Deep Learning-Based Beam Management and Interference...

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592 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 1, JANUARY 2019 Deep Learning-Based Beam Management and Interference Coordination in Dense mmWave Networks Pei Zhou , Xuming Fang , Senior Member, IEEE, Xianbin Wang , Fellow, IEEE, Yan Long, Member, IEEE, Rong He, and Xiao Han Abstract—Due to severe signal pathloss in millimeter wave (mmWave) band, beamforming enabled directional transmission is critical to overcome the attenuation challenge in future mmWave communication systems. Furthermore, in order to improve sig- nal coverage of mmWave networks, network densification has to be used at the same time. However, the concurrent use of direc- tional transmission and network densification will make the radio resource management (RRM) of dense mmWave network dramat- ically more complicated than that of microwave network. In order to maximize the sum-rate of the entire network, tedious and com- plex RRM algorithms are usually needed to obtain good results, which require high complexity of computation. To address this challenge, we proposed a deep learning-based beam management and interference coordination (BM-IC) method in dense mmWave network, through which the conventional complex BM-IC algo- rithm is transformed into a deep neural network (DNN)-based approximation. Because DNN only requires a series of simple cal- culations (e.g., some additions and multiplications), the complexity of computation is greatly reduced. Simulation results show that the proposed deep learning-based BM-IC approach can obtain comparable sum-rate to conventional BM-IC algorithm, but with much less computation time. Thus, deep learning could be a pow- erful tool to mitigate the complexity of RRM problems in dense mmWave networks. Index Terms—Millimeter wave (mmWave), wireless local area network (WLAN), deep learning, beam management, interference coordination. Manuscript received August 4, 2018; revised October 9, 2018 and Novem- ber 17, 2018; accepted November 19, 2018. Date of publication November 21, 2018; date of current version January 15, 2019. The work of P. Zhou, X. Fang, Y. Long, and R. He was supported in part by National Natural Sci- ence Foundation of China under Grants 61471303 and 61601380, in part by the NSFC Guangdong Joint Foundation under Grant U1501255, in part by the EP7-PEOPLE-2013-IRSES Project under Grant 612652, in part by the Huawei HIRP Flagship Project under Grant YB2015070106, and in part by Cultivation Program for the Excellent Doctoral Dissertation of Southwest Jiaotong Univer- sity. The work of X. Wang was supported in part by NSERC Discovery under Grant RGPIN-2018-06254. The review of this paper was coordinated by Prof. R. Dinis. (Corresponding author: Xuming Fang.) P. Zhou, X. Fang, Y. Long, and R. He are with the Key Lab of Information Cod- ing and Transmission, Southwest Jiaotong University, Chengdu 610031, China (e-mail:, [email protected]; [email protected]; yanlong@home. swjtu.edu.cn; [email protected]). X. Wang is with the Department of Electrical and Computer Engineering, University of Western Ontario, London, ON N6A 5B9, Canada (e-mail:,xianbin. [email protected]). X. Han is with the Wireless Technology Lab, 2012 Laboratories, Huawei 518129, China (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.2018.2882635 I. INTRODUCTION W ITH the increasing demand for ultra-high-speed wireless communications, microwave band (e.g., sub- 6 GHz) can no longer satisfy the future requirement due to its limited spectrum resources. As an alternative, millimeter wave (mmWave) band has rich spectrum resources which can support high data rate wireless transmissions [1]–[4]. MmWave com- munication is becoming one of the most prominent technologies in both the fifth-generation mobile communication systems (5G) and the next generation wireless local area networks (WLANs, e.g., IEEE 802.11ad and IEEE 802.11ay) [1], [2], [5]. However, mmWave band faces many challenges, such as severe pathloss, high oxygen absorption, and blockages [1], [2], [6]. Thanks to the short wavelength of mmWave, a large number of antennas can be deployed on a small size terminal and thus long distance and high quality mmWave communications can be realized by using antenna array technology [1], [2], [4], [5]. In addition, in order to improve the signal coverage and quality, network densification is often used [7]–[12]. However, the combined use of directional transmission and network densification will result in non-negligible interferences from other nodes, which means beam management and interference coordination (BM-IC) for future dense mmWave network could be very challenging [8], [9]. Most of the current WLANs adopt distributed network archi- tecture, which makes the radio resource management (RRM) very inefficient. Centralized network architecture is helpful to achieve more efficient RRM, because it can use global infor- mation to manage the base stations and users in a unified way [13]–[15]. As a recent development, there are some studies on centralized WLAN in order to achieve better RRM and system performance [13], [14], [16]–[18]. Dalvi et al. in [13] discussed various approaches proposed by Intel, Cisco and Meraki enter- prises for central management of WLAN. A centralized control architecture for dense WLAN access networks was proposed in [14], where the controller can coordinate the set of access points (APs) by collecting radio and network measurements and enforcing centralized configuration decisions. Similarly, Chen et al. studied the client association with quality-of-service (QoS) guarantees in high-density software-defined WLAN, and some features such as centralized association, global network state awareness, seamless handoff, and flow-level association were also considered [18]. However, these centralized WLAN ar- chitectures all work at low frequency band (e.g., 2.4 GHz and 5 GHz), and the links between controller and APs are wired in most of the studies. Recently, Facebook and Deutsche Telekom 0018-9545 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

Transcript of Deep Learning-Based Beam Management and Interference...

