to b achivd and no furthr bam sarching is ndd. In this papr, focus on th mmwav backhaul systm of [18] and prsnt a robust bam alignmnt mthod for irlss channls including a Lin-Of-Sight (LOS) componnt. Th proposd mthod intnds at achiving bam alignmnt in at most to rounds of control information xchang. Th cor ida of th mthod lis on th control information, hich is considrd to b th n positions of th nods aftr ach dclard bam misalignmnt vnt, on its xchang, and on its utilization in dsigning th BF tchniqu at all communication nds. Th position information of a nod is assumd to b availabl to it via an attachd position snsor. It is notd that positioning snsors hav bn also considrd in [19], [20], hovr, thy r adoptd for idntifying and circumvnting bam misalignmnt only at th transmit nod. Notation: Vctors and matrics ar dnotd by boldfac lorcas lttrs and boldfac capital lttrs, rspctivly. Th transpos and Hrmitian transpos of a matrix A ar dnotd by A T and A H, rspctivly, diag{a} dnots a squar diagonal matrix ith a s lmnts in its main diagonal, hras I n (n 2) is th n n idntity matrix. Th ith lmnt of a and th (i,j)th lmnt of A ar dnotd by [a] i and [A] i,j, rspctivly, and A F givs th Frobnius norm of A. C rprsnts th complx numbr st, card(f) is th cardinality of st F, dnots th amplitud of a complx numbr, and E{ } is th xpctation oprator. d(m,n) dnots th lngth of th lin sgmnt conncting th points M and N. Notation x CN ( 0,σ 2) indicats that x is a circularly-symmtric complx Gaussian random variabl ith zro man and variancσ 2, hilx U (α,β) rprsnts a uniformly distributd random variabl in [α, β]. II. SYSTEM AND CHANNEL MODELS Suppos a irlss backhaul communication systm oprating in th mmwav frquncy band and consisting of to half duplx multi-antnna transcivr nods A and B (s Fig. 1). Th fixd positions of th nods dfins a Cartsian coordinat

2 M t+1 -x t+1 d -y φ 1 (t+1) y d t t t+1 M t y t+1 M t θ 1 (t+1) 0 x t+1 M t+1 O t+ 1, t+ 1 Fig. 1. Th considrd point-to-point irlss backhaul communication systm. Th positions of th nods A and B at th tim instant t ar dnotd by th points M (A) t and M (B) t, rspctivly, and dfin a Cartsian coordinat systm. At th tim instant t+1 both nods A and B mov to n positions rprsntd by th points M (A) t+1 and M(B) t+1, rspctivly. Ths n positions dtrmin th coordinats of th point O t+1,t+1 ; its first subscript rfrs to M (A) t+1 and th scond to M(B) t+1. systm, according to hich th positions of nods A and B at th tim instant t ar rprsntd by th points M (A) t and M (B) t, rspctivly. Thir rspctiv coordinats ar (0, 0) and (0,d t ), hr d t dnots th physical distanc btn th nods at this tim instant. Rgarding th mmwav accss, ach nod is assumd to b quippd ith on RF chain and is capabl of ralizing only analog transmit BF hn bing in transmit mod, and only analog rciv combining hn bing in rciv mod. Nod A is assumd to hav a larg uniform linar antnna array (ULA) ith N A lmnts, hras nod B is quippd ith a larg N B -lmnt ULA. W hrinaftr assum for simplicity that th positions of th nods coincid ith th positions of th cntrs of thir antnna arrays. To stablish irlss communication btn nods A and B, i.., to mt a minimum prformanc thrshold for rliabl information xchang, a control phas for channl accss is adoptd. W assum that communication is