A D2D-based Protocol for Ultra-Reliable Wireless Communications for Industrial Automation

Transcription

1 1 A D2D-based Protocol for Ultra-Reliable Wireless Commuicatios for Idustrial Automatio Liag Liu, Member, IEEE ad Wei Yu, Fellow, IEEE arxiv: v3 [cs.it] 15 May 2018 Abstract As a idispesable use case for the 5G wireless systems o the roadmap, ultra-reliable ad low latecy commuicatios (URLLC) is a crucial requiremet for the comig era of wireless idustrial automatio. The key performace idicators for URLLC stad i sharp cotrast to the requiremets of ehaced mobile broadbad (embb): lowlatecy ad ultra-reliability are paramout but high data rates are ofte ot required. This paper aims to develop commuicatio techiques for makig a paradigm shift from the covetioal huma-type broadbad commuicatios to the emergig machie-type URLLC. Oe fudametal task for URLLC is to deliver short commads from a cotroller to a group of actuators withi the striget delay requiremet ad with high-reliability. Motivated by the factory automatio settig i which tasks are assiged to groups of devices that work i close proximity to each other thus ca form clusters of reliable device-to-device (D2D) etworks, this paper proposes a ovel two-phase trasmissio protocol for achievig URLLC. I the first phase, withi the latecy requiremet, the multi-atea base statio (BS) combies the messages of all devices withi each group together ad multicasts them to the correspodig groups; messages for differet groups are spatially multiplexed. I the secod phase, the devices that have decoded the messages successfully, herei defied as the leaders, help relay the messages to the other devices i their groups. Uder this protocol, we desig a iovative leader selectio based beamformig strategy at the BS by utilizig sparse optimizatio techique. The proposed strategy leads to a desired sparsity patter i user activity with at least oe leader beig able to decode its message i each group i the first phase, thus esurig full utilizatio of the reliability ehacig D2D trasmissios i the secod phase. Simulatio results are provided to show that the proposed two-phase trasmissio protocol cosiderably improves the reliability of the etire system withi the striget latecy requiremet as compared to existig schemes for URLLC. Idex Terms Ultra-reliable ad low latecy commuicatios (URLLC), 5G, idustrial automatio, device-to-device (D2D) commuicatios, machie-type commuicatios (MTC), multicastig, beamformig, sparse optimizatio. I. INTRODUCTION Ehaced mobile broadbad (embb), massive machie type commuicatios (mmtc), ad ultra-reliable ad low Mauscript received October 14, 2017, revised Jauary 28, 2018 ad March 6, 2018, accepted April 26, The associate editor coordiatig the review of this paper ad approvig it for publicatio was Dr. Li Dai. This work is supported by Nokia Bell Labs, NJ, USA, ad by Natural Scieces ad Egieerig Research Coucil (NSERC) of Caada. The authors are with The Edward S. Rogers Sr. Departmet of Electrical ad Computer Egieerig, Uiversity of Toroto, Toroto, Otario, Caada, M5S3G4, ( s:liaguot.liu@utoroto.ca; weiyu@comm.utoroto.ca). latecy commuicatios (URLLC) are the three mai use cases that the 5G techology must support [1]. Addressig the above requiremets i 5G calls for ew methods ad ideas at both the compoet ad architectural levels, icludig massive multiple-iput multiple-output (MIMO) [2], [3], millimeter wave (mmwave) commuicatios [4], ad cloud radio access etwork (C-RAN) [5] for embb, as well as multiple access schemes to support a massive umber of devices for mmtc [6] [8]. This paper focuses o URLLC. Specifically, we aim to tackle the latecy ad reliability requiremet motivated by idustrial automatio applicatios [9] [13]. I a typical closed loop idustrial cotrol sceario, groups of sesors ad actuators are deployed i a fixed area i a factory settig. Periodically or whe triggered by exteral evets, the sesors sed their measuremets to the cetral cotroller, which the makes decisios ad seds commads to the actuators for actio. Uder the curret techology, sesors ad actuators are typically coected to the cetral cotroller via a wired cofiguratio i most factories. I the ear future, uder the fourth idustrial revolutio roadmap (kow as Idustry 4.0), the commuicatio etworks i the factory settig are expected to migrate from wired to wireless for the purpose of icreasig the flexibility i movig machiery ad also for reducig the ifrastructure expediture [9] [13]. As factory automatio systems are highly sesitive to sigal delays or distortios, such a trasitio will impose challegig requiremets i terms of latecy as well as reliability for the wireless techologies. I the curret 4G cellular etwork, the ed-to-ed latecy (which icludes data trasmissio, packet retrasmissio, sigal processig, protocol hadlig, ad switchig ad etwork delays) ca be i the order of 30-40ms, with the physical-layer latecy accoutig for about 15-20ms. For missio-critical applicatios for idustrial automatio, the latecy requiremet of 5G physical layer is expected to be pushed dow to less tha1ms, a order of magitude shorter tha 4G. Further, such low latecy requiremet eeds to be satisfied with ultra-reliability, e.g., % or higher. This paper aims to address the challege of wireless factory automatio by focusig o the dowlik URLLC i oe cell (factory) of a cellular system, where the multiatea base statio (BS) (the cetral cotroller) eeds to sed a small amout of iformatio bits (commad) to each user (actuator) withi the latecy requiremet (1ms). The core questio this paper tries to aswer is how to achieve