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592 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 1, JANUARY 2019

Deep Learning-Based Beam Management andInterference Coordination in Dense

mmWave NetworksPei Zhou , Xuming Fang , Senior Member, IEEE, Xianbin Wang , Fellow, IEEE, Yan Long, Member, IEEE,

Rong He, and Xiao Han

Abstract—Due to severe signal pathloss in millimeter wave(mmWave) band, beamforming enabled directional transmission iscritical to overcome the attenuation challenge in future mmWavecommunication systems. Furthermore, in order to improve sig-nal coverage of mmWave networks, network densification has tobe used at the same time. However, the concurrent use of direc-tional transmission and network densification will make the radioresource management (RRM) of dense mmWave network dramat-ically more complicated than that of microwave network. In orderto maximize the sum-rate of the entire network, tedious and com-plex RRM algorithms are usually needed to obtain good results,which require high complexity of computation. To address thischallenge, we proposed a deep learning-based beam managementand interference coordination (BM-IC) method in dense mmWavenetwork, through which the conventional complex BM-IC algo-rithm is transformed into a deep neural network (DNN)-basedapproximation. Because DNN only requires a series of simple cal-culations (e.g., some additions and multiplications), the complexityof computation is greatly reduced. Simulation results show thatthe proposed deep learning-based BM-IC approach can obtaincomparable sum-rate to conventional BM-IC algorithm, but withmuch less computation time. Thus, deep learning could be a pow-erful tool to mitigate the complexity of RRM problems in densemmWave networks.

Index Terms—Millimeter wave (mmWave), wireless local areanetwork (WLAN), deep learning, beam management, interferencecoordination.

Manuscript received August 4, 2018; revised October 9, 2018 and Novem-ber 17, 2018; accepted November 19, 2018. Date of publication November21, 2018; date of current version January 15, 2019. The work of P. Zhou,X. Fang, Y. Long, and R. He was supported in part by National Natural Sci-ence Foundation of China under Grants 61471303 and 61601380, in part bythe NSFC Guangdong Joint Foundation under Grant U1501255, in part by theEP7-PEOPLE-2013-IRSES Project under Grant 612652, in part by the HuaweiHIRP Flagship Project under Grant YB2015070106, and in part by CultivationProgram for the Excellent Doctoral Dissertation of Southwest Jiaotong Univer-sity. The work of X. Wang was supported in part by NSERC Discovery underGrant RGPIN-2018-06254. The review of this paper was coordinated by Prof.R. Dinis. (Corresponding author: Xuming Fang.)

P. Zhou, X. Fang, Y. Long, and R. He are with the Key Lab of Information Cod-ing and Transmission, Southwest Jiaotong University, Chengdu 610031, China(e-mail:, [email protected]; [email protected]; [email protected]; [email protected]).

X. Wang is with the Department of Electrical and Computer Engineering,University of Western Ontario, London, ON N6A 5B9, Canada (e-mail:,[email protected]).

X. Han is with the Wireless Technology Lab, 2012 Laboratories, Huawei518129, China (e-mail:,[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2018.2882635

I. INTRODUCTION

W ITH the increasing demand for ultra-high-speedwireless communications, microwave band (e.g., sub-

6 GHz) can no longer satisfy the future requirement due to itslimited spectrum resources. As an alternative, millimeter wave(mmWave) band has rich spectrum resources which can supporthigh data rate wireless transmissions [1]–[4]. MmWave com-munication is becoming one of the most prominent technologiesin both the fifth-generation mobile communication systems(5G) and the next generation wireless local area networks(WLANs, e.g., IEEE 802.11ad and IEEE 802.11ay) [1], [2], [5].However, mmWave band faces many challenges, such as severepathloss, high oxygen absorption, and blockages [1], [2], [6].Thanks to the short wavelength of mmWave, a large numberof antennas can be deployed on a small size terminal and thuslong distance and high quality mmWave communications canbe realized by using antenna array technology [1], [2], [4],[5]. In addition, in order to improve the signal coverage andquality, network densification is often used [7]–[12]. However,the combined use of directional transmission and networkdensification will result in non-negligible interferences fromother nodes, which means beam management and interferencecoordination (BM-IC) for future dense mmWave network couldbe very challenging [8], [9].

Most of the current WLANs adopt distributed network archi-tecture, which makes the radio resource management (RRM)very inefficient. Centralized network architecture is helpful toachieve more efficient RRM, because it can use global infor-mation to manage the base stations and users in a unified way[13]–[15]. As a recent development, there are some studies oncentralized WLAN in order to achieve better RRM and systemperformance [13], [14], [16]–[18]. Dalvi et al. in [13] discussedvarious approaches proposed by Intel, Cisco and Meraki enter-prises for central management of WLAN. A centralized controlarchitecture for dense WLAN access networks was proposedin [14], where the controller can coordinate the set of accesspoints (APs) by collecting radio and network measurements andenforcing centralized configuration decisions. Similarly, Chenet al. studied the client association with quality-of-service (QoS)guarantees in high-density software-defined WLAN, and somefeatures such as centralized association, global network stateawareness, seamless handoff, and flow-level association werealso considered [18]. However, these centralized WLAN ar-chitectures all work at low frequency band (e.g., 2.4 GHz and5 GHz), and the links between controller and APs are wired inmost of the studies. Recently, Facebook and Deutsche Telekom

0018-9545 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

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ZHOU et al.: DEEP LEARNING-BASED BEAM MANAGEMENT AND INTERFERENCE COORDINATION IN DENSE mm WAVE NETWORKS 593

proposed a “mmWave distribution network” use-case in theIEEE 802.11ay standard draft [19], [20], where a controller isused for managing and controlling multiple “distribution nodes”(DNs, also known as APs in IEEE 802.11ay) by directionallinks. And we also stated that the future WLANs will probablybe evolved to adopt cloud radio access network (C-RAN)-basedcentralized control in [21]. Therefore, efficient and smart algo-rithms can be designed to address resource management, beammanagement, interference management, and mobility manage-ment in WLANs.

