Multiuser Millimeter Wave Communications With Nonorthogonal Beams

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 7, JULY 2017

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Multiuser Millimeter Wave Communications With Nonorthogonal Beams Qing Xue, Xuming Fang, Senior Member, IEEE, Ming Xiao, Senior Member, IEEE, and Li Yan

Abstract—Recently, millimeter-wave (mmWave) and even terax hertz wireless (with higher frequency) networks have attracted significant research interests as alternatives to support the formidable growth of wireless communication services. Normally, directional beamforming (BF) is shown as a promising technique to compensate its high path loss. We focus on mmWave communications and assume that both mmWave base stations (MBSs) and user equipments (UEs) can support directional BF. As mmWave spectrum has short wavelength, massive antenna arrays can be deployed at MBSs to form multiple directional beams through BF training. Then, an MBS can transmit simultaneously to multiple UEs (SUEs) with different beams in the networks. However, the beams that serve different SUEs may transmit (almost) in the same path, especially when SUEs are distributed densely. Thus, they are not in perfect orthogonal beams. Due to the leakage of transmission power, the interference among these beams may be severe. To address this problem, typically the MBS could serve these SUEs in time division multiplex. This will degrade the spectral efficiency. In this context, we investigate the effect of nonorthogonal beam interference and then propose two novel solutions (i.e., dynamic beam switching and static beam selection) to coordinate the transmitting beams effectively. Then, an improved downlink multiuser simultaneous transmission scheme is introduced. In the scheme, an MBS can serve multiple SUEs simultaneously with multiple orthogonal and/or nonorthogonal beams to guarantee SUEs’ Quality of Service. The theoretical and numerical results have shown that our scheme can largely improve the performance of the achievable rate and, meanwhile, can serve lots of SUEs simultaneously. Index Terms—Interference, millimeter wave (mmWave), multiuser (MU), nonorthogonal beams.

I. INTRODUCTION UE to the widespread use of mobile Internet applications by smart terminals, the next generation wireless networks use new available frequency spectra, i.e., the millimeter-wave

D

Manuscript received April 9, 2016; revised September 3, 2016 and September 25, 2016; accepted October 10, 2016. Date of publication October 12, 2016; date of current version July 14, 2017. The work of Q. Xue, X. Fang, and L. Yan was supported in part by EU FP7 QUICK project under Grant PIRSESGA-2013-612652, in part by NSFC under Grant 61471303, and in part by NSFC-Guangdong Joint Foundation under Grant U1501255. The work of M. Xiao was supported in part by EU FP7 QUICK project under Grant PIRSESGA-2013-612652. The review of this paper was coordinated by S. Mumtaz. (Corresponding author: Xuming Fang.) Q. Xue, X. Fang, and L. Yan are with the Key Lab of Information Coding and Transmission, Southwest Jiaotong University, Chengdu 610031, China (e-mail: [email protected]; [email protected]; liyan12047001@my. swjtu.edu.cn). M. Xiao is with the Department of Communication Theory, Royal Institute of Technology, Stockholm 100 44, Sweden (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2016.2617083

(mmWave) bands that operate at 30–300 GHz, or terahertz (THz) bands that operate at 0.1–10 THz, to overcome spectrum congestion at the conventional microwave band below 10 GHz [1]. The main characteristics of mmWave and THz include directionality, large bandwidth, and high attenuation [2]. In particular, 60 GHz mmWave band (FCC: 57–64 GHz; Japan: 59–66 GHz; Europe: 57–66 GHz; and China: 59–64 GHz [3], [4]) is more appropriate for indoor communications, in which line-of-sight (LOS) or short-distance transmissions are dominant than other mmWave bands. It has been widely studied by several standardization organizations, such as the IEEE 802.15.3 Task Group 3c (TG3c) [5] and WirelessHD [6], for indoor wireless personal area networks (WPANs), the IEEE 802.11ad (TGad) [7], [8] and wireless gigabit alliance (WiGig) [9] for wireless local area networks (WLANs). Experimental studies in [10] and [11] confirmed that 60 GHz indoor radio propagation channel is mostly comprised of LOS path (if available) and low-order non-LOS (NLOS) paths, i.e., the first- and second-order reflections from ceiling, floor, walls, and other objects in the environment. Furthermore, human activity can easily block the LOS path and its influence on 60 GHz indoor radio link is fully investigated in [12] and [13]. In this study, taking 60 GHz as an example, we focus on multiuser (MU) transmissions in mmWave networks without considering human blockage and the sensitivity to movement caused by pole sway [14]. The 60 GHz band signal with large available unlicensed spectrum exhibits severe oxygen absorption, which contributes about 15 dB/km of attenuation in addition to free space loss [15]. In view of this, a high-gain antenna array is required to improve the system efficiency and transmission range, and thus directional beamforming (BF) is considered as one of the key techniques to compensate the high path loss and limited power in mmWave networks [1], [16]–[19]. Thanks to the short wavelength (i.e., around 5 mm) of the 60 GHz mmWave radio, it is possible to pack massive antenna elements into the limited dimensions of mmWave transceivers [20], [21]. Additionally, antenna technologies, such as spatial division multiple access (SDMA) and/or (massive) multiple-input multiple-output (MIMO), can be implemented readily [1], [22], [23]. Normally, for the traditional MU transmission schemes in existing microwave networks (e.g., LTE/LTE-U and the IEEE 802.11ac WLAN), the multiple transmissions are considered to be orthogonal. For example, with BF and SDMA, the downlink MU-MIMO technique in the IEEE 802.11ac [24] is capable of implementing up to eight MIMO spatial streams and can support simultaneous transmissions for four users that are located in sufficiently

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Fig. 1.