2 2 M ateas successful users i Phase I (leaders) usuccessful users i Phase I D2D etwork i Phase II packet of oe user etire packet of oe group Fig. 1. Illustratio of the two-phase trasmissio protocol: i the first phase, BS combies each group s messages together ad multicasts them to the leaders i the correspodig groups; i the secod phase, each leader helps relay the messages to the usuccessful users i its group via the D2D etwork. the above goal with ultra-reliability i the sese that all the users ca decode their messages with a very high probability. Achievig URLLC with the covetioal broadcastig strategy is difficult due to the fact that a typical factory may have hudreds (or eve thousads) of actuators. Specifically, i a massive coectivity sceario where the umber of devices is larger tha the umber of ateas at the BS, it ca be difficult to trasmit at a appreciable data rate to each user reliably, especially for the cell-edge users that suffer from strog iter-cell iterferece. Moreover, timedivisio multiple-access (TDMA) may ot be a feasible strategy because each user would oly be allocated a fractio of the total trasmissio time, the the required sigal-tooise ratio (SNR) to achieve the target rate would be very high. This paper proposes a ovel trasmissio strategy for URLLC that relies o a key observatio that i practice, devices i a factory settig, e.g., robots or 3D priters, typically work i close proximity to each other ad thus ca potetially form a device-to-device (D2D) etwork for peer-to-peer commuicatios. It is evisioed that the commuicatio withi each D2D etwork is sigificatly more reliable tha that from the BS to the users due to the much stroger chaels betwee the users i the same group. To exploit the reliable D2D etworks, this paper proposes a ovel D2D-based two-phase trasmissio protocol as show i Fig. 1, i which the BS seds the messages to the users i the first phase, while i the secod phase, the users who have already decoded the messages successfully (defied as the leaders of the groups) help relay the iformatio to the other users i the same groups who have failed to receive their messages previously. Note that the reliability of the overall system is limited by the reliability of the cell-edge users. Our proposed protocol ca opportuistically activate the cell-edge users who happe to ot suffer from strog iter-cell iterferece due to the chael fadig ad let these leaders help the other cell-edge users with low sigal-to-iterferece-plus-oise ratio (SINR) to achieve high reliability i the secod phase. To eable the proposed relay strategy to work, the leaders of each group eed to receive the etire messages for all the users i their group. This paper devises a multi-group multicastig techique i the first phase [14], i which the user messages i each group are combied together as a sigle message ad multicast to the leaders i the correspodig group, while messages for differet groups are spatially multiplexed. Such a message combiatio strategy typically results i a maageable multicastig rate, sice i most URLLC scearios each device oly requires a very small umber of iformatio bits withi the latecy requiremet such that the total rate over all users i the same group is still reasoably small. Moreover, a substatially smaller umber of users eed to be activated i Phase I as compared to the broadcastig sceario sice oe group oly eeds oe leader. Sice the users i the same group usually belog to the same factory, the icetive mechaism ad security, which are challegig issues i practical D2D etworks [15], are o loger the mai cosideratios i our ivestigated setup. Istead, leader selectio i the first phase becomes the decidig factor of our protocol, sice the groups without leaders caot utilize the reliable D2D etworks i the secod phase. This paper proposes a dyamic leader selectio based beamformig solutio based oly o the istataeous dowlik chael state iformatio (CSI) (without eedig the CSI of the D2D etworks) such that at the ed of the first phase each group has at least oe leader with high probability. A. Prior Work The wireless iter-coectio of the traditioal maufacturig idustries is a crucial goal for future wireless stadards [9] [13]. The curret wireless techiques are ot desiged for the striget reliability ad latecy requiremets of the missio-critical applicatios. As a result, desigig ew techiques for URLLC is cosidered as a icreasigly importat goal for 5G [16], [17], with some iitial efforts already takig place. For example, [18] provides a highlevel discussio about the potetial to utilize diversity, e.g., MIMO, covolutioal codes, ad hybrid automatic repeat request (HARQ) scheme [19] to achieve URLLC. Moreover, coordiated multi-poit (CoMP) [20], deploymet strategies such as adjustig the cell size [21], adaptive modulatio ad codig (AMC) [22], as well as reduced trasmissio time itervals ad shorter symbol duratios i orthogoal frequecy-divisio multiplexig (OFDM) systems [23] are also ivestigated to improve the reliability of wireless commuicatios. However, these works i geeral are built o the traditioal wireless techiques that are maily drive by the broadbad commuicatios ad are ofte iefficiet for URLLC. There is geeral cosesus that some fudametal chage i the trasmissio protocols is ecessary to satisfy the striget latecy ad reliability requiremets imposed by the future wireless idustrial automatio [17]. A recet work [24] presets a iterestig two-phase trasmissio protocol, amed Optimizig Cooperative Com-

3 3 muicatio for Ultra-reliable Protocols Yokig Cotrol Oto Wireless (Occupy CoW), for both the uplik ad dowlik URLLC, that makes use of cooperative relayig to reach very high levels of reliability, while maitaiig a fixed cycle time of 2ms i a etwork of 30 odes. For the dowlik commuicatio, specifically, the BS combies all the users messages together ad multicasts them to the users i the first phase, while the users that ca decode the messages help relay them to the other users i the secod phase. However, if there are too may users i the system, such a combiatio of all users messages may lead to a very high multicastig rate, resultig i too few leaders i the first phase. Our work builds upo the Occupy CoW protocol but differs i the sese that the geographic iformatio of the users is utilized to divide them ito groups: oly the messages of each group is set to the correspodig leaders, as each leader ca subsequetly help its eighbors. Oe obvious advatage of such a groupig strategy is a lower multicastig rate for each group, istead of a higher multicastig rate across all the users i the etwork. It is also worth otig that the covetioal approach for sedig idividual messages to users i the dowlik is iformatio broadcastig. I the case of a sigle-atea BS, the joit power ad admissio cotrol problem for such a settig is ivestigated i [25], [26], i which the umber of users achievig their SINR targets is maximized i the evet that ot all of them ca achieve their SINR targets (e.g., whe the SINR feasibility coditio for power cotrol defied i [27] does ot hold). However, the goal for URLLC is to provide reliable services to all the devices, rather tha a subset of devices. As a result, our work ca be iterpreted as a effort to elarge