Many mechanisms have been proposed for BM-IC in densemmWave networks. For example, Feng et al. in [9] proposed alarge-scale channel state information (CSI)-based interferencecoordination approach to solve the co-channel interference indense mmWave network. Liu et al. in [10] studied the power con-trol and transmission duration allocation for self-backhaulingdense mmWave cellular network. The considered problem wasformulated as a non-cooperative game and thus better perfor-mance can be obtained in terms of network sum-rate and energyefficiency. Also, Liu et al. in [11] proposed a game theory-based decentralized beam pair selection method in heteroge-neous multi-beam C-RANs that provides a better performancethan other beam pair selection methods in terms of sum-rate andconvergence speed. However, the mechanisms mentioned aboveusually require very complicated computations and large num-ber of iterations to find an optimized solution in real-time [22],which will increase the processing latency, power consumptionand system cost.

Recently, the use of machine learning or deep learning to op-timize wireless communication systems has attracted significantlevel of attention [22]–[32]. The deep neural network (DNN)-based machine learning can treat the states of network as inputdata, and then regard the output of complicated optimization al-gorithm as a label, so as to get a data driven DNN model throughsupervised learning. When the new data are fed into the DNNmodel, the corresponding predicted output(s) can be obtainedimmediately, because the computations in DNN only containseveral layers of simple operations such as matrix-vector multi-plications [22], [23]. Sun et al. in [22] and [23] proposed to useDNN to approximate the weighted minimum mean square er-ror (WMMSE) power allocation algorithm. Performance anal-ysis proved that DNN can achieve almost the same accuracyof WMMSE algorithm with less computation time. Similarly,Lee et al. in [28] proposed to use convolutional neural network(CNN) to perform transmit power control. The objectives ofits optimization problem include both spectrum efficiency (SE)and energy efficiency (EE). Simulation results also show thatthe CNN-based power control method can achieve almost thesame or even higher SE and EE than conventional power controlscheme with much less computation time. In addition, Lee et al.in [29] proposed a DNN-based approach to solve the linear sumassignment problem (LSAP). They decomposed LSAP into sev-eral sub-assignment problems and then designed several DNNsto solve them respectively. However, all the machine learningor deep learning-based methods above are focused on the op-timization of low frequency wireless communication systems.So far, studies on mmWave network by applying machine learn-ing methods are still very limited. Va et al. in [30] proposed alearning-to-rank approach to leverage a vehicle’s position alongwith past beam measurements to rank desirable pointing di-rections, thus the required beamforming training (BFT) to asmall set of pointing directions can be reduced. However, this

method requires the location information of vehicles throughGlobal Position System (GPS) or other positioning technolo-gies. Long et al. in [31] considered the beam selection as amulticlass-classification problem, and then they exploited thesupport vector machine (SVM) algorithm to obtain a statisticalclassification model which maximizes the sum-rate. The resultsrevealed that, with sufficient training data, the proposed methodcan achieve a near optimal sum-rate performance, while thecomplexity could be reduced by several orders of magnitude,compared to the conventional method.

Inspired by the studies above, this paper proposes to use deeplearning for performing BM-IC in dense mmWave WLAN withcentralized architecture. By using deep learning methods, thein-depth patterns hidden in the input data can be abstractedlayer by layer [32]. The main contributions of this paper canbe summarized as follows. Firstly, in order to improve the effi-ciency of BFT in dense mmWave WLAN network, we proposean efficient BFT mechanism to establish directional links basedon the BFT mechanism in IEEE 802.11ay [19], [21]. Secondly,we model the BM-IC in dense mmWave network as an opti-mization problem and design a BFT information aided BM-ICalgorithm to improve the sum-rate of the entire mmWave net-work by globally optimizing the beam directions, beamwidthsand transmit power allocations. Thirdly, we obtain the trainingdata from the proposed BFT information aided BM-IC algorithmso that we can get a data driven DNN model to approximate theproposed algorithm. Finally, we use the obtained DNN modelto perform BM-IC in dense mmWave network in real-time.Different from the existing deep learning-based wireless net-work optimization researches, our proposed deep learning-basedBM-IC method can optimize the beam directions, beamwidthsand transmit power of each beam, simultaneously.

The remainder of this paper is organized as follows. InSection II, we first introduce the centralized architecture ofdense mmWave network and propose an efficient BFT mecha-nism to reduce the BFT overhead, and then formulate the BM-IC in dense mmWave network as an optimization problem. InSection III, we design a BFT information aided BM-IC algo-rithm to solve the formulated optimization problem, and thenpropose a DNN-based BM-IC method to approximate the de-signed algorithm. Section IV shows the numerical results onboth the proposed efficient BFT mechanism and DNN-basedBM-IC method. Finally, Section V concludes this paper.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. Dense mmWave Network Architecture WithCentralized Control

Fig. 1 shows the dense mmWave network architecture adoptedin this paper. There are n slave APs (SAPs), one master AP(MAP) and s stations (STAs). We mark the set of n + 1 APsas N = {MAP, SAP 1, . . ., SAP i, . . ., SAP n} and the set ofs STAs as S = {STA 1, . . ., STA j, . . ., STA s}, respectively.We assume all the SAPs are within the MAP’s signal coverageand controlled by the MAP through directional links (i.e., thegreen beams in Fig. 1). Each STA selects one of the APs arounditself to perform channel access and data transmission throughdirectional link (i.e., the blue or gray beams in Fig. 1).

To facilitate the evaluation of sum-rate and interferencefor dense mmWave network, we adopt the commonly usedswitch-based analog beam pattern [33], [34]. The normalized

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594 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 1, JANUARY 2019

Fig. 1. Dense mmWave network architecture.

beamforming gain G is

G (α, ϑ) =

{2π−(2π−α)ε

α , if |ϑ| ≤ α2 ,

ε, otherwise,(1)

where α is the beamwidth of the mainlobe in radian, ϑ is thebeam offset angle to the mainlobe in radian, ε is the gain of thesidelobe and 0 < ε� 1.