Multiple simultaneous transmissions with directional BF.

different directions. Furthermore, the transmitter as well as the receivers (i.e., users) are working in the omnidirectional mode and does not form directional beams, though it can enhance signal strength toward each user. Moreover, as described in [2], for mmWave communications, current applications are generally for point-to-point scenarios, such as cellular backhaul [25], [26], or WLAN [27] and WPAN [28], with a limited number of users or medium access control layer protocols that prohibit multiple simultaneous transmissions. Therefore, these schemes are very difficult to use in the mmWave networks with densely distributed simultaneously to multiple user equipments (SUEs). One challenge is that the interference issue is rather complex. In our study, the interference is caused by transmission power from one beam leaking into other beams that are transmitted simultaneously. To mitigate unaffordable signaling, the existing mmWave technology adopts a conservative resource allocation protocol, i.e., time division multiple access (TDMA) based resource allocation [5], [7]. However, since TDMA realizes orthogonal use of time resources, it activates only one link at a time. The effective link capacity of TDMA reduces with the number of links in the mmWave network, as investigated in [29]. Thus, we need an appropriate solution to handle the simultaneous served SUEs to achieve better system performance. In general, each beam comprises a main lobe and several side lobes. Especially, side lobes usually may be signals that cause interference to neighboring SUEs. For a case of MU simultaneous transmissions in mmWave networks depicted in Fig. 1, the mmWave base station (MBS) attempts to transmit simultaneously over the same frequency band to multiple SUEs (e.g., SUE1, SUE2, and SUE3) with orthogonal beams, while there is some cochannel interference (interbeam interference) to SUE1 generated by the signals (beams) transmitted to SUE2 and SUE3 and vice versa. Thanks to the orthogonality, the interference is considered to be caused only by side lobes of the beams. Moreover, when these SUEs are separated in directions with large enough angles between each other, the mutual interference among them can be ignored. However, when a group of SUEs (e.g., SUE2 and SUE4) cannot be distinguished from one another by the MBS in angular domain, there are some beams

transmitted (almost) in the same path to different SUEs. That is, they are nonorthogonal to each other. In this context, the main lobes of these beams are the major interfering signals for each other and we define it as nonor-beam interference in this study. As a result, the network performance is significantly degraded if there are no effective nonor-beam interference coordination solutions. To the best of the authors’ knowledge, for multiple simultaneous transmissions (i.e., point to multipoint) in mmWave networks, there has been no work on analysis and evaluation of the nonor-beam interference issue as described above. Our study focuses on this issue and, for mmWave networks with an ultradense user distribution, we will propose an applicable MU transmission scheme with nonor-beam interference estimation and coordination. In this study, we investigate the effect of nonor-beam interference and then propose two nonorthogonal beam scheduling solutions that are dynamic beam switching (DBS) and static beam selection (SBS). Although the notions of beam switching and beam selection have been used in some literatures, the research background and motivation of the proposed solutions are quite different from those of the existing methods. Nowadays, for mmWave networks, beam switching is generally used to resolve the link-blockage problem (e.g., [30]). In [31] and [32], orthogonal beam scheduling strategies (i.e., beam selection) for sparse user regime were investigated, whereas SBS in this study is used for scheduling nonorthogonal beams in dense user regime. Beam selection in [33] refers to an improved BF training process, which is also different from that in this study. The main contribution of this work includes the following aspects. First, the nonor-beam interference is analyzed and evaluated. Second, two effective solutions for guarantee densely distributed SUEs’ Quality of Service (QoS) are proposed (i.e., DBS and SBS) to address the nonor-beam interference. Finally, an improved MU transmission scheme with multiple orthogonal and/or nonorthogonal beams for mmWave networks is proposed. The rest of the paper is organized as follows. In Section II, we describe the structure of mmWave networks and discuss the interference issue. In Section III, the nonor-beam interference is analyzed and addressed by two coordination solutions. Furthermore, we introduce an improved MU simultaneous transmission scheme. Section IV shows numerical results to evaluate our scheme. Conclusions for the paper are provided in Section V. II. SYSTEM DESCRIPTION FOR MMWAVE NETWORKS As shown in Fig. 2, we consider an mmWave network with one reference MBS (i.e., MBS1) and several densely distributed SUEs in the coverage of the MBS. We define the coverage area of an MBS as an mmWave-Cell (mmCell). Both MBS1 and SUEs are equipped with massive antenna elements, thus enabling directional BF. In this study, the beams are formed depending on an analog BF that is a simple and effective method of generating high antenna gains. Besides, there are several neighboring MBSs as well. We assume that the system is two-dimensional. Consider MBS1 with an Nt -element antenna array and Nt RF radio frequency (RF) chains transmits Ns data streams to multiple SUEs, where an inherent constraint is Ns ≤ Nt RF ≤ Nt [34]. Meanwhile, without loss of generality, we consider that

XUE et al.: MULTIUSER MILLIMETER WAVE COMMUNICATIONS WITH NONORTHOGONAL BEAMS

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i,j ≥ 2) Beam i and beam j are orthogonal beams when θmain

ξ ti +ξ tj

. Definition 2 (Group): The group is defined as a set of SUEs served by multiple nonorthogonal beams. Randomly select an SUE served by beam im as a reference SUE, then this SUE and the SUEs served by beam jm ,x (x = 1, 2, ..., Xm ) that satisfies 2

i

,j

ξ i m +ξ

jm ,x

m m ,x θmain < t 2t can be classified into group m (0 ≤ m ≤ M ), where Xm is the number of transmitting beams that are nonorthogonal to beam im , and M is the number of groups in the mmCell. Note that the selected reference SUE in each group must not be the SUEs in other groups. If an SUE (e.g., SUE5 in Fig. 2) is classified into two different groups (e.g., group m1 and group m2 ), we will eventually classify it into the group that satisfies ⎧ ⎫ Xm 2 m1 ⎨ X i m ,j m , x ⎬ i m 1 ,j m 1 , x 1 max θmain , θmain2 2 2 . (1) ⎩ ⎭

x 1 =1

Fig. 2.