ralizd in discrt tim instants ach including a control and a data phas. Th control phas constituts of svral tim slots during hich data communication is bing st up. W assum that during ach discrt tim instant th channl rmains constant, but it may chang btn diffrnt instancs. During th control phas for channl accss, control information nds to b xchangd btn nods A and B. This control information xchang rquirs in gnral a much lss stringnt prformanc thrshold than data xchang. This mans that BF gain is not ncssary for control signaling, hnc, its rcivd SNR can b affordd to b lo. As such, assum that control signaling xchang can b in principl handld by th considrd communication systms. Bfor signal transmission from nod A, th unit por data stram s C (chosn from a discrt modulation st) is procssd by a BF vctor v A C NA 1, and upon signal rcption at nod B, th combining vctor u B C NB 1 is x usd for procssing th rcivd signal. Similarly, nod B maks us of th BF vctor v B C NB 1 hn transmitting, and nod A utilizs th combining vctor u A C NA 1 hn bing in rciv mod. Du to practical limitations ith th considrd analog antnna arrays [5], [18], th analog antnna ights at both nods ar supposd to tak valus from discrt sts. In particular, assum that v A and u A at nod A ar chosn from th finit st F A of prdfind N A -lmnt vctors. Th sam holds for nod B; v B and u B blong to th finit st F B of prdfind N B -lmnt vctors. Without loss of gnrality, it is assumd that for any f F A ith f C NA 1 and any z F B ith z C NB 1 holds [f] i 2 N 1 A ith i = 1,2,...,N A and [z] j 2 N 1 B ith j = 1,2,...,N B. Whn nodatransmits information to nod B, th output signal aftr th combinr at nod B can b mathmatically xprssd as y B = pu H B H BAv A s+u H B n B, (1) hr p is th transmit por, H BA C NB NA dnots th channl gain matrix btn nods B and A, and n B C NB 1 rprsnts th zro-man Additiv Whit Gaussian Nois (AWGN) vctor ith covarianc matrix σ 2 B I N B. W adopt a gomtric channl modl ith L scattrrs similar to [5], [12]. W assum that during ach discrt tim instant th irlss channl rmains constant, but it may chang btn diffrnt instancs. According to this channl modl, H BA includd in (1) is xprssd as H BA A B (θ)diag{a}a H A (φ), (2) hr A A (φ) C NA L, ith φ [φ 1 φ 2 φ L ], and A B (θ) C NB L, ith θ [θ 1 θ 2 θ L ], ar dfind as A A (φ) [a A (φ 1 ) a A (φ 2 ) a A (φ L )], A B (θ) [a B (θ 1 ) a B (θ 2 ) a B (θ L )]. (3a) (3b) In (3), variabl φ l [0,2π] ith l = 1,2,...,L dnots th lth path s Angl of Dpartur (AoD) from nod A and variabl θ l [0,2π] rprsnts thlth path s Angl of Arrival (AoA) at nod B. Folloing th invstigations in [21], assum that th 1st channl path is a LOS on ith nrgy much largr than ach of th rst L 1 paths. In addition, a A (φ l ) C NA 1 and a B (θ l ) C NB 1 ar th array rspons vctors at nods A and B, rspctivly (ths vctors ar givn by [5, q. (5)] for ULAs). In (2), a C L 1 includs th channl path gains α l l = 1,2,...,L. W furthr assum that ach path s amplitud is Rayligh distributd and, in particular, that ach α l CN(0,N A N B P L ), hr P L dnots th avrag pathloss btn nods B and A. In practical dploymnts of irlss backhaul systms, th antnna arrays of th communicating nods ar usually mountd on outdoor structurs that ar xposd to ind flo and gusts. Ths structurs ar suscptibl to movmnt (or say) du to ind or ground vibration, hich might caus unaccptabl Outag Probability (OP) if bam alignmnt is not frquntly prformd [18]. To captur th random movmnts