For analytical tractability, we assume that the number ofbeams of AP and STA is limited, and each beam covers aunique direction in a non-overlapping way. Then, the maxi-mum number of beams of AP and STA could be bAP = � 2π

αAP�

and bSTA = � 2παSTA�, respectively, where αAP and αSTA are the

beamwidths of AP and STA, respectively.

B. Efficient Beamforming Training Mechanism for DensemmWave Network

As shown in Fig. 1, when an STA is covered by multipleAPs (e.g., STA c is covered by SAP i and SAP j), in orderto allow the STA to select a suitable AP (e.g., SAP j) amongall APs for connecting in terms of smaller interference, theSTA should perform BFT with its surrounding APs in advance.However, the BFT mechanism in IEEE 802.11ad/ay focuses onthe BFT between one AP and one STA or between one AP andmultiple STAs. If the BFT mechanism in IEEE 802.11ad/ayis directly applied into dense mmWave network, there will beserious collision problem when multiple APs begin to performBFT simultaneously [19], [21], [35], [36]. Otherwise, if all APsare forced to perform BFT one by one to avoid collision, theBFT will be inefficient in dense mmWave network. As shownin Fig. 2 and Fig. 3, according to the BFT in IEEE 802.11ad/aywe propose an efficient BFT mechanism to coordinate the BFTprocesses of every AP and STA so that many duplicated BFTprocesses can be merged. The details of our proposed efficientBFT mechanism are shown as below:

Fig. 2. Step 1: Beamforming training between MAP and SAPs.

Step 1: BFT between MAP and SAPs.1) MAP transmits directional multi-gigabit (DMG) Beacon

frames in all its beams to perform initiator sector sweep(ISS).

2) Each SAP selects a training slot (i.e., association beam-forming training slot in IEEE 802.11ad/ay) to perform re-sponder sector sweep (RSS) by transmitting sector sweep(SSW) frames in all beams (the training results of ISS arecontained in SSW frames).

3) MAP transmits SSW-Feedback frames (i.e., “FB” inFig. 2) to the SAPs who have finished RSS through thebest beams indicated in the training results of ISS. In ad-dition, the best beam of each SAP will be contained inSSW-Feedback frames.

Step 2: BFT between APs and STAs.1) Each AP transmits SSW frames in all beams to perform

BFT of the AP side. At this moment, all the STAs arestaying in quasi-omni listening mode.

2) Each STA selects a training slot (i.e., association beam-forming training slot in IEEE 802.11ad/ay) to performBFT of the STA side by transmitting SSW frames in allits beams (the training results of the AP side are containedin SSW frames). At this moment, all the APs are stayingin quasi-omni listening mode.

3) After receiving the SSW frames from STAs, each SAPwill transmit the training results to MAP through “SAPFB” frame. Thus, MAP can obtain the BFT informationof every STA.

4) MAP transmits the BFT information of every STA to SAPsthrough “MAP FB” frames.

5) At last, one SAP will be selected based on the BFT infor-mation to transmit a “FB” frame to each STA. The “FB”frame will inform the STA the best beams between itselfand its surrounding APs.

It is worth noting that, after finishing Step 1 and Step 2, onlythe transmit BFT of APs and STAs were performed, while thereceive BFT of APs and STAs did not [21], [35], [36]. Accordingto the reciprocity of directional beams in mmWave band, we canconclude that both transmit BFT and receive BFT are done in asimilar way [1], [36]. However, if receive BFT is needed, beamrefinement protocol (BRP) phase in IEEE 802.11ad/ay can beperformed by applying the similar modifications of Step 1 andStep 2. For more details (e.g., training processes and specificframe formats), please refer to [19], [21], [36].

We assume each AP performs BFT one by one to avoid thecollision, and the detailed BFT processes can refer to [19], [21],[36]. Since each AP and STA can generate bAP and bSTA beams,respectively, for the BFT mechanism in IEEE 802.11ad/ay, the

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ZHOU et al.: DEEP LEARNING-BASED BEAM MANAGEMENT AND INTERFERENCE COORDINATION IN DENSE mm WAVE NETWORKS 595

Fig. 3. Step 2: Beamforming training between APs and STAs.

total number of training frames should be

bad/ay = (bAP + n · bAP + n) + (bAP + s · bSTA + s) · (n + 1).(2)

While for our proposed efficient BFT mechanism, the totalnumber of training frames should be

bpro = (bAP + n · bAP + n) + bAP · (n + 1)

+ s · (bSTA + 2n + 1). (3)

Proof: The proof is provided in Appendix A. �Therefore, the total number of training frames saved by our

proposed efficient BFT mechanism is

bsave = bad/ay − bpro = s · n · (bSTA − 1) . (4)

Compared to the BFT mechanism in IEEE 802.11ad/ay, ourproposed efficient BFT mechanism can reduce BFT overhead.More importantly, the proposed BFT mechanism will be moreefficient when there are more APs and STAs in dense mmWavenetwork.

C. Problem Formulation

In dense mmWave network, if the beams between STA i andAP j are aligned, according to equation (1) we can obtain thedirectional transmit gain Gt

i,j and directional receive gain Gri,j

as

Gti,j =

2π − (2π − αti,j )ε

αti,j

, (5a)

Gri,j =

2π − (2π − αri,j )ε

αri,j

, (5b)

where αti,j is the beamwidth of the transmitter, αr

i,j is thebeamwidth of the receiver.

