Dealing with Link Blockage in mmwave Networks: D2D Relaying or Multi-beam Reflection?

Transcription

1 Deaing with Lin Bocage in mmwave etwors: DD Reaying or Muti-beam Refection? Mingjie Feng, Shiwen Mao Dept. Eectrica & Computer Engineering Auburn University, Auburn, AL , U.S.A. Tao Jiang Schoo of Eectronic Information & Communications Huazhong Univ. Science & Technoogy, Wuhan 4374 China Abstract Device to device (DD) reaying and muti-beam refection are two effective approaches to dea with the bocage probem in miimeter-wave (mmwave) communication, each with its own imitations when serving a arge number of user equipments (UE). A combination of DD reaying and mutibeam refection is expected to enhance the performance, but the seection of UEs to be served by each approache remains a chaenge. In this paper, we consider adaptive mode seection between DD reaying and muti-beam refection in a time division dupex (TDD) mmwave networ. We formuate a joint mode seection and resource sharing probem with the objective of maximizing the sum ogarithm rate, and propose a two-stage soution agorithm. In the first stage, we derive the optima resource sharing soution under the case that a UEs are served by DD reaying. In the second stage, an adaptive agorithm is proposed to determine the set of UEs that switch from DD reaying to muti-beam refection. Simuation resuts demonstrate that the proposed scheme achieves considerabe performance gain compared to severa benchmar schemes /7/$3. c 7 IEEE I. ITRODUCTIO With the growing popuarity of data-intensive appications, the next generation (i.e., 5G) wireess networ is expected to provide x data rate []. Miimeter-wave (mmwave) communication is one of the ey enabing technoogies of 5G wireess to meet such chaenges [], [3], aong with massive MIMO [4] and sma ces [5], [6]. Operating in the higher end of spectrum ranging from 3GHz to 3GHz, a arge bandwidth is avaiabe (e.g., a 7 GHz icense-free spectrum between 57 GHz and 64 GHz was approved by FCC), resuting in significanty improved data rate. Despite such great potentia, a major chaenge of mmwave communications is to overcome bocages. Due to the short wave ength, the mmwave cannot penetrate obstaces such as was and human bodies. Thus, the ine-of-sight (LOS) path between a base station (BS) and a user equipment (UE) may be easiy boced due to the mobiity of the UE or other UEs. To maintain connectivity, aternative ins have to be found and used. To this end, there are three possibe approaches, incuding (i) device to device (DD) reaying by other UEs, (ii) refection of beams [8], [9], (iii) handover to other BSs. The DD enabed mmwave networ was considered in [], [], in which effective MAC protocos were proposed. A mutibeam refection architecture was recenty proposed in [], where the concept of beamspace MIMO was introduced and a mutipexing gain was achieved. In [3], an inter-bs coordination mechanism is designed to dea with the LOS chaenge by optimizing the set of BSs serving each UE. Athough these soutions are effective in deaing with bocage, the performance gain is imited by some inherent factors of these approaches. For DD reaying, a reaying UE must share part of its resource with other UEs. Besides, mutihop reaying increases the deay since the pacets have to be forwarded mutipe times. The major chaenge of mutibeam refection is the arge path oss exponent of LOS ins. Compared to LOS ins with a typica path oss exponent of, the path oss exponent of LOS can be as arge as 4 [4]. Hence, ony a certain set of UEs are suitabe for mutibeam refection. In addition, in case of serving a arge number of UEs, the transmission power aocated to each UE woud be imited, resuting in degraded quaity of service (QoS). The handover approach, which seems easy to impement in traditiona ceuar networ, requires intensive coordination among BSs in an mmwave networ. Due to the narrow beam of mmwave transmissions, discovering an aternative BS and tracing roaming UEs may incur additiona overhead, such as that caused by beam sweeping [5]. To avoid these drawbacs and fuy harness the benefits of these approaches, a combination of mutipe approaches with a proper integra design has the potentia to enhance the system performance. As the UEs are served by mutipe approaches, the number of UEs served by each approach is reduced, the resource aocated to each UE can be increased, resuting in improved performance. Then, how to seect the sets of UEs served by different approaches is a ey factor that impacts the system performance, but has not been investigated in previous wors. In this paper, we consider a combination of DD reaying and muti-beam refection with an adaptive seection between the two approaches in a singe ce time division dupex (TDD) mmwave networ. We formuate a joint mode seection and resource sharing probem with the objective of maximizing the sum ogarithm rate, and propose a two-stage soution agorithm. In the first stage, we consider the case that a LOS UEs are served by DD reaying, and derive the optima resource sharing soution. Based on the soution, an adaptive mode seection agorithm is then proposed in the second stage to determine the sets of LOS UEs served by DD reaying and muti-beam refection. The proposed scheme is evauated with simuations and compared with severa benchmar schemes, where considerabe performance gains are achieved.