3 of th antnna arrays at both nods A and B, modl th displacmnts at th x-axis and y-axis for both of thm as x (A) U( x (A),x(A) ), y (A) U( y s (A),y n (A) ), x (B) U( x (B),x (B) ), y (B) U(y (B) s,y (B) n ). (4a) (4b) In th lattr xprssions, x (A), x (A), x (B), and x (B) rval th position limits in th x-axis for both nods, hil y s (A), y n (A), y s (B), and y n (B) rprsnt thir position limits in th y-axis. III. POSITION AIDED BEAM ALIGNMENT Suppos that at th tim instant t + 1 both nods A and B mov to n positions rprsntd by th points M (A) t+1 and M(B) t+1, rspctivly, ith rspctiv coordinats (x (A) t+1,y(a) t+1 ) and (x(b) t+1,d t y (B) t+1 ). According to th prsntd channl modl, th channl btn nod B and nod A at th discrt tim instant t + 1 can b xprssd as H BA (t+1) A B (θ(t+1))diag{a(t+1)}a H A (φ(t+1)), ith φ(t + 1) [φ 1 (t + 1)φ 2 (t + 1) φ L (t + 1)] and θ(t+1) [θ 1 (t+1)θ 2 (t+1) θ L (t+1)] dnoting th AoDs and AoAs, rspctivly, rsulting from th n nod positions, hil a(t+1) includs th channl gains. Th bam alignmnt objctiv in this tim instant is to dsign th BF vctor at nod A and th combining vctor at nod B as {v A (t+1),u B (t+1)}= max f F A,z F B z H H BA (t+1)f 2, (5) hich implis BF gain maximization. If prfct knoldg of H BA (t+1) as availabl at both nods, nodsa andb should us th principal right and lft singular vctors of H BA (t+1) as th BF and combining vctors, rspctivly, to maximiz th BF gain [22]. Hovr, nithr H BA (t+1) for any t can b stimatd at any of th nods du to th assumd hardar limitations nor th nods ar capabl of ralizing any arbitrary vctor (thy possss th finit vctor sts F A and F B ). A. Proposd Mthod Lt us considr that, upon installation of th considrd mmwav backhaul systm at th initial discrt tim instant t, both nods A and B ar aar of th coordinat systm dfind by th coordinats of th points M (A) t and M (B) t. In th nxt discrt tim instant t+1, suppos that both nods mov to th n position pointsm (A) t+1 and M(B) t+1. Each nod s displacmnt in th x and y axs is assumd to b availabl to th nod. Th lattr indicats that ach nod is aar of th coordinats of its n position, i.., nod A larns th coordinats (x (A) t+1,y(a) t+1 ) and B obtains (x(b) t+1,d t y (B) t+1 ). If also th coordinats of th position of nod B bcom availabl to A (through, for xampl, a ddicatd control channl), thn th lattr nod may stimat th AoD of th LOS channl path for its transmission at this tim instant as { arcsin(g ˆφ 1 (t+1) = t+1 ), x (B) t+1 x(a) t+1 π arcsin(g t+1 ), x (B) t+1 <, (6) x(a) t+1 hr th positiv ral g t+1 is givn by ( ) d O t+1,t+1,m (B) t+1 g t+1 = ( ) (7) d M (A) t+1,m(b) t+1 ith pointo t+1,t+1 having th coordinats(x (B) t+1,y(a) t+1 ). From th spcific nods positions at th tim instant t+1 yilds g t+1 = ( x (A) t+1 +x(b) t+1 d t y (A) ) 2 ( + t+1 y(b) t+1 d t y (A) t+1 y(b) t+1 ) 2. (8) In a similar ay, if nod A shars its coordinats at th sam tim instant ith B, thn nod B can stimat th AoA of th LOS path for A s transmission as { π +φ ˆθ 1 (t+1) = 1 (t+1), x (B) t+1 x(a) t+1 2π φ 1 (t+1), x (B) t+1 <. (9) x(a) t+1 Th AoD and AoA of th LOS path can b obtaind