According to [37] and [38], the channel between STA i andAP j is given by

hi,j (τ) =C H∑ch=1

(ch)

Gti,j

(ch)Gr

i,j

(ch)χc

i,j δ

(τ − (ch)

τi,j

), (6)

where CH is the number of paths, the superscript “(ch)” stands

for the ch-th path.(ch)

Gti,j and

(ch)Gr

i,j , as shown in equation (5a) and

equation (5b), are the directional transmit gain and directional

receive gain of the ch-th path between STA i and AP j.(ch)χc

i,j is theamplitude of the ch-th path, and δ (·) is the Dirac delta function.(ch)τi,j is the propagation delay of the ch-th path,

(ch)τi,j =

(ch)di,j /c,

where(ch)di,j is the distance of the ch-th path between STA i and

AP j, and c is the speed of light.For analytical tractability, we assume the line-of-sight (LoS)

path (i.e., ch = 1) always exists [38], then the rest of the CH-1paths (i.e., ch = 2 to ch = CH) are non-line-of-sight (NLoS).As for the LoS path, the amplitude is given as the followingequation [38]

(1)χc

i,j =λ

4π(1)di,j

, (7)

where λ is the wavelength and λ = c/fc , fc is the carrier fre-

quency.(1)di,j is the distance of the LoS path between STA i and

AP j. As for the NLoS paths,(ch)χc

i,j includes both pathloss andreflection coefficients, and it can be given by [38]

(ch)χc

i,j =λ

4π(ch)di,j

REF∏ref =1

(ch)Γref , ch ∈ [2, CH], (8)

where(ch)Γref is the reflection coefficient of the ref -th reflection

for the ch-th path, and REF is the number of reflections of thepath. Since the reflection loss is very high in mmWave band [1],we only consider one reflection of a given path (i.e., REF =

1). Then,(ch)χc

i,j can be rewritten as

(ch)χc

i,j =λ

4π(ch)di,j

(ch)Γref , ch ∈ [2, CH]. (9)

Finally, according to [39], the channel gain can be derived by

(ch)Gc

i,j =

∣∣∣∣∣(ch)χc

i,j δ

(τ − (ch)

τi,j

)∣∣∣∣∣2

. (10)

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596 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 1, JANUARY 2019

Let the directional beam’s transmit power from AP j to STAi to be pt

i,j , then at STA i side, the received power from AP jcan be determined by

pri,j = pt

i,j

C H∑ch=1

(ch)

Gti,j

(ch)Gr

i,j

(ch)Gc

i,j . (11)

Similarly, the interference power received at STA i from otherAPs (e.g., AP b (b ∈ N\j)) and STAs (e.g., STA a (a ∈ S\i))should be

pIa,b→i,j = pt

a,b

C H∑ch=1

(ch)

Gta,b→i,j

(ch)Gr

a,b→i,j

(ch)Gc

i,b , (12)

where(ch)

Gta,b→i,j and

(ch)Gr

a,b→i,j are the directional transmit gainand directional receive gain from the ch-th path between STAa and AP b, respectively. According to equation (1), the di-rectional transmit-receive gain of each path can be derived byequation (13) shown at the bottom of this page, where ϑt

a,b→i,j

and ϑri,j→a,b are the beam offset angles from AP b’s (AP b trans-

mits to STA a) transmit beam direction to the position of STA iand from the STA i’s (STA i receives from AP j) receive beamdirection to the position of AP b, respectively.

We suppose that there is no multi-connectivity capability forSTAs, thus an STA can only connect to one AP at a time in densemmWave network. We set xi,j = {0, 1} as the binary associa-tion variable. If STA i (i ∈ S) is connected to AP j (j ∈ N),then xi,j = 1; otherwise xi,j = 0. When STA i connects to APj, according to equation (11) and equation (12) the signal-to-interference plus noise ratio (SINR) between AP j and STA ican be derived by

SINRi,j =xi,j p

ri,j∑

a∈S\i∑

b∈N\j xa,bpIa,b→i,j + W ·N0

, (14)

where W and N0 represent the bandwidth of mmWave band andthe background noise power spectrum density, respectively.

Then, the sum-rate of the entire mmWave network is

T =∑i∈S

∑j∈N

xi,jW log2 (1 + SINRi,j ). (15)

In order to maximize the sum-rate of the entire mmWave net-work, the BM-IC problem can be transformed into the following

optimization problem:

P1: maxX ,P ,A

∑i∈S

∑j∈N

xi,jW log2 (1 + SINRi,j )

s.t. C1 : xi,j = {0, 1} ,∀i ∈ S, j ∈ N,

C2 :∑j∈N

xi,j ≤ 1,∀i ∈ S,

C3 :∑i∈S

xi,j ≤ bAP,∀j ∈ N,

C4 :∑i∈S

xi,j pi,j ≤ Pmaxj ,∀j ∈ N,

C5 : αmin ≤ αi,j ≤ αmax ,∀i ∈ S, j ∈ N,

C6 :∑i∈S

xi,jαi,j ≤2π,∀j ∈ N, (16)

where X is a matrix with element xi,j , P is a matrix with el-ement pt

i,j and A is a matrix with element αi,j . Constraint C2ensures that each STA can only connect to one AP. ConstraintC3 indicates that the number of STAs an AP can serve is lessthan or equal to bAP. Constraint C4 is the power consumptionconstraint for each AP, which cannot exceed Pmax . ConstraintC5 stands for the beamwidth limited to [αmin , αmax]. ConstraintC6 means that for an AP, the sum of beamwidths used for serv-ing the connected STAs cannot exceed 2π, since the beams of anode are assumed to be non-overlapping in Section II-A. How-ever, the optimization problem P1 could not be solved directlybecause it is NP-hard and not convex. Accordingly, we designan algorithm to find a sub-optimal solution for problem P1 inSection III.

mmWave links could be easily influenced by obstacles suchas human beings, which will bring two kinds of problems: thefirst one is reflection, and thus NLoS paths might be found tocontinue the communications. The second one is blockage, thencommunications will be interrupted. In order to handle theseproblems, the channel model we adopted supports both multi-path effects and reflections. As for the blockage scenarios, theworking links between STAs and APs are interrupted. Redoingbeamforming training processes and finding other suitable linksare needed. Then, the STAs and APs can perform Step 2 ofSection II-B.