Proposed system model for mmWave wireless networks.

each SUE is equipped with a single RF chain and can receive a single data stream. Therefore, MBS1 can support maximally Nt RF SUEs simultaneously by employing Nt RF beams. By completing the BF training process, MBS1 and each SUE (i.e., MBS1–SUE pair) can find their best transmitting and receiving beam (T–R beam pair) between them. We make the following assumptions in our study. 1) BF training operations of each MBS1–SUE pair have already carried out before MU simultaneous transmissions, i.e., MBS1 already knew the transmit direction of each transmit beam that serves different SUEs. 2) As short-distance transmissions are dominant in mmWave networks, we focus our attention on the interference among multiple beams in the angle domain without considering the effect of the transmission distance. For ease of illustration, similar to [35], we replace MBS1 with Nt RF virtually duplicated MBSs (vMBSs) that are located at the same position. Each vMBS has only one different beam and serves different SUEs. For the densely distributed SUEs, there are two interesting situations: 1) some SUEs are operating (almost) on the same direction toward MBS1 (e.g., SUE1 and SUE2), and 2) some SUEs are (almost) colocated (e.g., SUE3 and SUE4). After BF training operations, the beams that transmit to these SUEs are probably nonorthogonal. We group these SUEs that are indistinguishable by MBS1 (in the angular level) in multiple groups. Definition 1 (Nonorthogonal Beams): The nonorthogonal beams are defined as the beams whose main lobes are partially overlapping. That is, denoting ξti and ξtj as the transmitting beamwidth of beam i and beam j (i.e., the operating beams of i,j is the included vMBS i and vMBS j), respectively, and θmain angle between the main lobe of beam i and that of beam j, we have the following conditions. i,j < 1) Beam i and beam j are nonorthogonal beams when θmain ξ ti +ξ tj 2

.

x 2 =1

Let U and V denote the set of SUEs and vMBSs in the whole mmCell, respectively; Um (Um ⊆ U ) denote the set of SUEs in group m; Vm (Vm ⊆ V ) denote the set of vMBSs that serve group m; Q (0 ≤ Q ≤ Nt RF ) be the total number of SUEs in the mmCell; and Qm be the number of SUEs in group m (i.e., in Um ), Qm = 1 + Xm . Moreover, as there is approximately 7 GHz available unlicensed spectrum in 60 GHz band, to divide the whole system bandwidth of mmWave networks into multiple relatively narrower subbands is considered as a promising approach to alleviate the interference between different MBSs and to fully utilize the spectrum resources. In this study, different MBSs operate on different subbands. For MU simultaneous transmissions in mmWave networks, the interference is somewhat more complex than that in microwave communications, and there are mainly three types of interference that should be addressed. 1) Interbeam interference: It is the interference caused by side lobes of the beams, which are mutually orthogonal to each other in the mmCell. 2) Nonor-beam interference: It refers to the interference among the beams that serve a group, and the main lobes act as interfering signals. 3) Adjacent channel interference (ACI): As defined in [36], it is caused by the energy bleeding over to neighboring channel. Here, it means the interference between different mmCells using different subbands that are adjacent to each other. As we can see, the ACI is intercell interference, while the interbeam/nonor-beam interference can be interpreted as intracell interference. In [37], the effects of ACI in WLAN were measured. Through the results, we know that the most simple and effective method to overcome ACI is to make the subbands for nearby MBSs nonadjacent. The intracell interference is a well-known problem in wireless communications (either in mmWave or in microwave bands) when using hybrid precoding (e.g., joint spatial division and multiplexing studied in [38] and [39]). It may not be negligible, even with digital precoders. In this study, we mainly focus on

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TABLE I SUMMARY OF MAIN NOTATIONS Symbol

Definition

U V M Um Vm Q Qm ξti ξt min ξt max ξrk ξrk min ξrk max pi p max Ri , k αi , k i,j θmain i,j θover P Ik inter P Ik nonor Y C Csui V switch m U switch m select Um V select m Q switch m Q select m U ortho U nonor Q ortho Q nonor Group RateMU;m

The set of SUEs in the mmCell The set of vMBSs in the mmCell Number of groups in the mmCell The set of SUEs in group m (0 ≤ m ≤ M ) The set of vMBSs that serve group m Total number of SUEs in the mmCell Number of SUEs in group m (i.e., in Um ) Transmitting beamwidth of vMBS i Minimum transmitting beamwidth Maximum transmitting beamwidth Receiving beamwidth of SUE k Minimum receiving beamwidth Maximum receiving beamwidth Transmission power of beam i (i.e., vMBS i) Maximum transmission power Transmission distance from vMBS i to SUE k Angle of beam i off boresight direction Included angle between beam i and beam j Overlapping area of beam i and beam j Interbeam interference power Nonor-beam interference power Number of links between vMBS i and SUE k Candidate T–R beam pair set Suitable candidate T–R beam pair set vMBS set in which vMBSs can switch their beams SUE set served by V switch m Selected SUE set vMBS set that serves U select m Number of SUEs in U switch m Number of SUEs in U select m SUE set served by orthogonal beams SUE set served by nonorthogonal beams Number of SUEs in U ortho Number of SUEs in U nonor Achievable rate of group m

RateM U

Achievable rate of nongroup SUEs

Nongr

nonor-beam interference of MU simultaneous transmissions in mmWave networks with densely distributed SUEs. III. MU SIMULTANEOUS TRANSMISSION SCHEME In this section, we propose an MU simultaneous transmission scheme for mmWave networks. First, the nonor-beam interference is analyzed and evaluated. Then, two solutions are offered to coordinate it, to guarantee the QoS of SUEs in groups and to improve the performance in terms of the achievable rate of the network. Table I summarizes the main notations used throughout this paper. A. Modeling Nonor-Beam Interference By the standard Friis transmission equation for mmWave, the received power at the receiver from transmitter is given as a function of range R as [40]

2 λ e−β R , (2) Pr = Pt Gt Gr 4πR where Pt is the transmitted power; Gt and Gr are the antenna gains of transmitter and receiver, respectively; λ is the operating

wavelength; β is the attenuation factor due to absorption in the medium. After converting to units of frequency and putting them in decibel (dB) form, the transmission loss of mmWave 2 [i.e., L = 4πλR eβ R ] can be modeled as [8] L[dB] = A + 20 log10 (fc ) + 10n log10 (R) ,

(3)

where fc is the carrier frequency in GHz, R in km, A is the attenuation value, and n is the path loss exponent. For tractability of the analysis, we approximate the actual antenna patterns by a sectored antenna model [41], [42]. Moreover, in an ideal sectored antenna pattern, the directivity gains are constant for all angles in the main lobe and equal to a smaller constant in side lobes. In this context, for the link between vMBS i (i ∈ V ) and SUE k (k ∈ U ), the transmission gain can be expressed as [35], [43] ⎧ ⎨ 2π − 2π − ξti z , in the main lobe, (4) Git ξti = ξti ⎩ z, in side lobes, where 0 ≤ z < 1 is the average gain of side lobes. Similarly, we can obtain the reception gain Gkr ξrk as ⎧ k z 2π − 2π − ξ ⎨ r , in the main lobe, k (5) Gkr ξrk = ξ r ⎩ z, in side lobes, where ξrk is the receiving beamwidth of SUE k. On this basis, as shown in Fig. 3, we investigate the effects of interbeam interference and nonor-beam interference between beam i and beam j for the following four cases. ξ j −ξ i