similarly if nod B transmits and nod A oprats in rciv mod. Capitalizing on (6) and on our channl modl for ach tim instant t+1, propos that transmit nod A uss its stimat ˆφ 1 (t+1) to raliz a bam string toards th dirction of rciv nodb. To accomplish this, it sarchs insid its bam codbook F A for th vctor that is closst to a A (ˆφ 1 (t+1)). In mathmatical trms and ithout loss of gnrality, nod A dsigns its BF vctor at ach tim instant t+1 as ) f 2 v A (t+1) = min aa (ˆφ1 (t+1). (10) f F A F Similarly, rciv nod B uss its stimat ˆθ 1 (t+1) at ach t+1 to raliz a bam as clos as possibl to th dirction of nod A. It, thrfor, constructs its combining vctor as ) z ab 2 u B (t+1) = min (ˆθ1 (t+1). (11) z F B F By using th vctors givn by (10) and (11) at nods A and B, rspctivly, th instantanous rcivd SNR at nod B is givn by γ t+1 = µ t+1 2 /σ 2 B, hr µ t+1 C is dfind as µ t+1 = L l=1 ) α l (t+1)u H B(t+1)a B (ˆθl (t+1) ) a H A(ˆφl (t+1) v A (t+1). (12) It is notd that for th spcial cas of L = 1 LOS channl path, prfctly stimatd AoD and AoD for this path, and infinit rsolution bam codbooks at both nods A and B yilds µ t+1 = α 1 (t + 1). This indicats that for this idal cas th vctors givn by (10) and (11) maximiz th BF gain dscribd in (5) and givn by µ t+1 2. Th proposd bam alignmnt mthod is summarizd in Algorithm 1.

4 Algorithm 1 Position Aidd Bam Alignmnt Initialization: Construct a coordinat systm upon installation of nods A and B at th initial tim instant t. Dtrmin th minimum rquird SNR γ o for data communication. 1: for n = t+1,t+2,... do Nod A Rcovry Phas 1: 2: if γ n γ o, thn 3: St v A (n) = v A (n 1), u B (n) = u B (n 1), 4: ls 5: Obtain th coordinats of th n position M n (A). 6: Comput th AOD ˆφ 1 (n) using (6) and th coordinats of th positions M n (A) and M (B) n 1, and th point O n,n 1. 7: Comput a A (ˆφ 1 (n)) and dsign v A (n) using (10). 8: nd if 9: if γ n γ o thn 10: St v A (n) as in stp 7, u B (n) = u B (n 1), 11: ls 12: Snd th coordinats of M n (A) to Nod B. 13: nd if Nod B Rcovry Phas: 14: Upon rcption of a control signal ith th coordinats of M n (A), obtain th coordinats of M n (B). 15: Comput th AOA ˆθ 1 (n) using (9) and th coordinats of th positions M n (A) and M n (B), and O n,n. 16: Comput a B (ˆθ 1 (n)) and dsign u B (n) using (11). 17: if γ n γ o, thn 18: Triggr nod A to transmit data. 19: St v A (n) as in stp 7, u B (n) as in stp 16, 20: ls 21: Snd th coordinats of M n (B) to Nod A and us u B (n) dsignd in stp : nd if Nod A Rcovry Phas 2: 23: Upon rcption of a control signal ith th coordinats of M n (B), comput th AOD ˆφ 1 (n) using (6) and th coordinats of M n (A) and M n (B), and O n,n. 24: Comput a A (ˆφ 1 (n)) and dsign v A (n) using (10). 25: St v A (n) as in stp 23, u B (n) as in stp 16, 26: nd for IV. NUMERICAL RESULTS AND DISCUSSION In this sction valuat th prformanc of th proposd bam alignmnt mthod ovr th considrd mmwav channl modl. W particularly valuat th OP prformanc dfind as th probability that th instantanous SNR falls blo a minimum SNR thrshold γ o. To carry out this valuation, hav simulatd 10 4 channl sampls according to (2) ith normalizd σ 2 B and P L = d , hr ach channl sampl Outag Probability (OP) No Action A1 A1 and B A1, B and A2 Optimum BF SNR Thrshold γ o in db Fig. 2. OP vrsus th SNR thrshold