III. BEAM MANAGEMENT AND INTERFERENCE COORDINATION

IN DENSE MMWAVE NETWORK

In this section, we will first propose a BFT information aidedBM-IC algorithm to solve problem P1 so as to reduce the inter-ference and improve the sum-rate of dense mmWave network.After that, we will generate training data for our proposed deep

Gta,b→i,jG

ra,b→i,j =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

2π−(2π−αta , b )ε

αta , b

· 2π−(2π−αri , j )ε

αri , j

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2 and∣∣∣ϑr

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2 ,

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αta , b

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a,b→i,j

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2 and∣∣∣ϑr

i,j→a,b

∣∣∣ >αr

i , j

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αri , j

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a,b→i,j

∣∣∣ >αt

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2 and∣∣∣ϑr

i,j→a,b

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(13)

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learning-based BM-IC method by running the BFT informationaided BM-IC algorithm. The implementations of deep learning-based BM-IC method will be also introduced.

A. Beamforming Training Information Aided BeamManagement and Interference Coordination

Since the pathloss of mmWave band is serious and the trans-mit power is limited in practical scenarios, an STA may notreceive from all the APs in the network. That is to say, an STAcan only connect to its available surrounding APs. Each AP canget a candidate STA set based on the BFT results in Section II-B.Assume the candidate STA set of AP j (j ∈ N) is Sj (Sj ⊆S),then the directional link’s quality (SNRi,j ) between STA i(i ∈ Sj ) and AP j should be greater than a predefined thresholdSNRpre [19], [36]. Therefore, problem P1 can be rewritten as

P2: maxX ,P ,A

∑j∈N

∑i∈Sj

xi,jW log2 (1 + SINRi,j )

s.t. C1 : xi,j = {0, 1} ,∀i ∈ Sj , j ∈ N,

C2 :∑j∈N

xi,j ≤ 1,∀i ∈ S,

C3 :∑i∈Sj

xi,j ≤ bAP,∀j ∈ N,

C4 :∑i∈Sj

xi,j pi,j ≤ Pmaxj ,∀j ∈ N,

C5 : αmin ≤ αi,j ≤ αmax ,∀i ∈ Sj , j ∈ N,

C6 :∑i∈Sj

xi,jαi,j ≤2π,∀j ∈ N. (17)

It is noteworthy that MAP can obtain all the signal-noise-ratio (SNR) values (i.e., SNRi,j (i ∈ Sj , j ∈ N)) when BFTis done [19], [36]. For the sake of simplicity of analysis, westore all the SNR values into Z = {z1, . . . ,zk , . . . ,zK } in de-scending order. Then, there is a one-to-one match betweenelements zk (k = 1, 2, . . . ,K) and SNRi,j (i ∈ Sj , j ∈ N),where K =

∑j∈NCard(Sj ), Card (·) stands for the number

of elements in a set. Since there are Card(Sj ) candidate STAsfor AP j, there will be Card(Sj ) SNR values for AP j whenBFT is done. For all the APs in N, there will be

∑j∈NCard(Sj )

SNR values in total. In addition, the number of elements in X,P and A is also

∑j∈NCard(Sj ).

Since problem P2 is also NP-hard and not convex, it cannotbe solved directly neither. We propose an algorithm that candecompose problem P2 into three sub-problems to find the sub-optimal solution, i.e.:

1) initialize P and A to obtain the optimized X∗;2) use the optimized X∗ and initialized P to get the optimized

A∗;3) use the optimized X∗ and A∗ to find the optimized P∗.Our proposed algorithm is shown in Algorithm 1. To obtain

the optimized X∗, we first initialize P and A by average powerallocation (i.e., pt

j,init = Pmaxj /bAP) and maximum beamwidth

(i.e., αi,j = αmax ), respectively. After that, we initialize X =0 and select the AP and STA pair corresponding to z1, thencalculate the sum-rate T1 and set x1 to 1. And then, we selectthe AP and STA pair corresponding to z2 and calculate the sum-rate T2. If T2 > T1, set x2 to 1; otherwise set x2 to 0. By repeating

Algorithm 1: Beamforming Training Information AidedSolution for P2.

1: Initialize X = {0}, A = {αmax}, P = {Pmax/bAP};2: get the SNRi,j (i ∈ Sj , j ∈ N) values from BFT

stage;3: store the SNRi,j values into Z = {z1, . . . ,zk , . . . ,zK }

in descending order, zk ← SNRi,j , where K =∑

j∈N

Card(Sj );4: k = 1, compute Tk , set xk = 1;

Repeat5: k = k + 1, compute Tk ;6: if Tk > Tk+17: set xk = 1;8: else set xk = 0;

Until k = K;9: obtain X∗ ← {x1, . . . , xk , . . . , xK };

10: get the SINRi,j (i ∈ Sj , j ∈ N) values by adoptingX∗ and P;

11: store the SINRi,j values into Z(1) = {z1, . . . , zq , . . . ,zQ} in descending order, zq ← SINRi,j , where Q =∑

xk ∈X∗xk ;12: q = 1, compute Tq , set αq = αmin ;Repeat13: q = q + 1;14: decrease αq ;15: compute Tq ;16: if Tq > Tq−1

17: if αq > αmin

18: go to step 14;19: else go to step 13;20: else go to step 13;Until q = Q;21: obtain A∗ ← {α1, . . . , αq , . . . , αQ};22: obtain P∗ by applying X∗ and A∗ into WMMSE

algorithm;23: output X∗, P∗ and A∗.