the feasible SINR regime of the covetioal power cotrol ad beamformig techique [27] by a utilizatio of the D2D etwork such that URLLC ca be achieved i more challegig settigs. B. Mai Cotributios The mai cotributios of this paper are summarized as follows. First, this paper proposes a ovel two-phase trasmissio protocol for URLLC based o the observatio that a group of devices i close proximity to each other ca form a D2D etwork i which reliable commuicatio is possible. Uder the proposed protocol, the BS combies each group s messages together ad multicasts them to the correspodig groups i the first phase, while the users that decode the messages successfully, i.e., leaders, help relay the messages to the other users i the same group i the secod phase. We poit out that sice reliable commuicatio is possible i each D2D etwork, the core issue uder our proposed protocol is the beamformig desig i the first phase that aims to successfully trasmit to at least oe leader i each group, while the other users ca rely o the leaders i the secod phase. Secod, we formulate the leader selectio based beamformig problem i the first phase from a sparse optimizatio perspective by itroducig a set of auxiliary variables that idicate the gap betwee each user s SINR ad its SINR target. Such a formulatio eables us to desig the beamformig at the BS ad select the leaders of each group joitly rather tha separately. Moreover, leader selectio results i a ew ad o-trivial sparsity patter for the auxiliary variables sice i each group at least oe auxiliary variable should be zero (which implies zero gap betwee the SINR ad SINR target ad thus a leader). To achieve this desired sparsity patter, we itroduce a ovel geometricmea based pealty for the auxiliary variables of each group, which is miimized to zero whe each group has at least oe leader. Numerical results are provided to show that such a pealty guaratees a fair leader assigmet amog groups. Fially, we provide a comprehesive performace compariso betwee our proposed strategy ad the existig oes i the literature, e.g., Occupy CoW [24] ad traditioal iformatio broadcastig. For various schemes, the probability of URLLC is defied as the probability that all the users i the system receive their messages successfully withi the delay requiremet. It is show by simulatio that with itercell iterferece, our proposed scheme is able to achieve a probability of URLLC above 99.99% for a much larger rate regime as compared to all the existig URLLC schemes. C. Orgaizatio The rest of this paper is orgaized as follows. Sectio II describes the system model for URLLC. Sectio III itroduces the D2D-based two-phase trasmissio protocol for URLLC. Sectio IV describes the correspodig leader selectio based beamformig desig. Sectio V itroduces some bechmark schemes. Sectio VI provides the umerical simulatio results pertaiig to performace compariso betwee our proposed scheme ad bechmark schemes. Fially, Sectio VII cocludes this paper. II. SYSTEM MODEL Cosider the dowlik commuicatio i oe cell (factory) cosistig of oe BS (cotroller) ad K users (actuators) as show i Fig. 1. It is assumed that the BS is equipped with M ateas, ad each user is equipped with oe sigle atea. It is further assumed that the K users form N disjoit groups based o their geographic locatios, while the users i each group are i close proximity to each other. Let G deote the set of users that belog to group, ad its cardiality K = G deote the umber of users i this group, = 1,,N, respectively. Note that each user belogs to oly oe group, thus G Gj = if j, ad N K = K. I practice, the BS ca decide how to group the users based o its kowledge of user locatios, ad sed this iformatio to all the users such that each user is aware of which group it belogs to. For coveiece, i this paper we assume that user groupig is already doe at the etwork plaig stage ad also the user groupig iformatio is kow to the users. The dowlik chael from the BS to the kth user i group is deoted by h C M 1, k = 1,,K,

4 4 = 1,,N, while the chael from the ith user i group j to the kth user i group is deoted by h,i,j C, () (i,j). This paper adopts a block-fadig model, i which all the chaels follow idepedet quasi-static flat-fadig withi a block of coherece time, where h s ad h,i,j s remai costat, but vary idepedetly from block to block. For coveiece, it is assumed that the coherece time ad badwidth of h s are the same as those of h,i,j s. They are deoted by T secod ad B Hz, respectively. It is further assumed that the dowlik chaels h s are perfectly kow at the BS, but the chaels betwee the users h,i,j s are ot kow at the BS. At last, we assume that for ay user k i group, it kows its dowlik chael h ad the chaels from other users to it, i.e., h,i,j s, (i,j) (), for iformatio decodig. For URLLC, let τ deote the delay requiremet for all the users, which i geeral is much smaller tha the chael coherece time, i.e., τ < T. Furthermore, let Ω ad D deote the set ad the umber of iformatio bits that eed to be coveyed to the kth user i group withi the delay requiremet, i.e., τ, respectively. The core questio for ultrareliable commuicatios i this sceario is the followig: How to desig a protocol such that each of the K users ca receive its messages with a very low decodig error probability withi τ secods? III. PROPOSED PROTOCOL FOR ULTRA-RELIABLE COMMUNICATIONS I this sectio, we propose a D2D-based two-phase trasmissio protocol to achieve ultra-reliable commuicatios for the K users located i N groups. We assume that h,i,j is very strog if = j sice the users i the same group are close to each other, but relatively weak otherwise. As a result, the users i the same group ca form a D2D etwork i which the commuicatios ca be made reliable. The D2D-based two-phase trasmissio protocol is briefly outlied as follows: i the first phase with a duratio of τ 1 < τ, the BS combies each group s messages together, i.e., Ω () = K Ω with K D bits iformatio,, ad seds Ω () s to the correspodig groups simultaeously via multi-group multicastig; i the secod phase with a duratio of τ 2 = τ τ 1, the users that decode the iformatio successfully i the first phase ca help relay the messages to the other users i the same group via the D2D etwork. Note that uder the proposed protocol, each user ot oly decodes its ow messages, but also receives its eighbors messages, sice the successful users i Phase I eed to relay