γ o in db for N A = N B = 16, p/σ 2 B = 5dB, card(f A) = card(f B ) = 17, L = 3, κ = 13.2dB, and diffrnt phass of th proposd mthod. Curvs for th unfasibl optimum BF cas and th cas of no action for bam alignmnt ar includd. appars at on discrt tim instant. W hav considrd Rican fading channls ith th κ-factor dnoting th ratio of th nrgy in th LOS channl path to th sum of th nrgis in th othr non LOS paths [21]. Th distanc of th nods A and B at th initial tim instant t = 1 is assumd to b d 1 = 10m and th random displacmnts of th nods in th x-axis and y-axis du to ind gusts ar obtaind from (4) ith x (A) y (A) = y (A) = y (B) = x (A) = y (B) = x (B) = 1.5m and = 1.5m. Th bam codbooks = x (B) F A and F B ar constructd by quantizing th fasibl sts of dpartur and arrival angls, rspctivly. Spcifically, for th ith BF vctor blonging in F A ith i card(f A ) th dpartur angl χ i taks discrt valus ith stp siz 2 1 q (χ max χ min ) ithin [χ min,χ max ], hr q rprsnts th numbr of angl quantization bits. Similarly, for ach jth combining vctor insid F B ith j card(f B ) th arrival angl ψ j [ψ min,ψ max ] has bn quantizd ith q bits. W hav st χ min = 60 o, χ max = 120 o, ψ min = 240 o, and ψ max = 300 o ith rspct to th nods orintation. In Fig. 2, plot th OP ith th proposd bam alignmnt mthod as a function of th SNR thrshold γ o in db for th transmit SNR p/σ 2 B = 5dB and N A = N B = 16, card(f A ) = card(f B ) = 17 rsulting from q = 5, L = 3, and th Rican factor κ = 13.2dB. Within this figurs, th OP curvs for th cas of no action for bam alignmnt and th cas of optimum BF [22] hn prfct channl knoldg is availabl ar also sktchd. As for th proposd mthod, th prformanc for diffrnt squncs of phass is also dmonstratd. In particular, provid th prformanc for th cas hr only NodARcovry Phas 1 is usd, dnotd by A1; th cas hr Nod A Rcovry Phas 1 follod by Nod B Rcovry Phas ar usd, dnotd by A1 and B; and th cas hr all phass ar utilizd, dnotd by A1, B and A2. As sn and as xpctd, OP dgrads ith incrasing γ o. It is also shon that th xchang of position information improvs this probability for any γ o valu. In fact,

5 th availability of nods position at both nods, ith only 2 control signals according to th proposd mthod, rsults in th bst prformanc. Evidntly, actions from only th transmittr or xchang of only th lattr s position information rsult in poor OP. W hav also compard th proposd bam alignmnt mthod ith an xhaustiv bam sarch similar to [15] that sks to find th first bam pair mting γ o hnvr bam misalignmnt occurs. For th paramtr sttings of Fig. 2 quot th folloing rprsntativ rsults: i) th proposd mthod achivs 98% of th avrag rcivd SNR of optimum BF irrspctiv of γ o, hil th xhaustiv sarch only th 28% for γ o = 1dB aftr 30 control signals on avrag; and ii) for γ o = 3dB th xhaustiv sarch rachs th 72% of th optimum BF SNR rquiring on avrag 153 control signals. V. CONCLUSION In this papr, invstigatd th problm of bam alignmnt btn ntork nods in irlss backhaul communication systms oprating in th mmwav frquncy band. W considrd th practical cas of random movmnt of th larg phasd antnna arrays of th nods du to ind flo or ground vibration, and prsntd a simpl modl that capturs thir small displacmnts. A robust bam alignmnt mthod for irlss nvironmnts including a LOS componnt