2 st hop nd hop 3rd hop 4th hop (-) th hop th hop Downin period divided into time sots BS st transmission:,,,, 3 3,, 3 4 4,, 4 5 5,, o shared node for concurrent transmissions - - -, - nd transmission:,,-,,- 3 3,, , LOS LOS 3rd transmission:,, , : DD reaying and BS - LOS UEs : Muti-beam refection Fig.. System mode of a DD and muti-beam enabed muti-hop mmwave ceuar networ.. In the remainder of this paper, we present the system mode and probem formuation in Section II. The soution agorithm is given in Section III. The simuation resuts are discussed in Section IV. We concude this paper in Section V. II. PROBLEM FORMULATIO We consider an mmwave ceuar networ that supports directiona transmissions with a sma beamwidth, e.g., ess than. Due to the pseudo-wired property and arge propagation oss, the performance gain achieved from inter- BS interference coordination is imited. Thus, we focus on in scheduing of one BS and the UEs it serves. Assume the set of UEs served by each BS is predetermined, we focus on a tagged BS serving K UEs indexed by =,,...,K.The UEs are subject to random bocage and can reay data for other UEs in case of bocage. The boced UEs are served by either muti-hop DD reaying or muti-beam refection. We assume the system operate in the TDD mode, so that channe reciprocity can be expoited for efficient channe estimation. As shown in Fig., we consider in scheduing for downin transmissions. Each LOS UE receives its pacets from a singe reaying UE. Then, the networ architecture of muti-hop DD reaying can be viewed as a tree, whie mutibeam refection can be viewed as an aternative (or, augment) connection from the root to a node that corresponds to an LOS UE. Define x and y as indicators for muti-hop DD reaying and muti-beam refection for user, respectivey, given as x {., user is served by DD reaying or LOS in = () y. = {, user is served by muti-beam refection We assign x =to LOS UEs since they are part of the DD reaying architecture. We then use a descendent matrix to indicate the reaying route of each LOS UEs, defined as a,. = {, user is a descendent of user () (3) If is an even number: If is an odd number: / th transmission: From i th hop to (i+) th hop The set of hops with pacets transmitted, (+)/ th transmission: Fig.. Transmission pattern of a TDD-based muti-hop DD mmwave ceuar networ. Since a, is defined for UEs invoved in the DD reaying process, we have a, x and a, x.letρ be the depth of UE in the DD reaying tree, given by ρ = = a, +. (4) That is, ρ is aso the number of hops required to transmit the pacets of UE. Let be the maximum vaue of ρ. To accommodate -hop DD reaying and guarantee that the pacets of UEs at the th hop can be deivered at the end of each downin transmission, we divide the downin transmission period into time sots as shown in Fig.. Each time sot is used for transmission from UEs in one hop to UEs in the next hop. For a UE served with muti-beam refection, the entire downin period is aocated to the UE. We assume that a UEs can ony perform haf dupex reaying two adjacent ins that share the same UE cannot operate concurrenty [6]. Under this constraint, a tota number of transmissions can be impemented, as shown in Fig.. For exampe, after the nd stage of the st transmission, which is from UEs with ρ = to UEs with ρ =, the nd transmission can be initiated since UEs with ρ = have finished transmission and are free for reception. ote that, as the index of transmissions increases, the pacets of UEs with arger ρ are not contained since there is no enough time for the transmissions of these UEs. In particuar, the pacets of UEs with ρ = and ρ = are not contained in the nd transmission, the pacets of UEs with ρ = 3,..., are not contained in the 3rd transmission, and so on. Then, the tota number of transmissions for UE, θ, is given by { θ = ρ +, is even + ρ (5), is odd, The BS is abe to serve mutipe users on the same timefrequency resource boc with advanced techniques, such as