other users messages i the same group i Phase II. I the followig, we elaborate this protocol i details. A. Phase I I the first phase with a duratio of τ 1 secods, let s deote the combied symbol iteded for all the users i group, which is modeled as a circularly symmetric complex Gaussia (CSCG) radom variable with zero-mea ad uit-variace, i.e., s CN(0,1),. The, the trasmit sigal of the BS i Phase I is expressed as x (I) = w (I) s, (1) where w (I) C M 1 deotes the trasmit beamformer for the combied user massages of group. Note that messages of differet groups are spatially multiplexed. Suppose that the BS has a trasmit power costrait P BS ; from (1), we thus have w (I) 2 P BS. (2) The received sigal of the kth user i group i Phase I is expressed as y (I) = ht x(i) +z (I) = h T w (I) s +h T j w (I) j s j+z (I), k,, (3) where z (I) CN(0,I(I) ) deotes the superpositio of the additive white Gaussia oise (AWGN) ad the iter-cell iterferece at the kth user i group i Phase I, with a power I (I). The SINR of the kth user i group i Phase I is the expressed as γ (I) = j h T w (I) 2 h T w (I) j 2 +I (I). (4) For the first trasmissio phase, i total there are τ 1 B symbols available for the BS to perform iformatio multicastig. Note that although the semial work [28] shows that i a AWGN chael, ecodig over fiite blocklegth ca result i a pealty o the chael capacity, it is recetly show i [29] that i a fadig chael, the error evet is domiated by the outage due to chael fadig, rather tha the fiite blocklegth effect. As a result, i this paper we igore the effect of fiite blocklegth codig, ad the miimum SINR target required to covey K D bits messages to ay user i group usig τ 1 B symbols is the expressed as γ (I) = 2 φ (I) = K D τ 1 B 1,. (5) The, we defie a idicator fuctio for each user as follows: { 1, if γ (I) γ(i), 0, if γ (I) < γ(i). Defiitio 1: The kth user i group is defied as a leader of group if it ca decode the messages Ω () i the first trasmissio phase, i.e., φ (I) = 1. Moreover, the set of leaders i group is defied as Φ (I) = {k : φ (I) = 1}, = 1,,N. (6)

5 5 B. Phase II I the secod phase over the remaiig τ 2 secods, the leaders i each group relay the messages to the usuccessful users i their respective group via the local D2D etworks. To esure that all the leaders i oe group trasmit the same message without geeratig itra-group iterferece, we ca use oe of the followig two strategies. I the first strategy, each leader ca re-trasmit the etire data packet for all the users i its group (icludig the data for those who already decoded their data). I this case, k D bits are trasmitted by the leaders of group over τ 2 secods i Phase II. As a alterative strategy, if each leader is made aware of which other users have successfully decoded their packet (i.e., which other users become leaders), they ca subtract the messages of all the leaders from the data packet, re-ecode the rest of the messages together, ad trasmit the ewly combied packet i the secod phase. Sice the leaders messages k Φ (I) Ω are ot ecoded, oly D k/ Φ (I) iformatio bits eed to be trasmitted by the leaders of group over τ 2 secods i Phase II. This paper advocates the first trasmissio strategy metioed above i Phase II. Although the secod strategy trasmits fewer umber of iformatio bits i Phase II, it requires more overhead for the feedback of cotrol iformatio after Phase I so that each leader is made aware of the other leaders i its group. Specifically, each user eeds to feed back oe bit message at the ed of Phase I to report whether it becomes a leader, the the BS eeds to sed cotrol messages to the leaders to let them kow about the other leaders i their groups. The overhead ivolved is sigificat ad is likely to overwhelm the beefit of shorter message i Phase II. For this reaso, the rest of the paper assumes the use of the first strategy above. Due to the lack of global CSI of the D2D etworks, i this paper we assume that power cotrol is ot performed amog users ad each leader simply trasmits at its full power for relayig the messages. Suppose that all the users possess a commo trasmit power costraitp. The trasmit sigal of the kth user i groupi the secod phase is thus expressed as x (II) = φ(i) Ps, k = 1,,K, = 1,,N. (7) As a result, i Phase II, the received sigal for each usuccessful user i Phase I is expressed as y (II) = (i,j) () = i k h,i,j x (II) i,j +z(ii) h,i, φ (I) i, Ps + K j j i=1 h,i,j φ (I) i,j Psj +z (II), if φ(i) = 0, (8) where z (II) CN(0,I(II) ) deotes the superpositio of the AWGN ad the iter-cell iterferece at the kth user i group i Phase II, with a power I (II). thus The correspodig SINR to decode s based o y (II) is γ (II) = j i k h,i, φ (I) 2 i, P K j i=1 h,i,j φ (I) i,j P 2 +I (II), if φ (I) = 0. Similar to (5), the miimum SINR requiremet to relay k D bits of iformatio usig τ 2 B symbols i Phase II ca be expressed as γ (II) = 2 K D (9) τ 2 B 1,. (10) The, we defie a idicator fuctio for each user as follows: { φ (II) = 1, if γ (I) < γ(i) ad γ (II) γ(ii), (11) 0, otherwise. As a result, φ (II) = 1 if a usuccessful user i Phase I decodes the messages i Phase II, ad φ (II) = 0 otherwise. Defie Φ (II) = {k : φ (II) = 1} as the set of users that ca decode the messages successfully i group, = 1,,N, i Phase II. The, the cardialities of Φ (I) (Defiitio 1) ad Φ (II), i.e., Φ (I) ad Φ (II), idicate the umbers of users i group who have decoded their messages successfully i Phase I (leaders) ad Phase II, respectively. Moreover, N Φ(I) + N Φ(II) deotes the total umber of successful users withi the cell after τ secod. We defie reliable commuicatios i the whole system as follows. Defiitio 2: Give a time slot of duratio τ secods, if some beamformig vectors w (I) s satisfyig the trasmit power costraits (2) ca be foud at the BS such that all the users ca receive their messages uder the proposed two-phase trasmissio protocol, i.e., N Φ(I) + N Φ(II) = K, the ultra-reliable commuicatio is achieved over the τ secods. Otherwise, we say that a outage has occurred. C. Problem Formulatio To achieve ultra-reliable commuicatio over ay particular duratio τ, we eed to desig the beamformig vectors at the BS to maximize the total umber of the successful users, i.e., maximize {w (I) } subject to Φ (I) + Φ (II) w (I) 2 P BS. (12a) (12b) If the optimal value to the above problem is K, the ultrareliable commuicatio is achieved accordig to Defiitio 2.