the above steps, we select the AP and STA pair correspondingto zk , and calculate the sum-rate Tk . If Tk > Tk−1, set xk to1; otherwise set xk to 0, until all the xk are set. Therefore, wecan get the optimized X∗ after mapping xk to xi,j . Since X∗indicates which AP each STA should connect to, that is to say,the beam directions are determined. At this stage, we can usethe optimized X∗ and average power allocation P to obtain A∗.Then, start from the directional link with the highest SINR valuedetermined by X∗ and decrease the beamwidth from αmax . Ifthe sum-rate increases, continue decreasing beamwidth until itreaches αmin ; otherwise optimize the beamwidth of link withthe second highest SINR value. Repeating the above steps untilall the αk are optimized. We can get A∗ after mapping αk toαi,j . Then, the optimized P∗ can be obtained by applying X∗and A∗ into power allocation (i.e., WMMSE) algorithm [22],[23], [40]. Finally, we can obtain X∗, A∗ and P∗.

Note that in Algorithm 1 K is greater than Q, which meansthat the number of elements in A∗ is not equal to that of X∗.We fill A∗ with 0 when xi,j = 0 so as to make the number ofelements in A∗ equal to that of X∗. Similarly, the number ofelements in P∗ should be equal to that of X∗. We can also fillP∗ with 0 when xi,j = 0. Therefore, X∗, A∗ and P∗ all havethe same number of elements (i.e., K).

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Fig. 4. The DNN structure used for approximating the proposed BM-ICalgorithm.

B. Deep Learning Based Beam Management andInterference Coordination

According to Theorem 1 of [22] we can know that, a multi-layer neural network can be used to approximate the behaviorof a given iterative algorithm (i.e., Algorithm 1) for solving thenon-convex optimization problem P2. Thus, we design a DNN tosolve the BM-IC in dense mmWave network. The preparationsof our proposed DNN method are provided in DNN Structureand Data Generation, then the analysis methodology and op-timization process are shown in Training Process. Finally, thetesting method and results are provided in Testing Process andSection IV-B, respectively.

1) DNN Structure: In [29], a linear sum assignment problemis decomposed into several sub-assignment problems, andeach of them can be solved effectively with DNNs. Thismotivates us to develop a DNN which contains three parts forapproximating Algorithm 1. As shown in Fig. 4, the upperpart is used for obtaining X∗, the middle part is used forobtaining A∗, and the lower part is used for obtaining P∗. Ourproposed method uses a fully connected neural network withone input layer, three hidden layers and one output layer. Theinput of the three parts is the value of {SNRi,j} obtainedfrom the BFT in Section II-B, thus the size of the input layeris s · (n + 1). We assume the size of each hidden layer is lh .The outputs of the upper part, the middle part and the lowerpart are binary association matrix XDNN, beamwidth matrixADNN and power allocation matrix PDNN, respectively. Then,the size of the output layer is 3

∑j∈NCard(Sj ). Therefore,

the computational complexity of our proposed DNN isO(s · (n + 1) · lh + lh · lh + lh · lh + lh · 3

∑j∈NCard(Sj )).

Since s · (n + 1) and∑

j∈NCard(Sj ) are constant values inthe actual communication scenario, and they are both less thanlh in our proposed DNN structure, thus the computationalcomplexity will be O(l2

h).

Similar to [22], [23], [28], we choose rectified linear unit(ReLU) as the activation function for the hidden layers of thethree parts, because ReLU can improve the training efficiencyby mapping negative values to zero and keeping positive values[32]. In order to reach the constraint that each STA can onlyconnect to one AP, we have to limit xk to either 0 or 1. Thus,we use min(max(0, x), 1) as the activation function for the out-put layer of the upper part. In order to limit the beamwidth to[αmin , αmax], we adopt min(max(αmin , x), αmax) as the acti-vation function for the output layer of the middle part. Similarly,pk has the constraint that satisfies 0 ≤ pk ≤ Pmax , we can usemin(max(0, x), Pmax) as the activation function for the outputlayer of the lower part.

2) Data Generation: For analytical and computationaltractability, we let the n + 1 APs uniformly distributed in the net-work and fix the distance between any two adjacent APs. Then,we assume the s STAs randomly and uniformly distributed inthe network. The value SNRi,j between STA i (i ∈ S) and APj (j ∈ N) can be obtained by

SNRi,j =pr

i,j

W ·N0. (18)

Since we considered the scenario that STAs are static in ourcurrent work, the effect of channel coherence time and beamcoherence time (defined as the average time that the beam staysaligned) to our method can be ignored. The scenario that STAswith high mobility is left as our future work. Similar to [22],[23], [28], [29], we treat the entire {SNRi,j} as the inputs ofAlgorithm 1, then we can obtain the optimized {xk}, {αk} and{pk} from the outputs of Algorithm 1. After repeating the abovesteps for enough times, we can obtain three training sets (TΔ , T�and T∇) which correspond to the three parts of DNN in Fig. 4.The input-output pair ({SNRi,j}, {xk}) in TΔ can be usedto train the upper part of DNN. The middle part of DNN canbe trained by the input-output pair ({SNRi,j}, {αk}) in T�.Similarly, the input-output pair ({SNRi,j}, {pk}) in T∇ can beused to train the lower part of DNN. Also, the correspondingtesting sets (VΔ , V� and V∇) can be obtained by the samemethod. Generally, the data points of testing set are significantlyless than those in the training set.