3 hybrid beamforming [7]. Due to hardware constraints, when a UE reays the pacets of mutipe UEs, resource sharing is required among these UEs. Without oss of generaity, we assume time division mutipe access (TDMA) is appied when a UE forwards the pacets to mutipe UEs. Specificay, a fraction of time in each time sot is aocated to each DD in between the reaying UE and a UE at the next hop. We define t i,j as the fraction of time aocated to UE on its ith hop during the jth transmission. From the perspective of outfow, t i,j shoud satisfy a, t ρ +,j ρ, { ρ },j=,..., θ +.(6) = For UEs with ρ =, i.e., the LOS UEs, the infow constraint is given as a, t,j +t,j, { ρ =},j=,...,. (7) = The infow constraint (7) is ony required for the st hop transmission, since the infow of other hops woud ony be part of a time sot due to TDMA at the previous hop the eft-hand side of (7) woud aways be no arger than. Ina muti-hop transmission, the data rate of a in at the current hop shoud be no ess than the data rate of the in at the next hop. Thus, {t i,j } shoud aso satisfy C i t i,j Ci+ t i+,j, { ρ },i=,..., ρ, (8) where C i is the in capacity of hop i of UE, given by C i = B og ( +γ) i, (9) where B is the system bandwidth and γ i is the SIR of hop i of UE. Here, the SIR is constant over a θ transmissions, since the duration of upin and downin periods is ess than the coherence interva in a TDD system. ext, we derive the SIR expressions under different transmission schemes, empoying the baseine SIR mode presented in [4]. For UEs served by DD reaying, we have γ i = pi hi Gi (di ) σ, () where h i is the sma scae fading, which is a normaized Gamma random variabe [4] G i is antenna array gain di is the distance of the in and p i is the transmission power of the BS or UE for the ith hop of UE. The noise power is σ, and we negect the impact of interference. In (), we assume that the LOS path oss exponent is. For UEs served by BS with muti-beam refection and UEs served by BS with an LOS in, we assume the power of BS is equay aocated to these UEs. Then, the transmission power aocated to each UE is P p = y, () + LOS where P is the BS power and LOS is the number of LOS UEs. Simiar to (), the SIR of an LOS UE is given by γ = p h G (d ) σ. () Suppose UE is served with the refection of M beams indexed by m =,..., M.Let γ m be the SIR of the path corresponding to the m th beam of UE, given as γ m = pm hm Gm (dm ) 4 σ, (3) where p m, hm, Gm, and dm are the power, sma-scae fading, antenna array gain, and distance of the mth path, respectivey. We negect the interference caused by side obes. Without oss of generaity, we assume p is equay aocated to the M beams. The path oss factor for LOS refection is 4. For UE served by muti-hop DD reaying, its downin data rate is the sum of a θ transmissions. In each muti-hop transmission, the effective data rate is determined by data rate of the fina hop divided by the number of hops. Then, the data rate of UE when served by muti-hop DD reaying in the downin period is given by R = θ j= C ρ tρ,j. (4) ρ The data rate of LOS UEs is a specia case of (4) with ρ =. When UE is served by muti-beam refection in the downin period, its data rate is given by R = M m= B og ( + γ m ). (5) In this paper, we aim to maximize the ogarithm rate sum of a UEs with adaptive seection between DD reaying and muti-beam refection for a LOS UEs. Let x, y, a, and t be the vector/matrix forms of {x }, {y }, {a, }, and {t i,j }. The probem is formuated as { K } K P: max x og R + y og R (6) {x,y,a,t} = = subject to: x + y, (7) a, t ρ +,j ρ, { ρ },j=,..., θ + (8) = a, t,j +t,j, { ρ =},j=,..., (9) = C i t i,j C i t i,j, { ρ },i=,..., ρ () a =,, { ρ }, () a, x,. () t i,j x, t i,j,, i, j. (3) x,y,a, {, },. (4) Constraint () is due to the fact that each node in the DD reaying tree can ony have one parent node.