6 6 IV. LEADER SELECTION BASED BEAMFORMING DESIGN Sice i practice it is hard to acquire the CSI of the D2D etworks, i.e., h,i,j s, at the BS, i this sectio, we propose a reformulatio of problem (12) without assumig ay kowledge of h,i,j s. A. Problem Reformulatio The proposed two-phase trasmissio protocol i Sectio III arises from the observatio that if a group has at least oe leader i the first phase, the with a very high probability, all the other users i the group would be able to decode the messages successfully over the D2D etwork i the secod phase due to their proximity to the leaders. Motivated by this observatio, this paper reformulates the problem by settig the costrait of Phase I so as to esure that each group has at least oe leader. This ca be doe without kowledge of h,i,j s. Moreover, amog all beamformig strategiesw (I) s that yield at least oe leader for each group, we choose the oe that maximizes the total umber of leaders i Phase I, so that fewer users eed to satisfy their SINR requiremets i Phase II. I this way, we formulate the followig beamformig desig problem, assumig o kowledge of h,i,j s: maximize {w (I) } Φ (I) subject to Φ (I) 1,, w (I) 2 P BS. (13a) (13b) (13c) I problem (13), φ (I) s as give i (6) are complicated ad discrete fuctios over the beamformig vectors, which make it challegig to apply optimizatio techique to solve problem (13). To tackle the issue arisig from the discrete φ (I) s, let us defie t(i) = [t (I) 1,,,t(I) K, ]T C K 1,. It ca the be show that problem (13) is equivalet to the followig problem: miimize {w (I),t (I) } t (I) 0 subject to γ (I) +t(i) γ(i), k,, (14b) t (I) 0 K 1,, t (I) 0, k,, (14d) w (I) 2 P BS, (14a) (14c) (14e) where γ (I) s are give i (4). The equivalece betwee problem (13) ad problem (14) is due to the fact that the auxiliary variables t (I) s characterize the gap betwee the SINR targets ad achievable SINRs i Phase I, thus the umber of zero t (I) s deotes the umber of leaders i Phase I, ad costrait (14c) guaratees at least oe leader i each group. Such a equivalet trasformatio based o the auxiliary variables t (I) s results i a cotiuous problem (14). Moreover, sice we optimize the umber of zero elemets i t (I) s, sparse optimizatio techiques ca ow be used to solve the problem. The difficulty to solve (14) lies i the multiple cardiality costraits (14c). To esure that there is at least oe leader i each group i Phase I without havig to deal with the complicated cardiality costraits (14c), i this paper, we propose the followig ovel leader selectio based beamformig problem: miimize t (I) {w (I),t (I) } K 1 + β K t (I) (15a) subject to (14b), (14d), (14e), (15b) where β > 0 is the correspodig pealty weight for group, = 1,,N. Note that i the objective fuctio of problem (15), we use the covex fuctios t (I) 1 s to approximate ocovex fuctios t (I) 0 s i problem (14) based o stadard sparse optimizatio techique. I additio, we defie a K ew pealty 1 K for each group as β t(i) i the objective fuctio of problem (14). It is easily observed that for each group, its pealty is zero if at least oe elemet of t (I) is zero. As a result, the ew pealty ca lead to the desired sparsity patter, i.e., at least oe zero i t (I),. Moreover, sice the geometric mea f(x = [x 1,,x N ]) = N N x is a cocave fuctio over x [30], the fuctio N β K K t(i) is cocave over t (I) > 0 s. The objective fuctio of problem (15) is thus the differece of covex fuctios, ad stadard techiques such as the successive covex approximatio method ca be used to solve the problem to a local optimum. I the rest of this sectio, we give details o how to solve the above leader selectio based beamformig desig problem. B. Beamformig Desig to Problem (15) The ew pealty i problem (15) eables us to bypass the complicated cardiality costraits of t (I) s i problem (14). However, problem (15) is a o-covex problem ad it is thus difficult to fid its globally optimal solutio. O oe had, the pealty i the objective fuctio is o-covex. O the other had, the SINR costraits give i (14b) are also o-covex. I the followig, we propose a algorithm based o the successive covex approximatio techique that ca yield a locally optimal solutio to problem (15). First, we provide a covex upper boud to the objective fuctio of problem (15). Sice the fuctio N β K K t(i) is cocave over t(i) > 0 s as 1 I this paper, we set the pealty weight as β = 2 K,, i.e., a higher pealty is itroduced to the groups with more users sice a leader i such groups ca help more users i the secod phase.

7 7 illustrated i Sectio IV-A, its first-order approximatio at ay give poit ˆt (I) (I) (I) = [ˆt 1,,,ˆt K, ]T, : N f({t (I) (I),ˆt }) = K β K ˆt (I) + β K K K ˆt (I) [ ] 1 1,, (t (I) ˆt (I) 1, ˆt (I) ˆt (I) ), K, (16) serves as its upper boud. Next, we deal with the o-covex SINR costraits (14b). Well-kow methods to deal with the multicastig SINR costraits iclude semidefiite relaxatio (SDR) [31] ad successive covex approximatio [32]. Recetly, it is show i [33] that the successive covex approximatio based algorithm i geeral achieves better performace i multicastig tha the SDR-based algorithm whe the umber of ateas at the BS ad the umber of devices are large. As a result, i this paper, we adopt the successive covex approximatio techique to deal with the o-covex SINR costraits (14b). First, the SINR costraits (14b) ca be re-formulated as h T w(i) 2 γ (I) +I (I) t(i) h T w (I) j j 2 +I (I), k,. (17) The mai issue is that h T w(i) 2 is a covex fuctio, rather tha a cocave fuctio, over w (I). We use the firstorder approximatio to provide cocave upper bouds to h T w(i) 2 s as i [32]. Specifically, defie a = R(h T w(i) ), k,, (18) b = I(h T w (I) ), k,. (19) The we have h T w(i) 2 = a 2 +b2,. Give ay s that satisfy the trasmit power costrait (2), we ca ŵ (I) defie â s ad ˆb s as (18) ad (19). The, the firstorder approximatio to h T w (I) 2 at this particular poit is give by g (a,b,â,ˆb ) = â 2 +ˆb 2 ([ ] [ ]) a â +2[â,ˆb ],. (20) b ˆb To summarize, by itroducig the auxiliary variables a s ad b s, give ay fixed ŵ (I) s, we ca use the followig covex costraits to approximate the o-covex costraits (17): g (a,b,â,ˆb ) γ (I) j +I (I) t(i) h T w (I) j 2 +I (I), k,. (21) Algorithm 1 Proposed Algorithm for Solvig Problem (15) Iitializatio: Set the iitial values forˆt (I) s ad ŵ (I) s ad set l = 1; Repeat: 1) Fid the optimal solutio to problem (22) usig CVX as {w (I,l),t (I,l),a (l),b (l) 2) Update ŵ (I) = w(i,l) ˆt (I) = t(i,l), ; 3) l = l+1. Util covergece }; (thus â = a (l) ad ˆb = b (l) ), With the above approximatios, give ay fixedˆt (I) s ad s, we ca solve the followig covex problem: ŵ (I) miimize t (I) {w (I),t (I),a,b} 1 +f({t (I) (I),ˆt }) (22a) subject to (18), (19), (21), (14d), (14e), (22b) where a = [a 1,,,a K,] T, b = [b 1,,,b K,1] T,, ad f({t (I) (I),ˆt }) are as give i (16). Sice problem (22) is a covex problem, it ca be globally solved usig existig stadard package such as CVX [34]. The successive covex approximatio based algorithm to solve the leader selectio based beamformig problem, i.e., (15), proceeds by iteratively updatig ˆt (I) s ad ŵ (I) s (thus â s ad ˆb s) based o the solutio to problem (22). The proposed algorithm is summarized i Algorithm 1. The covergece behavior of Algorithm 1 is guarateed i the followig propositio. Propositio 1: Mootoic covergece of Algorithm 1 is guarateed, i.e., t (I,l+1) 1 + K β K t (I,l) 1 + t (I,l+1) K β K t (I,l), (23) where l deotes the idex of iteratio of Algorithm 1. Moreover, the coverged solutio satisfies all the costraits as well as the Karush-Kuh-Tucker (KKT) coditios of problem (15). Proof: Please refer to Appedix A. The leader selectio based beamformig desig for solvig problem (12) to maximize the total umber of active users uder the proposed two-phase trasmissio scheme i Sectio III ad to achieve ultra-reliable commuicatio as defied i Defiitio 2 is summarized as follows. First, we solve problem (15) via Algorithm 1 ad use w (I) s to calculate φ (I) s based o (6). The, we calculate s based o (11). Reliable commuicatio is achieved φ (II) if N Φ(I) + N Φ(II) = K.