1) Case I [see Fig. 3(a)]: When 0 ≤ |αj,k − αi,k | ≤ t 2 t , where ξtj ≥ ξti , the interference factor in a desired direction is therefore

(6) Gjt αi,k , αj,k , ξti , ξtj = Gjt,main ξtj , where αi,k and αj,k are the angles in which beam i and beam j are off the boresight direction of vMBS i and SUE k, respectively, 0 ≤ |αi,k | ≤ π and 0 ≤ |αj,k | ≤ π;

2π − 2π −ξ j z ( t ) Gjt,main ξtj = is the main lobe’s directivity ξ tj gain of beam j. 2) Case II [see Fig. 3(b)]: When 0 ≤ |αj,k − αi,k | ≤ where ξtj < ξti , we have

Gjt αi,k , αj,k , ξti , ξtj =

Gjt,main ξtj · ξtj + z · ξti − ξtj . ξti 3) Case III [see Fig. 3(c)]: When ξ ti +ξ tj 2

|ξ ti −ξ tj | 2

,

(7)

< |αj,k − αi,k |
0, we assume that P1 can be decomposed to on g r , two independent parts. The first part is to maximize RateN MU which can be solved by Proposition 1. The second part is to M RateGroup maximize MU;m , which depends on α, ξt , ξr , p, Qm , m

and M . To tackle this problem, we further assume that groups in the mmCell are independent of each other, and then we focus on only one group’s optimization problem. Given that the beam topology of a group is known as a priori information in this study (that is, α is known through BF training operations), when α is fixed, theoptimal transmit ∗ ting and receiving beamwidth are given by ξti = ξt min and k ∗ ξr = ξrk min , respectively. Then, the second part’s optimization problem (P2) can be formally stated as maximize RateGroup B · log2 (1 + SINRk ) (15a) MU;m = α,p,Q m

k ∈Um

subject to 0 ≤ |αi,k | ≤ π,

∀i ∈ Vm ,

(15b)

0 ≤ pi ≤ pm ax ,

∀i ∈ Vm ,

(15c)

1 < Qm ≤ Q,

0 < m ≤ M.

(15d)

This problem is generally nonconvex, and hence making it difficult to be optimally solved. As SINRk and consequently the objective function depend on α and Qm , we investigate beam scheduling properties of P2 in Section III-C, which enable us to propose two low complexity and easy to implement algorithms for nonor-beam interference coordination to suboptimally address P2. Note that optimal multibeam power allocation for P2 is left as future work. C. Nonor-Beam Interference Coordination Since the beam energy in mmWave networks is mainly concentrated in the main lobe, for SUE k in group m, PIk nonor is generally much larger than PIk inter . To avoid nonor-beam interference, MBS1 will generally serve the SUEs in group m in a time division manner (e.g., TDMA). However, this method is time consuming and has low efficiency. In this section, we aim to coordinate nonor-beam interference by beam scheduling to efficiently address P2. 1) Algorithm Description Suppose there are Y (Y > 0) transmission paths (including LOS path and reflection, i.e., NLOS paths) between vMBS i and SUE k, then after BF training operations, this vMBS–SUE pair can find Y T–R beam pairs that best match these paths. We regard the T–R beam pair that satisfies max {SINRk } as the best T–R Y

beam pair and the others as candidate beam pairs. Generally, for MU simultaneous transmissions in mmWave networks, each vMBS–SUE pair will give priority to the best T–R beam pair as its transmission beams without considering the nonor-beam interference. Consequently, when SUE k is a nongroup SUE, it can achieve a good QoS; otherwise, its achievable rate may

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Algorithm 1: Candidate Beam Selection for DBS Input: • beam topology of group m, i.e., αm ; • optimal beamwidths of the best T-R beam pair, i.e., (ξt )∗best and (ξr )∗best ; • optimal beamwidths of candidate beam pair c, i.e., (ξt )∗c and (ξr )∗c ; • path loss model for LOS and NLOS paths, i.e., LLOS and LNLOS ; • transmission power of the best and candidate beams of vMBS i, i.e., pi and pi;c ; 1: Initialize C sui = ∅ and Ysui = 0; 2: Calculate SINRLOS k ; 3: for each c ∈ C do 4: Calculate SINRNLOS k ;c ; 5: if c is a suitable candidate T-R beam pair then 6: Record c into C sui ; 7: Ysui = Ysui + 1; 8: end if 9: end for 10: if Ysui > 0 then SINRNLOS ; 11: Find copt that satisfies max k ;c

c ∈C sui

12: end if Output: the optimal suitable candidate T-R beam pair copt (if available)

be greatly degraded. In this case, we consider two effective nonor-beam interference coordination solutions. a) Dynamic beam switching: When Y > 1, a vMBS–SUE pair (here, the SUE belongs to a group) can switch its best T–R beam pair to a suitable candidate T–R beam pair to avoid severe nonor-beam interference. Here, it is assumed that the best T–R beam pair operates on the LOS, path and candidate beam pairs operate on the NLOS paths. Definition 3 (Suitable Candidate T–R Beam Pair): Let C be the set of candidate T–R beam pairs between vMBS i and SUE k, ξtc be the transmitting beamwidth of candidate beam s and V switch be the set of vMBSs that pair c (c ∈ C), V switch m m decide to switch their beams and that have switched their beams, respectively, a suitable candidate T–R beam pair is a candidate beam pair that satisfies the following constraints. 1) SINR should be above the given threshold, i.e., ≥ η. SINRNLOS k ;c 2) It should provide better performance than the best T–R beam pair that may be subject to nonor-beam interference, ≥ SINRLOS i.e., SINRNLOS k ;c k . 3) It should be orthogonal to other simultaneξ c +ξ tj

c,j ≥ t2 transmissions, i.e., θmain M M switch s V switch )∪( Vm )). ((V \i − m

ous

m =1

for

∀j ∈

m =1

As described in Algorithm 1, based on the status of group m and the information of T–R beam pairs between vMBS i and SUE k, we can find Ysui suitable candidate T–R beam pairs for this vMBS–SUE pair, where C sui (C sui ⊆ C) denotes the