4 III. SOLUTIO ALGORITHM Probem P is a mixed integer programming probem with mutipe sets of variabes, which cannot be soved with standard techniques. To derive an effective soution, we propose a two-stage agorithm for adaptive seection between DD reaying and muti-beam refection. In the first stage, we consider the case that a LOS UEs are served with DD reaying and derive the optima resource aocation soution. Based on the soution, the UEs that can be served by mutibeam refection are evauated in the second stage, then the set of UEs to be served by muti-beam is determined. A. First Stage We assume that path seection for DD reaying is predetermined with a routing approach, e.g., adopting Dijstra s Agorithm by setting the weight of each in as the inverse of its channe gain [7]. With a LOS UEs served by DD reaying, probem P is reduced to the foowing resource aocation probem. K θ P: max og C ρ tρ,j (5) {t} = j= subject to: (8) () It can be verified that probem P is a convex optimization probem and strong duaity hods. The Lagrangian dua method can be appied to obtain the optima soution. B. Second Stage Based on the optima soution of probem P, we then evauate the performance gain of switching a UE from DD to muti-beam, and determine the set of UEs to be served with muti-beam refection. We define Δ as the performance gain of a UEs by seecting UE to switch from DD reaying to muti-beam refection at the τ th round. For a UE with descendent UE(s) in the DD tree, we assume that a of its descendent UEs woud aso switch to mutibeam refection since re-constructing the DD tree is timeconsuming, which shoud not be carried out frequenty. Then, the performance gain is given as: Δ =og R og R ( + og R og R ). a, = ρ Since the objective function is to maximize the sum ogarithm rate, the vaue of t ρ,j woud be cose to each other among different UEs. Thus, when an LOS UE switches from DD reaying to muti-beam refection, we approximate the vaues of t ρ,j of other UEs to be increased by tρ,j x tρ,j + or = a, tρ,j x, depending on whether UE has any descendent in the DD tree. Since we assume equa power aocation, the transmission power aocated to each LOS UE and muti-beam LOS UE is decreased by a factor of y + LOS y ++ LOS or y + LOS y ++ = a, depending on, +LOS whether UE has any descendent in the DD tree. Let η = { a, =} and Φ be the set of UEs served by DD reaying. The adaptive agorithm for seection between Agorithm : Adaptive Mode Seection Agorithm Initiaize: x =,y =,, Φ={,..., K} τ =, [] =argmax { x =} Δ [] 3 whie Δ > do 4 if ρ =then 5 Set y =, x =, Φ=Φ {} 6 for =:K do 7 Update R with (4) by adding t ρ,j / x to each t ρ,j, Φ 8 Update R with (5) by mutipying p by ( y + LOS)/( y ++ LOS) 9 Cacuate Δ end ese Set y =, x = y =, x =,for η 3 Φ=Φ {} η 4 for =:K do 5 Update R with (4) by adding (t ρ,j + = a, tρ,j )/ x to each t ρ,j, Φ 6 Update R with (5) by mutipying ( y + LOS)/( y ++ = a, +LOS) to each p m, / Φ 7 Cacuate Δ 8 end 9 end =argmax { Φ} Δ τ = τ + end DD and muti-beam is summarized in Agorithm. In each round of Agorithm, the UE or the set of UEs that brings the argest performance gain is seected to switch from DD reaying to muti-beam refection. Such process terminates unti no positive gain can be achieved. IV. SIMULATIO STUDY We vaidate the performance of the proposed scheme through MATLAB simuations. We consider one BS serving mutipe UEs with coverage range of 5 m. The system bandwidth is GHz. The UEs are randomy distributed in the coverage area. Each UE is subject to random bocage with probabiity P b. We assume that the bocage probabiity is proportiona to the distance between the UE and the BS with coefficient κ, given as P b =min{κ D, }. As an exampe, when κ =.4, a UE that is m away from the BS has a probabiity of.4 to be boced for UEs that are more than 5 m away, they are aways boced. We compare with a heuristic scheme. In each round of the heuristic scheme, the UE with the argest vaue of R is seected to be served with muti-beam refection. Such process terminates unti y R decreases. We aso consider the case of setting the objective function of Probem P as sum rate maximization, which serves as an upper bound for the sum rate performance. Fig. 3 shows the sum rate performance under different number of UEs. The sum rate of the muti-beam ony scheme is ower than other schemes due to the arge path oss exponent of LOS ins and the increased transmission distance brought by refection. The DD ony scheme achieves higher sum rate than the muti-beam ony scheme, but its performance is