8 8 V. BENCHMARK SCHEMES FOR ULTRA-RELIABLE COMMUNICATIONS I this sectio, we briefly itroduce several other potetial approaches for URLLC as bechmark schemes. Numerical simulatio comparisos are provided i Sectio VI to show the performace gai of our proposed scheme over the bechmark schemes. A. Bechmark Scheme 1: Our Proposed Scheme but without Leader Selectio First, to illustrate the importace of leader selectio i our proposed two-phase trasmissio scheme, i the followig we cosider oe bechmark scheme i which the umber of leaders is maximized i Phase I without ecouragig at least oe leader for each group. I this case, problem (15) reduces to miimize t (I) {w (I),t (I) } 0 (24a) subject to (14b), (14d), (14e). (24b) I other words, the pealty for ecouragig at least oe leader i each group is removed. Problem (24) ca be solved i a similar way as problem (15). As a remark, the strategy that maximizes the total umber of leaders i Phase I is expected to activate more users i the cell-ceter groups that are close to the BS, because they have strog direct chaels ad do ot suffer from iter-cell iterferece. As a result, it is expected that the optimized beamformers for problem (24) would result i may leaders i the cell-ceter groups, while havig o leader i the cell-edge groups. I cotrast, our proposed scheme tries to activate at least oe leader i each group by solvig problem (15). It promotes fairess amog differet groups i Phase I ad thus makes the best use of the D2D etwork i Phase II, as later verified by umerical results i Sectio VI. B. Bechmark Scheme 2: Occupy CoW Protocol [24] The Occupy CoW protocol is proposed i [24] for achievig URLLC i a similar setup as i this paper. Specifically, Occupy CoW protocol is also a two-phase trasmissio protocol where user messages are trasmitted from the BS to the users i the first phase ad the successful users help relay the messages to the other users via the D2D etwork i the secod phase. The mai differece of Occupy CoW protocol as compared to our proposed protocol lies i the fact that all the users form oe group, rather tha N groups based o their geographic locatios. As a result, i the first phase, the BS combies all users messages together, i.e., Ω = Ω, ad multicasts this etire message to all the users, while i the secod phase, the successful users i Phase I ca help all the usuccessful users via the D2D etwork. Note that [24] oly cosiders the case that the BS has oe sigle atea. To make a fair compariso, i the followig we briefly itroduce how to desig the beamformig uder the Occupy CoW protocol if the BS has multiple ateas. Let s CN(0,1) deote the etire message iteded for all the users. The received sigal at each user i the first phase is expressed as y (I) = ht w (I) s+z (I),, (25) where w (I) C M 1 deotes the multicast beamformig at the BS i Phase I. The correspodig SINR to decode s is = ht w(i) 2,. (26) γ (I) I (I) Similar to (5) i Sectio III, to decode a message of N K D bits usig Bτ 1 symbols, the idetical miimum SINR requiremet for all the users is expressed as: γ (I) = 2 K D Bτ 1 1. (27) The idicator fuctio of each user i Phase I the depeds o whether its SINR satisfies this commo SINR target or ot, i.e., φ (I) = { 1, if γ (I) γ(i), 0, if γ (I) < γ(i). (28) The users that decode the messages successfully i the first phase ca the relay the messages to the other users i the secod phase. Similar to Sectio III-B, each leader oly eeds to relay the message Ω k/ Φ (I) with N D k/ Φ (I) bits iformatio to the other users, where Φ (I) deotes the set of leaders located i group. The miimum SINR required to sed the above message usig Bτ 2 symbols is γ (II) = 2 D k/ Φ (I) Bτ 2 1. (29) The key to achieve ultra-reliable commuicatios for the Occupy CoW protocol is the assumptio that full diversity gai ca be achieved i the secod phase eve though there is o cooperatio betwee the BS ad leaders. Specifically, [24] assumes that if the kth user i group does ot decode the messages i Phase I, based o some space-time codig techique, its SINR achieved from the secod phase trasmissio is where γ (II) = max γ (i,j) = φ(i) (i,j) () γ(i,j), if φ(i) = 0, (30) i,j P h,i,j 2, (i,j) (), (31) I (II) deotes the idividual SINRs of the orthogoal sigals from the ith user i group j. Depedig o whether its SINR

9 9 i Phase II satisfies the SINR target or ot, the idicator fuctios of the usuccessful users i Phase I are defied as { φ (II) = 1, if γ (II) < γ(ii) ad γ (II) γ(ii), (32) 0, otherwise. Uder the Occupy Cow protocol, the objective of desigig the beamformig vectors w (I) is to maximize the total umber of successful users i Phase I such that more leaders ca help relay the messages i Phase II, i.e., miimize {w (I),t (I) } t (I) 0 subject to γ (I) +t(i) γ(i),, t (I) 0,, (33c) w (I) 2 P BS. (33a) (33b) (33d) Similar to Algorithm 1, we ca use sparse optimizatio ad successive covex approximatio techiques to solve problem (33), ad the determie whether URLLC is achieved uder the Occupy CoW protocol, i.e., whether all the users receive their messages over τ secods. Note that i [24], all the users chaels are assumed to have the same distributio sice the locatios of the users are ot cosidered i the chael model. This paper shows that if i practice the effect of user locatios o user chaels is cosidered, we should group the users i close proximity together sice the gai of D2D etwork i Phase II maily comes from the adjacet users. Note that i Phase I, user groupig leads to multi-group multicast, istead of siglegroup multicast uder the Occupy CoW protocol i [24]. If there is oly oe omidirectioal atea at the BS, Occupy CoW works well sice there is o iter-group iterferece i Phase I if the BS does ot separate users ito groups i the spatial domai. If the BS is equipped with multiple ateas, however, our proposed scheme i Sectio III works better sice the BS ca adjust N beams i Phase I ad utilize the spatial multiplexig gai to activate oe leader i each group as