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Algorithm 2: Static Beam Selection Input: • beam topology of group m, i.e., αm ; • optimal beamwidths, i.e., (ξt )∗best and (ξr )∗best ; • path loss model for LOS path, i.e., LLOS ; • transmission power of vMBS i, i.e., pi ; = ∅; 1: Initialize U select m 2: Select a reference SUE (e.g., SUE k) served by beam i and record it into U select m ; 3: Select the SUE served k by beam j which satisfies PI nonor;i,j and record it into min j ∈(Vm −V switch m )\i select Um ; do 4: for each SUE k ∈ U select m ; 5: Calculate SINRLOS

k 6: end for ≥ η ( for ∀ k ∈ U select 7: if SINRLOS m ) then k

8: Select the SUE served by beam x which satisfies k min max PI nonor;s,x select s∈V select x∈(Vm −V switch m m −V m ) select and record it into U m ; 9: Go back to step 4; 10: else 11: Remove the last selected SUE from U select m ; 12: end if Output: the selected SUE set U select m

set of these beam pairs. Moreover, to achieve the maximum switching performance, each vMBS–SUE pair should switch its T–R beam pair to the optimal suitable candidate T–R beam pair copt (copt ∈ C sui ). Note that the beam topology of group m need to be updated regularly for the next vMBS–SUE pair’s optimal candidate beam selection. That is, the information related to the vMBS–SUE pairs whose best T–R beam pairs have been switched should be eliminated. In addition, thanks to some SUEs’ beam switching, the nonor-beam interference of the other SUEs in the same group will be reduced accordingly. b) Static beam selection: With the updated beam topology of group m, we can further reduce the nonor-beam interference by selecting beams that can transmit simultaneously with tolerable nonor-beam interference among them, that is, selecting SUEs in group m as described in Algorithm 2. Here, the beams imply the best T–R beam pairs working on LOS paths. (U switch ⊆ Um ) be the set of SUEs who can Let U switch m m ) be the (U select ⊆ Um − U switch switch their beams; U select m m m select select switch set of selected SUEs; V m (V m ⊆ Vm − V m ) be the k set of vMBSs that serves U select m ; PI nonor;i,j be the nonor-beam interference between beam i and beam j. The main steps of Algorithm 2 can be outlined as follows. as a reference SUE and i) Select an SUE in Um − U switch m record it into U select . This reference SUE can be the initial m reference SUE in group m, but if the initial reference SUE has switched its best reception beam to the optimal candidate


beam, we should select SUE k served by beam i, which satisfies {PIknonor } as new reference SUE. min i∈(Vm −V switch m ) ii) Select another SUE that causes minimal nonor-beam interference for the selected SUE and record it into U select m . iii) Gradually increase the selected SUEs, i.e., repeat the procedure of ii), until ∃ SUE k ∈ U select m that SINRk < η. In other words, the last selected SUE should ensure that it will not cause severe nonor-beam interference with other selected SUEs. The intention of SBS is to make MBS1 serve as many SUEs as possible simultaneously with nonorthogonal beams, thus improving the performance of dense mmWave networks. Note that user/beam activation, which is based on maximal independent sets, aims to find the maximal independent (i.e., orthogonal) beam sets in the network, whereas the selected beams of SBS are nonindependent. 2) Complexity Analysis The computational complexity of Algorithm 1 consists of two parts: determining whether a candidate T–R beam pair is a suitable one and finding out C sui . Given N vMBSs in the mmCell, from Definition 3, the complexity of the suitable candidate T–R beam pair determination can be measured by the number of the third constraint operation(s), which is given by T11 (N ) = (N − 1) ∈ O (N ). Meanwhile, given K candidate T–R beam pairs between vMBS i and SUE k, the complexity for finding out C sui is evaluated by the number (c ∈ C) operation, which is given by of calculate SINRNLOS k ;c T12 (K) = K ∈ O (K). Thus, the complexity of Algorithm 1 is given by T1 (K, N ) = T12 (K) · T11 (N ) ∈ O (KN ). , and K2 Given Nm vMBSs in Vm , K1 SUEs in U switch m SUEs in U select m , where K1 = 0, 1, 2, ..., Nm − 1 and K2 = 1, 2, ..., Nm − K1 , for Algorithm 2, the computational complexity denoted by T2 (Nm ) can be measured by the number of calculate PIknonor;s,x operation, which outputs a new selected SUE of 3 . group m. We have T2 (Nm ) = (N m +2)·(N6 m +1)·N m ∈ O Nm D. MU Transmission Scheme According to the system model shown in Fig. 2 and the two solutions for the nonor-beam interference coordination offered above, we propose an improved MU simultaneous transmission scheme with multiple orthogonal and/or nonorthogonal beams in mmWave networks, as given in Scheme 1, where U ortho (U ortho ⊆ U ) is the set of SUEs served by orthogonal beams; U nonor (U nonor ⊆ U − U ortho ) is the set of SUEs served by nonorthogonal beams; Qortho and Qnonor are the number of SUEs in U ortho and U nonor , respectively; and Qselect m and Qswitch are the number of SUEs in U select and U switch , m m m respectively. When M > 0, MBS1 can address the optimization problem P2 by beam scheduling, which includes the following three cases. 1) Only DBS needs to be carried out, i.e., (Qm − 1) ≤ ≤ Qm . Qswitch m = 0. 2) Only SBS is available, i.e., Qswitch m 3) Both solutions are effective. Note that the first two cases are special cases of the third one. Assuming that the best T–R beam pair for each vMBS–SUE pair


operates on the LOS path, then RateGroup MU;m , by carrying out both DBS and SBS, can be expressed as (16) shown at the bottom of the page. To quantify the benefits of Scheme 1, we investigate the maximum RateGroup MU;m by carrying out DBS and SBS, respectively. Proposition 2: When M > 0, consider P2 with DBS, the maximum achievable rate RateGroup* MU - DBS;m is given by (17) at the bottom of the page. Proof: Since DBS can eliminate nonor-beam interference, we can optimize each link individually to solve P2 when they are operating with narrow beams, which is similar to the proof ∗ of Proposition 1. Then, we can obtain p∗i = pmax , ξti 1 best = i 2 ∗ k ∗ ∗ ξt c = ξt min , ξr 1 best = ξrk 1min , and ξrk 2 c = ξrk 2min . In addition, when Qswitch = Qm − 1, SUE k1 is the one in group m m who cannot switch its beam to others and should use its initial = Qm , we allow the SUE whose SNR best beam; when Qswitch m performance is the best in group m still use its initial best beam. Thus, we obtain the maximum achievable rate RateGroup* MU - DBS;m shown in (17). Proposition 3: When M > 0, consider P2 with SBS, the maximum achievable rate RateGroup* MU - SBS;m is given by RateGroup* , (18) log2 1 + SINRLOS∗ k MU - SBS;m = B ·