as prsntd that capitalizs on th xchang of position information btn th nods to dsign thir BF and combining vctors. Through rprsntativ OP prformanc valuation rsults th impact of som ky paramtrs on th prformanc of th proposd mthod as highlightd. [13] K. Hosoya t al., Multipl sctor ID captur (MIDC): A novl bamforming tchniqu for 60 GHz band multi-gbps WLAN/PAN systms, IEEE Trans. Antnnas Propag., vol. 63, no. 1, pp , Jan [14] J. Wang t al., Bam codbook basd bamforming protocol for multi- Gbps millimtr-av WPAN systms, IEEE J. Sl. Aras Commun., vol. 27, no. 8, pp , Oct [15] C. Jong t al., Random accss in millimtr-av bamforming cllular ntorks: Issus and approachs, IEEE Commun. Mag., vol. 53, no. 1, pp , Jan [16] C. Barati t al., Dirctional cll discovry in millimtr av cllular ntorks, IEEE Trans. Wirlss Commun., vol. 14, no. 12, pp , Dc [17] V. Raghavan t al., Bamforming tradoffs for initial UE discovry in millimtr-av MIMO systms, IEEE J. Sl. Topics Signal Procss., vol. 10, no. 3, pp , Apr [18] S. Hur t al., Millimtr av bamforming for irlss backhaul and accss in small cll ntorks, IEEE Trans. Commun., vol. 61, no. 10, pp , Oct [19] R. Maibrgr t al., Location basd bamforming, in Proc. IEEE IEEEI, Eliat, Isral, Nov. 2010, pp [20] A. W. Doff, K. Chandra, and R. V. Prasad, Snsor assistd movmnt idntification and prdiction for bamformd 60 GHz links, Availabl at [21] Z. Muhi-Eldn t al., Modlling and masurmnts of millimtr avlngth propagation in urban nvironmnts, IET Microavs, Ant. Propag., vol. 4, no. 9, pp , May [22] D. J. Lov and R. W. Hath, Jr., Equal gain transmission in multiplinput multipl-output irlss systms, IEEE Trans. Commun., vol. 51, no. 7, pp , Jul REFERENCES [1] T. S. Rappaport t al., Millimtr av mobil communications for 5G cllular: It ill ork! IEEE Accss, vol. 1, pp , May [2] F. Boccardi t al., Fiv disruptiv tchnology dirctions for 5G, IEEE Commun. Mag., vol. 52, no. 2, pp , Fb [3] J. G. Andrs t al., What ill 5G b? IEEE J. Sl. Aras Commun., vol. 32, no. 6, pp , Jun [4] IEEE irlss LAN MAC and PHY spcifications Amndmnt 3: Enhancmnts for vry high throughput in th 60 GHz band, IEEE Std ad, [5] A. Alkhatb t al., Channl stimation and hybrid prcoding for millimtr av cllular systms, IEEE J. Sl. Topics Signal Procss., vol. 8, no. 5, pp , Oct [6] S. Chia t al., Th nxt challng for cllular ntorks: Backhaul, IEEE Microav Mag., vol. 10, no. 5, pp , Aug [7] X. G t al., 5G irlss backhaul ntorks: Challngs and rsarch advancs, IEEE Nt., vol. 28, no. 6, pp. 6 11, Dc [8] N. Bhushan t al., Ntork dnsification: Th dominant thm for irlss volution into 5G, IEEE Commun. Mag., vol. 52, no. 2, pp , Fb [9] Z. Marzi t al., Comprssiv channl stimation and tracking for larg arrays in mm-av picoclls, IEEE Trans. Signal Procss., vol. 11, no. 3, pp , Apr [10] A. Bazzi t al., A comparativ study of spars rcovry and comprssd snsing algorithms ith application to AoA stimation, in Proc. IEEE SPAWC, Edinburgh, UK, 3-6 Jul. 2016, pp [11] G. C. Alxandropoulos and S. Chouvardas, Lo complxity channl stimation for millimtr av systms ith hybrid A/D antnna procssing, in Proc. IEEE GLOBECOM, Washington D.C., USA, 4-8 Dc. 2016, pp [12] H. Zhang t al., Channl modling and MIMO capacity for outdoor millimtr av links, in Proc. IEEE WCNC, Sydny, Australia, Apr. 2010, pp. 1 6.