log as M > N. Note that for Occupy CoW, the BS oly desigs oe beam i Phase I to satisfy the SINR targets of all the users, which is hard. The icreased degree of freedom, i.e., optimizatio of N beams rather tha oe beam, esures that our proposed scheme is more powerful tha Occupy CoW, as later verified by umerical results i Sectio VI. C. Bechmark Scheme 3: Modified Occupy CoW Protocol with Leader Selectio Leader selectio itroduced i Sectio IV ca be applied i Occupy CoW as well to improve its performace, if the users are geographically located i separate groups.. I the first phase, although all users messages are combied together, we ca desig w (I) to activate at least oe leader i each geographical group. The cosidered problem is thus formulated as miimize {w (I),t (I) } t (I) 0 + subject to (33b), (33c), (33d). K β K t (I) (34a) (34b) This problem ca be solved similarly as problem (15). For Occupy CoW, combiig all users messages together sigificatly icreases the SINR targets of all the users as compared to our proposed scheme, thus leads to a reductio of the umber of leaders i Phase I. I Phase II, a geographically isolated group without a leader evertheless caot rely o the far away leaders i other groups. As a result, eve if leader selectio is cosidered i Occupy CoW, its probability of reliable commuicatios is much lower tha our proposed scheme, as later verified by umerical results i Sectio VI. D. Bechmark Scheme 4: Oe-Phase Trasmissio Protocol with Broadcastig The proposed scheme i Sectio III ad Occupy CoW proposed i [24] both advocate a two-phase trasmissio for achievig ultra-reliable commuicatios by utilizig the D2D etwork i the secod phase. I the rest of this sectio, we itroduce possible approaches with oe-phase trasmissio where oly the dowlik commuicatio from the BS to the users is cosidered. First, cosider the case of broadcastig. I this case, the received sigal of the kth user i group is y = h T w s +h T (i,j) () w i,j s i,j +z,, (35) where s CN(0,1) deotes the message for the kth user i group, w C M 1 deotes the correspodig beamformig vector, ad z CN(0,I ) deotes the superpositio of the AWGN ad iter-group iterferece, with a power I. The SINR for decodig s is thus γ = (i,j) () h T w 2 h T w i,j 2 +I,. (36) Note that the miimum SINR target to deliver D bits iformatio usig Bτ symbols is: γ = 2 D Bτ 1,. (37)

10 10 The, we ca desig the beamformig vectors w s to maximize the umber of users whose SINRs satisfy their SINR targets, i.e., miimize {w,t } K t 0 (38a) subject to γ +t γ,, t (I) 0,, (38c) K w 2 P BS. (38b) (38d) Similar to [35], we ca trasform the SINR costrait (38b) ito the followig covex form: h T w +I t γ h T w i,j 2 +I,. (39) (i,j) () The, via relaxig t 0 s by t 1 s i the objective fuctio (38a), we ca desig the beamformig vectors by solvig the followig covex problem: miimize {w,t } K t 1 (40a) subject to (39), (38c), (38d). (40b) URLLC via broadcastig is achieved if with the obtaied beamformig vectors, all the users satisfy their SINR targets. As a remark, i most use cases for URLLC the rate requiremet of each user is very low, thus eve if we combie each group s messages together, the SINR requiremet for each group is still reasoable. I this case, ituitively, with M ateas at the BS, approximately M leaders ad thus M groups with oe leader i each group ca be supported uder our proposed scheme. O the other had, iformatio broadcastig ca oly support approximately M users i toal, i.e., URLLC is ot possible if K M. With a reliable D2D etwork, our proposed scheme ca achieve URLLC eve whe K M as log as the umber of groups satisfy N < M. E. Bechmark Scheme 5: Oe-Phase Trasmissio Protocol with TDMA Aother strategy to covey Ω to the kth user i group, k,, is TDMA. Specifically, whe the kth user i group is scheduled, the BS ca implemet a maximal-ratio trasmissio (MRT) beamformig, ad the received sigal at the user is y = h T p h h s +z,, (41) where p deotes the power to trasmit the message Ω. The correspodig SINR at the user is γ = p h 2 I,. (42) Note that with TDMA, D bits of iformatio eeds to be trasmitted to the kth user i group with oly Bτ/K symbols. The correspodig miimum SINR target for each user is: ˆγ = 2 KD Bτ 1,. (43) The, the trasmit power to satisfy each user s SINR target is p = ˆγ I h 2,. (44) If the total trasmit power at the BS satisfies the trasmit power costrait, i.e., K p P BS, (45) the all the users ca be supported via TDMA, ad thus URLLC is achieved. I a massive coectivity sceario, the umber of users, i.e., K, ca be large. If each user is oly allocated τ/k secods for iformatio trasmissio, the resultig SINR target as show i (43) is quite high. As a result, as later show i Sectio VI, TDMA caot achieve reliable commuicatios i geeral. F. Bechmark Scheme 6: Oe-Phase Trasmissio Protocol with Multi-Group Multicastig Moreover, similar to the first phase i our proposed scheme, we ca also apply multi-group multicastig to covey the message Ω () with K D bits to all the users i group,, but usig all the Bτ symbols i oe shot. The SINR of each user is give i (4). However, sice the trasmissio time is doubled compared to our proposed two-phase trasmissio scheme, the SINR target for each group is reduced. Specifically, the miimum SINR requiremet for the users i group is: γ = 2 K D Bτ 1,. (46) We ca proceed to solve problem (24) i Bechmark Scheme 1 with the ew SINR targets γ s. If oe beamformig solutio ca be foud such that all the users ca decode their messages, the URLLC is achieved for this scheme. However, similar to Bechmarks 4 ad 5, the lack of utilizatio of the reliable D2D etwork makes it difficult for this oe-phase scheme to guaratee the performace of cell-edge users who experiece strog iter-cell iterferece. VI. NUMERICAL RESULTS This sectio presets the umerical results to verify the effectiveess of the proposed two-phase trasmissio protocol i Sectios III ad IV for URLLC as compared to the bechmark schemes itroduced i Sectio V.