Scheme 1: Procedure for the proposed MU transmission scheme 1: Initialize U ortho = ∅, U nonor = ∅, Qortho = 0 and Qnonor = 0; 2: Count M ; 3: if M = 0 then 4: Qortho = Q and record these SUEs into U ortho ; 5: else M 6: Qortho = Q − Qm ; m =1

7: 8: 9: 10:

for group m = 1 to M do Carry out Algorithm 1 (i.e., DBS) for each SUE in group m and count Qswitch ; m = Q then if Qswitch m m Let SUE k served by vMBS i that satisfies max k ∈Um i ∗ ∗ p i ·G t , main ((ξ ti )best )·G kr , main ((ξ rk )best )· L 1 ( R ) LOS P N +P Ik i n t e r

11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21:

still work on its best T-R beam pair; Qortho = Qortho + Qm ; = Qm − 1 then else if Qswitch m Qortho = Qortho + Qm ; else ; Qortho = Qortho + Qswitch m Carry out Algorithm 2 (i.e., SBS), then Qnonor = Qnonor + Qselect m ; end if Record the corresponding SUEs in U ortho and U nonor , respectively; end for end if MBS1 serves U ortho with orthogonal beams and simultaneously serves U nonor with nonorthogonal beams; RateGroup MU - Both;m

=B·

where

SINRNLOS k 11

and

SINRLOS k 12

=

=

i 11

11 ξt pi 11 · Git,main

12 pi 12 · Git,main

k ∈U select m p ∗i ·G it , main (ξ t min )·G kr , main (ξ rk min )· L 1 ( R ) LOS where SINRLOS∗ = . k P N +P Ik ∗nonor Proof: Similarly, to minimize the interbeam interference, the ∗ optimal beamwidths of T–R beams should be ξti best = ξt min ∗ and ξrk best = ξrk min , respectively. The optimal power allocation problem is our future study. Additionally, from (6)–(8) and (10), we know that, when α is fixed and combine with (ξti )∗best , (ξrk )∗best , and p∗i , the nonor-beam interference 1 can be expressed as PIk ∗nonor = Gkr,main ((ξrk )∗best ) · L (R ) ·

log2 1 + SINRNLOS k 11

k 11 ∈U switch m

5683

k 11 · Gkr,main ξr 11 ·

PN + PIk 11inter k 12 ξti 12 · Gkr,main ξr 12 ·

+

k 12 ∈U select m 1 L NLOS (R )

1 L LOS (R )

PN + PIk 12inter + PIk 12nonor ⎛

LOS∗

⎝log2 1 + SNRk RateGroup* MU - DBS;m = B · 1

+

, log2 1 + SINRLOS k 12

.

(16)

⎞ ⎠, log2 1 + SNRNLOS∗ k 2 ;c

k 2 ∈U switch m \k 1

where and

SNRLOS∗ k1

SNRNLOS∗ k2

= =

1 (ξt pmax · Git,main

min )

k 1 ξr 1min · · Gkr,main

1 L LOS (R )

PN

pmax ·

2 ;c Git,main

(ξt

min )

k 2 ;c ξr 2min · · Gkr,main PN

1 L NLOS (R )

.

(17)

5684

j ∈V select m \i


p∗j · Gjt,main (αi,k , αj,k , (ξti )∗best , (ξtj )∗best ). Hence, we

have the maximum achievable rate RateGroup* MU - SBS;m as given in (18). To provide more insights into Scheme 1, we compare it with the time division (TD) scheme that implies that only one SUE in group m can be served at a time. Suppose the transmission time for each SUE in the TD scheme is distributed evenly within each time slot, the achievable rate RateTD;m is given as 1 · B · log2 (1 + SINRk ), (19) RateTD;m = Qm k ∈Um

p i ·G it , main (ξ ti )·G kr , main (ξ rk )· L 1 ( R ) LOS . To make the rewhere SINRk = P N +P Ik i n t e r sults more general, we can approximate (19) by RateTD;m = B · log2 1 + SINRk

SINRk = B · log2 1 + k ∈Um . (20) Qm ∗

Denoting SINRk , the critical value of average SINR of group m with the TD scheme for RateGroup MU;m = RateTD;m , which is given in Proposition 4, we know that the proposed Scheme 1 shows better performance than TD scheme when SINRk ≤ ∗ SINRk . Proposition 4: Let SINRk be the average SINR of group m and SINRLOS with the TD scheme, SINRNLOS k 11 k 12 be the SINR with DBS and SBS, respectively, the critical value of SINRk for RateGroup MU;m = RateTD;m is given by ∗ SINRk

k 11 ∈U switch m

=

1 + SINRNLOS k 11

k 12 ∈U select m

·

1+

SINRLOS k 12

− 1.