5 5 5 Average sum rate (bps) 4 x Proposed Heuristic DD ony.5 Muti beam ony Upper bound umber of UEs Average sum rate (bps) 7 x Proposed Heuristic DD ony Muti beam ony Upper bound Bocage coefficient κ Fairness index Sum ogarithm rate maximization Sum rate maximization 5 5 umber of UEs Fig. 3. Average sum rate under different numbers of UEs. κ =.. Fig. 4. Average sum rate under different vaues Fig. 5. Fairness with different objective functions. of κ. The number of UEs is 5. The number of UEs is 5 and κ =.. significanty degraded when the number of UEs is arge. The degraded performance of DD ony scheme resuts from both resource sharing among UEs and the increased time spent on muti-hop transmission. By seecting some UEs to be served by muti-beam refection, the heuristic scheme and the proposed scheme achieve better performance, due to the reduced number of UEs invoved in DD transmission. The proposed scheme outperforms the heuristic scheme since the proposed adaptive agorithm jointy considers the performances of UEs served by DD and muti-beam, whie the heuristic scheme is ony based on UEs served by muti-beam. The performance of the proposed scheme is cose to its upper bound, showing that the performance oss due to fairness concern is reativey sma. The resuts of Fig. 3 indicate that both DD reaying and mutibeam refection are highy imited by the increasing traffic. A combination of the two approaches with proper UE seection can effectivey improve the system performance. The performances under different bocage coefficients, κ, is shown in Fig. 4. As κ increases, the performances of a schemes are degraded due to increased ratio of LOS UEs. It can be seen that the performance of both DD ony and mutibeam ony schemes are highy sensitive to bocage, since the time and power resources are shared by the increasing number of LOS UEs. With adaptive seection between DD and muti-beam, the proposed scheme achieves considerabe performance gain, especiay when κ is arge. Fig. 5 shows the fairness performance by setting different objective functions for Probem P. We use the Jain s fairness index, ( x R + y R ) /K (x R + y R ),to measure fairness between different UEs. It can be seen from Fig. 5 that when the objective is set to sum rate maximization, the fairness is poor, since the ins with high channe gain woud be aocated with much more transmission time than the ins with ow channe gain. With the objective of sum ogarithm rate maximization, the proposed scheme achieves a good tradeoff between system performance and fairness. V. COCLUSIOS We considered a combination of DD reaying and mutibeam refection to overcome bocage as we as enhance performance of a TDD mmwave networ. A two-stage soution agorithm was proposed to determine the set of UEs served by DD reaying and muti-beam refection. The effectiveness of the proposed scheme was vaidated with simuations. ACKOWLEDGMET This wor is supported in part by the SF under Grant CS-3664, and by the Wireess Engineering Research and Education Center (WEREC) at Auburn University. REFERECES [] Quacomm, The x data chaenge, [onine] Avaiabe: [] J.G. Andrews, S. Buzzi, W. Choi, S.V. Hany, A. Lozano, A.C.K. Soong, and J.C. Zhang, What wi 5G be? IEEE J. Se. Areas Commun., vo.3, no.6, pp.65 8, June 4. [3] T. S. Rappaport, et a., Miimeter wave mobie communications for 5G ceuar: It wi wor! IEEE Access J., vo., May 3, pp [4] M. Feng and S. Mao, Harvest the potentia of massive MIMO with muti-ayer techniques, IEEE etwor, vo.3, no.5, pp.4 45, Sept./Oct. 6. [5] M. Feng, T. Jiang, D. Chen, and S. Mao, Cooperative sma ce networs: High capacity for hotspots with interference mitigation, IEEE Wireess Commun., vo., no.6, pp.8 6, Dec. 4. [6] M. Feng, S. Mao, and and T. 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