11 11 base statio (cotroller) oe group devices (actuators) oe cell (factory) Fig. 2. The cellular-based model for idustrial automatio: the cell, BS, ad user act as factory, cotroller, ad actuator, respectively, i idustrial automatio. I this setup, the ceter cell is the referece cell of iterests, while the other 6 cells geerate iter-cell iterferece to the users i the referece cell. The simulatio setup is as follows. As show i Fig. 2, we cosider a etwork cosistig of 7 cells i a wrapped aroud topology, i which the ceter cell is the referece cell the performace of which we are iterested i, ad the other 6 adjacet cells geerate iter-cell iterferece to the users i the referece cell. 2 This cellular-based topology is a proper model for idustrial automatio: each cell, BS, ad device ca be viewed as the factory, cotroller, ad actuator, respectively, i which each factory cosists of several groups of actuators. As a result, the simulatio results show i this sectio are valid i a idustrial automatio topology. I the simulatio, the cell radius is 500m. It is assumed that there are N = 6 groups i the referece cell, while each group cosists of 8 users, i.e, K = 48. The ceter of each group is radomly located i a doughut shape of ier radius R ier ad outer radius R outer. Moreover, each group covers a area with a radius of 20m, ad its users are radomly located i the area covered by this group. The BS is assumed to be equipped with M = 8 ateas. The dowlik chael from the BS to the kth user i group is modeled as h = η g, where η deotes the pathloss compoet, ad g CN(0,I) deotes the Rayleigh fadig compoet. Moreover, the path-loss compoet is modeled as log 10 (d ) i db, where d i km deotes the distace from the kth user i group to the BS. For the commuicatios betwee the users over the D2D etwork, if two users are i the same group, we model their chael as Ricia fadig; otherwise, we model their chael as Rayleigh fadig. Specifically, the chael from the ith user i group to the kth user i the same group is modeled as h,i, = η,i, ( δ/(δ +1)ĝ,i, + 1/(δ +1) g,i, ), where η,i, deotes the path-loss 2 I our simulatio, for each chael realizatio, we first radomly geerate the other 6 cells beamformers at the BSs i Phase I ad leader locatios i Phase II. The, we calculate the iter-cell iterferece for the referece cell ad desig its beamformig accordigly as show i Sectio IV. I other words, oly the reliability of the referece cell is cosidered. compoet, ĝ,i, with ĝ,i, 2 = 1 deotes the lie-ofsight (LOS) determiistic compoet, g,i, CN(0,1) deotes the Rayleigh fadig compoet, ad δ deotes the Ricia factor specifyig the power ratio betwee the LOS ad fadig compoet. I this paper, we set δ = 4 ad characterize the path-loss compoet as log 10 (d,i, ) i db accordig to the idoor chael model i [36], where d,i, deotes the distace betwee the two users. Moreover, the chael from the ith user i group j to the kth user i aother group is modeled as h,i,j = η,i,j g,i,j, where the path-loss compoet is modeled as log 10 (d,i,j ) i db, ad g,i,j CN(0,1) deotes the Rayleigh fadig compoet. The total badwidth used is assumed to be B = 100kHz for both the dowlik chaels h s ad D2D chaels h,i,j s. We assume flat fadig across this badwidth B. The delay requiremet for the commuicatio is τ = 1ms. As a result, there are i total Bτ = 100 trasmit symbols available for deliverig the messages Ω s to each user. Moreover, we set τ 1 = 0.75ms i Phase I ad τ 2 = 0.25ms i Phase II. The motivatio for allocatig more time to Phase I is to reduce its SINR requiremet (see (5)) such that there is at least oe leader i each group. The trasmit power costrait at the BS is P BS = 43dBm, ad at the user is P = 23dBm. The power spectral desity of the AWGN at the users is assumed to be 169dBm/Hz. For coveiece, it is assumed that the message sizes of all the users are the same, i.e., D = D,. I the simulatio, we geerate 10, 000 chael realizatios ad for each realizatio, we measure whether all the users decode their messages withi τ = 1ms for each ivestigated scheme. The probability of URLLC for each scheme is the defied as the percetage of istaces achievig reliable commuicatio. A. Performace Compariso betwee Proposed Scheme ad Bechmark Schemes whe D = 22 I this umerical example, we assume that each user requires a 22-bit message, i.e., D = 22. Moreover, we assume that R ier = 250m ad R outer = 350m, i.e., the ceter of each group is radomly located i a doughut shape of ier radius 250m ad outer radius 350m. The probabilities of reliable commuicatios ad the averaged umbers of users that decode their messages successfully uder the proposed scheme versus Bechmark Schemes 1 6 are give i Tables I ad II, respectively. It is observed that our proposed scheme ca achieve a probability of reliable commuicatios above 99.99% (o outage is observed i 10,000 chael realizatios) i this setup, which is much higher tha the bechmark schemes. Specifically, if leader selectio is ot cosidered i our proposed scheme, i.e., Bechmark Scheme 1, the probability of reliable commuicatios is 0, although the averaged umber of successful users is It is worth otig that uder the proposed scheme with leader selectio, all the 8 groups have at least oe leader after Phase I i all the 10,000 chael realizatios, while uder Bechmark Scheme 1 without leader selectio, o average