TABLE II SIMULATION PARAMETERS Parameters Carrier frequency, fc Transmitting power, p Transmission distance, R Operating bandwidth, B Attenuation value, A Path loss exponent, n Beamwidth, ξt , ξr The side lobe gain, z Noise figure, NF

Values 60 GHz 5 mW 15 m 1.5 GHz A LOS = 32.5; A NLOS = 45.5 n LOS = 2.0; n NLOS = 1.4 10°, 20°, 30° (for Tx, i.e., MBS); 30° (for Rx, i.e., SUEs) 0.1 6 dB

BF training operations between each vMBS–SUE pair, there is a best T–R beam pair that works on the LOS path and several candidate T–R beam pairs that work on NLOS paths; moreover, ξti = ξtj = ξt , pi = pj = p (i, j ∈ Vm ), and ξrk = ξru = ξr (k, u ∈ Um ). Table II summarizes the detailed simulation parameters. The path loss for LOS scenario is LLOS = 32.5 + 20 log10 (fc ) + 20 log10 (R) and that for NLOS scenario is LNLOS = 45.5 + 20 log10 (fc ) + 14 log10 (R) [8]. In addition, at a standard temperature of 17 ◦ C, the thermal noise level is PN [dB] = −174 [ dBm /Hz] + 10 log10 (B) + NF [dB], where NF is noise figure in dB. To analyze the intergroup interference and the intragroup interference (i.e., nonor-beam interference), we take the mmCell with two groups (i.e., M = 2) into account in our simulations. A. Inter-/Intragroup Interference

(21)

Proof: Combining (16) with (20), we obtain the critical value of SINRk shown in (21). Moreover, to further reduce the nonor-beam interference, MBS1 can be assisted by its nearby MBSs. For instance, if the nonor-beam interference of SUE1 (see Fig. 2) is severe and there are no suitable candidate T–R beam pairs between MBS1 and SUE1, SUE1 can be handed over to MBS2 for improving the achievable rates. However, as the handover process and redo BF training operations may take a long time, we consider adopting this method only when MBS1 cannot provide a good QoS for SUE1 in a long period of time. As this is beyond the scope of this work, we will not describe it in detail here. IV. PERFORMANCE EVALUATION In this section, we present simulation results on nonor-beam interference and achievable rate of 60 GHz WLANs. To simplify simulation, we assume that all SUEs are placed on the same horizontal plane above the ground, and MBS1 can be replaced with multiple vMBSs that are all located at the same position. Meanwhile, the transmission distance between MBS1 and each SUE is assumed to be the same [see Assumption (2) in Section II]. We further assume that, after

We consider the intergroup interference among group m1 and group m2 , as shown in Fig. 2. In this scenario, there are some SUEs (e.g., SUE5) that can not only be classified into group m1 but also be classified into group m2 . Suppose SUE5 is ultimately classified into group m2 , it will cause nonorbeam interference to the SUEs in group m1 (e.g., the reference SUE k) and the other (Qm 2 − 1) SUEs will cause interbeam interference. Here, both the nonor-beam interference and the interbeam interference can be interpreted as intergroup interference. In Fig. 5, we investigate the intergroup interference power PIk intergr of SUE k and the achievable rate of link that change i,j with Qm 2 and ξt . It shows that when θmain and ξt are fixed (e.g., i,j k θmain = 9° and ξt = 20°), PI intergr increases with the increase of Qm 2 and Rate decreases accordingly. From (8) and (10), we can see that when Qm 2 is fixed, PIk intergr with a larger ξt (e.g., ξt = 30°) is not necessarily bigger than that with a smaller ξt (e.g., ξt = 20°). Moreover, we consider the intragroup interference (e.g., in group m) that mainly refers to the nonor-beam interference in this simulation. From (6)–(8) and (10), we can see that the nonori,j , ξt , and Qm . The beam interference is mainly related to θmain k nonor-beam interference power PI nonor of SUE k that changes i,j with θmain and ξt is shown in Fig. 6, where transmit beam i (i.e., vMBS i) serves SUE k, and beam j denotes an interfering i,j beam. If ξt is fixed (e.g., ξt = 20°), when θmain
SINRk in this example. We observe that the rate performance of Scheme 1 with only DBS (i.e., in the first case) can reach the best because DBS can avoid severe nonor-beam interference among the Qm SUEs in group m. Since there is still nonor-beam interference (although tolerSUEs, the performance with DBS+SBS able) among the Qselect m (i.e., in the third case) is worse than that with only DBS. In the same cause, the worst performance of the three cases is that of the case with only SBS (i.e., in the second case). For the proposed scheme with DBS and/or SBS, an MBS can serve multiple SUEs simultaneously with multiple orthogonal and/or nonorthogonal beams to guarantee SUEs’ QoS. Although by adopting TD one can obtain better rate performance than that with SBS, it can serve only one SUE at a time in time domain.

V. CONCLUSION We have investigated the interference issue of MU simultaneous transmissions in mmWave networks, especially for the scenarios with densely distributed SUEs. In particular, the nonor-beam interference defined in this study can severely degrade achievable rates if not properly addressed. Then, we proposed two nonor-beam interference coordination solutions, that is, DBS and SBS, where DBS can avoid the nonor-beam interference by switching the interfered beam to the candidate one, and SBS can further reduce the nonor-beam interference by selecting simultaneous transmission beams. On this basis, an MU simultaneous transmission scheme in mmWave networks that supports multiple orthogonal and/or nonorthogonal beams


is introduced. The numerical results demonstrate that DBS and SBS are effective in addressing the nonor-beam interference issue and, moreover, they can maximize the achievable rate of the networks by beam scheduling. Furthermore, power allocation strategies for multiple orthogonal and/or nonorthogonal beams will also be our future work. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers and the editor for their valuable comments. REFERENCES [1] Z. Pi and F. Khan, “An introduction to millimeter-wave mobile broadband systems,” IEEE Commun. Mag., vol. 49, no. 6, pp. 101–107, Jun. 2011. [2] S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter-wave cellular wireless networks: Potentials and challenges,” Proc. IEEE, vol. 102, no. 3, pp. 366–385, Mar. 2014. [3] C. Park and T. S. Rappaport, “Short-range wireless communications for next-generation networks: UWB, 60 GHz millimeter-wave WPAN, and ZigBee,” IEEE Wireless Commun., vol. 14, no. 4, pp. 70–78, Aug. 2007. [4] C. J. Hansen, “WiGiG: Multi-gigabit wireless communications in the 60 GHz band,” IEEE Wireless Commun., vol. 18, no. 6, pp. 6–7, Dec. 2011. [5] Wireless Medium Access Control (MAC) and Physical Layer (PHY) Specifications for High Rate Wireless Personal Area Networks (WPANs) Amendment 2: Millimeter-Wave-Based Alternative Physical Layer Extension, IEEE 802.15.3c—Part 15.3, 2009. [6] WirelessHD specification overview, WirelessHD, Aug. 2009. [7] Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications Amendment 3: Enhancements for Very High Throughput in the 60 GHz Band, IEEE 802.11ad—Part 11, 2012. [8] A. Maltsev et al., “Channel models for 60 GHz WLAN systems,” IEEE 802.11-09/0334r8, May 2010. [9] “WiGig white paper: Defining the future of multi-gigabit wireless communications,” Wireless Gigabit Alliance, pp. 1–5, Jul. 2010. [10] H. Xu, V. Kukshya, and T. S. Rappaport, “Spatial and temporal characteristics of 60 GHz indoor channels,” IEEE J. Sel. Areas Commun., vol. 20, no. 3, pp. 620–630, Apr. 2002. [11] A. Maltsev et al., “Characteristics of indoor millimeter-wave channel at 60 GHz in application to perspective WLAN system,” in Proc. 4th Eur. Conf. Antennas Propag., Apr. 2010, pp. 1–5. [12] S. Collonge, G. Zaharia, and G. E. Zein, “Influence of the human activity on wide-band characteristics of the 60 GHz indoor radio channel,” IEEE Trans. Wireless Commun., vol. 3, no. 6, pp. 2396–2406, Nov. 2004. [13] G. Yang, J. Du, and M. Xiao, “Maximum throughput path selection with random blockage for indoor 60 GHz relay networks,” IEEE Trans. Commun., vol. 63, no. 10, pp. 3511–3524, Oct. 2015. [14] S. Hur, T. Kim, D. J. Love, J. V. Krogmeier, T. A. Thomas, and A. Ghosh, “Millimeter wave beamforming for wireless backhaul and access in small cell networks,” IEEE Trans. Commun., vol. 61, no. 10, pp. 4391–4403, Oct. 2013. [15] M. Marcus and B. Pattan, “Millimeter wave propagation: spectrum management implications,” IEEE Microwave Mag., vol. 6, no. 2, pp. 54–62, Jun. 2005. [16] S. Wyne, K. Haneda, S. Ranvier, F. Tufvesson, and A. F. Molisch, “Beamforming effects on measured mm-Wave channel characteristics,” IEEE Trans. Wireless Commun., vol. 10, no. 11, pp. 3553–3559, Nov. 2011. [17] W. Roh et al., “Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results,” IEEE Commun. Mag., vol. 52, no. 2, pp. 106–113, Feb. 2014. [18] L. Wei, R. Hu, Y. Qian, and G. Wu, “Key elements to enable millimeter wave communications for 5G wireless systems,” IEEE Wireless Commun., vol. 21, no. 6, pp. 136–143, Dec. 2014. [19] S. Han, C.-L. I, Z. Xu, and C. Rowell, “Large-scale antenna systems with hybrid analog and digital beamforming for millimeter wave 5G,” IEEE Commun. Mag., vol. 53, no. 1, pp. 186–194, Jan. 2015. [20] Y. P. Zhang and D. Liu, “Antenna-on-chip and antenna-in-package solutions to highly integrated millimeter-wave devices for wireless communications,” IEEE Trans. Antennas Propag., vol. 57, no. 10, pp. 2830–2841, Oct. 2009.

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Qing Xue received the B.E. degree in communication engineering from University of Jinan, Jinan, China, in 2007. She is currently working toward the Ph.D. degree in information and communication engineering at the Key Laboratory of Information Coding and Transmission, School of Information Science and Technology, Southwest Jiaotong University, Chengdu, China. Her research interests include radio resource management for mmWave wireless networks.

Xuming Fang (M’00–SM’16) received the B.E. degree in electrical engineering in 1984, the M.E. degree in computer engineering in 1989, and the Ph.D. degree in communication engineering in 1999, all from Southwest Jiaotong University, Chengdu, China. He was a Faculty Member with the Department of Electrical Engineering, Tongji University, Shanghai, China, in September 1984. He then joined the School of Information Science and Technology, Southwest Jiaotong University, where he has been a Professor since 2001, and the Chair of the Department of Communication Engineering since 2006. He held visiting positions with the Institute of Railway Technology, Technical University at Berlin, Berlin, Germany, in 1998 and 1999, and with the Center for Advanced Telecommunication Systems and Services, University of Texas at Dallas, Richardson, TX, USA, in 2000 and 2001. He has, to his credit, around 200 high-quality research papers in journals and conference publications. He has authored or coauthored five books or textbooks. His research interests include wireless broadband access control, radio resource management, multihop relay networks, and broadband wireless access for high-speed railway. Dr. Fang is the Chair of the IEEE Vehicular Technology Society of Chengdu Chapter, and an Editor of the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.

Ming Xiao (S’02–M’07–SM’12) received the Bachelor’s and Master’s degrees in engineering from the University of Electronic Science and Technology of China, Chengdu, China, in 1997 and 2002, respectively, and the Ph.D. degree in telecommunication theory from Chalmers University of Technology, G¨oteborg, Sweden, in November 2007. From 1997 to 1999, he was a Network and Software Engineer with China Telecom, Beijing, China. From 2000 to 2002, he also held a position in the SiChuan Communications Administration, Chengdu, China. Since November 2007, he has been with the School of Electrical Engineering, Royal Institute of Technology, Sweden, where he is currently an Associate Professor in communications theory. Dr. Xiao received Best Paper Awards at the International Conference on Wireless Communications and Signal Processing in 2010 and the IEEE International Conference on Computer Communication Networks in 2011. He also received the Chinese Government Award for Outstanding Self-Financed Students Studying Abroad in March 2007, the Hans Werthen Grant from the Royal Swedish Academy of Engineering Science in March 2006, and Ericsson Research Funding from Ericsson in 2010. Since 2012, he has been an Associate Editor for the IEEE TRANSACTIONS ON COMMUNICATIONS, the IEEE COMMUNICATIONS LETTERS (Senior Editor since January 2015), and the IEEE WIRELESS COMMUNICATIONS LETTERS. Li Yan received the B.E. degree in communication engineering from Southwest Jiaotong University, Chengdu, China. She is currently working toward the Ph.D. degree in communication and information systems at the Key Laboratory of Information Coding and Transmission, School of Information Science and Technology, Southwest Jiaotong University, Chengdu, China. Her research interests include handover, network architecture, and reliable wireless communication for high-speed railways.