3) Training Process: We use the training set TΔ to train theupper part of DNN; the cost function is the root-mean-squareerror between the output (X∗) of Algorithm 1 and the output ofthe upper part of DNN (XDNN),

LΔ =√‖X* −XDNN‖2, (19)

when training the middle part of DNN with training set T�, thecost function is the root-mean-square error between the output(A∗) of Algorithm 1 and the output of the middle part of DNN(ADNN),

L� =√‖A* −ADNN‖2, (20)

Similarly, we can use training set T∇ to train the lower part ofDNN. The cost function is the root-mean-square error betweenthe output (P∗) of Algorithm 1 and the output of the lower partof DNN (PDNN),

L∇ =√‖P* −PDNN‖2. (21)

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Similar to [22] and [23], the optimization scheme used by theDNN is root-mean-square prop (RMSprop) algorithm, whichcan accelerate the learning processes [41]. Its main idea is di-viding the gradient by a running average of its recent magnitude[41]. In addition, we choose the decay rate to be 0.9 and selecta proper learning rate by cross-validation.

4) Testing Process: We use the testing sets (VΔ , V� and V∇)generated in the Data Generation stage to evaluate the perfor-mance of the proposed DNN-based BM-IC method. Firstly, weapply the inputs of the testing set into Algorithm 1 to get thecorresponding outputs {x∗k}, {α∗k} and {p∗k}. Secondly, we cal-culate the sum-rate T * of the entire network based on {x∗k},{α∗k} and {p∗k}. Then, we calculate the sum-rate T DNN of theentire network based on the outputs of the testing set. Finally,we compare T * and T DNN.

IV. NUMERICAL RESULTS

A. The Performance of Efficient BeamformingTraining Mechanism

We regard the total number of training frames as the overheadof BFT. In order to evaluate the impact of the number of STAsand APs on the overhead of BFT, we assume the beamwidth ofAPs and STAs (i.e., αAP and αSTA) is 10◦. Then, the number ofAPs ranges from 1 to 10, and the number of STAs ranges from1 to 100. The overhead of BFT in IEEE 802.11ad/ay is shownin Fig. 5(a). We can see that, as the number of APs and STAsgrows, the overhead of BFT grows significantly. The overhead ofour proposed efficient BFT mechanism is depicted in Fig. 5(b).With the increasing number of APs and STAs, the overhead ofour proposed efficient BFT mechanism is much less than thatof the BFT in IEEE 802.11ad/ay. In addition, comparing thetwo sub-figures in Fig. 5, we can see that the larger the numberof APs and STAs is, the more obvious the advantage of theproposed efficient BFT mechanism will be. When the numberof APs and STAs is 10 and 100, respectively, the BFT overheadof the proposed efficient BFT mechanism is about 16% of theBFT in IEEE 802.11ad/ay.

In order to evaluate the impact of beamwidth (or the numberof beams) on the overhead of BFT, we fix the number of APs andSTAs to 10 and 100, respectively. The beamwidths of APs andSTAs are selected from {10◦, 20◦, 30◦, 45◦, 60◦ }, respectively.Fig. 6 shows the performance comparison between the BFT inIEEE 802.11ad/ay and our proposed efficient BFT mechanismwith respect to different beamwidths. For analytical tractability,we assume the beamwidth of APs is equal to the beamwidthof STAs (i.e., αAP = αSTA). We can see from Fig. 6 that, ourproposed efficient BFT mechanism needs fewer training framesthan those of the BFT in IEEE 802.11ad/ay. Furthermore, withnarrower beamwidth, our proposed efficient BFT mechanismwill be superior to the BFT in IEEE 802.11ad/ay. When thebeamwidth is 10◦, the result in Fig. 5 is the same as Fig. 6:the overhead of the proposed efficient BFT mechanism is about16% of the BFT in IEEE 802.11ad/ay. Even if the beamwidthequals to 60◦, the overhead of our proposed efficient BFT isabout 36% of the BFT in IEEE 802.11ad/ay. Therefore, fromFig. 5 and Fig. 6 we can conclude that the proposed efficientBFT mechanism can reduce the overhead of BFT significantlyin dense mmWave network.

Fig. 5. The performance comparison between the BFT in IEEE 802.11ad/ayand our proposed efficient BFT mechanism with different number of APs andSTAs.

Fig. 6. The performance comparison between the BFT in IEEE 802.11ad/ayand our proposed efficient BFT mechanism with different beamwidths.

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Fig. 7. The mmWave network topologies used for simulation.

Fig. 8. Learning rate selection.

B. The Performance of Deep Learning Based BeamManagement and Interference Coordination

The proposed DNN-based BM-IC method is implemented inPython 3.5.2 with TensorFlow 0.12.0. We set the number ofhidden layers to 3 and the neurons of the first layer to 500,the second layer and the third layer all have 300 neurons. Weconsider the following four scenarios as shown in Fig. 7:

a) there are 3 APs with 6 and 12 STAs, respectively;b) there are 7 APs with 14 and 28 STAs, respectively.The distance between any two adjacent APs is set to 100 m,

and all the STAs are randomly and uniformly distributed inthe mmWave network. Firstly, we generate 20000 training datapoints to train the DNN. Next, we generate 5000 testing datapoints to evaluate the performance of obtained DNN model withdifferent seeds. As shown in Fig. 8, for the sake of complex-ity/performance tradeoff, we have made several attempts withdifferent learning rates to find a proper one by cross-validation.Then, the initial learning rate is set to 0.001 since it can achieve afaster convergence rate with lower validation error. Meanwhile,we choose to gradually decrease the learning rate when the vali-dation error does not decrease. The other simulation parametersare listed in Table I. Without loss of generality, similar resultscan also be obtained with other reasonable simulation param-

TABLE ISIMULATION PARAMETERS

Fig. 9. The performance comparison among different BM-IC methods withrespect to different mmWave network scenarios.

eters. For the sake of simplicity, we limit the beamwidths thatcan be adjusted in Algorithm 1 to {10◦, 20◦, 30◦} (i.e., αmin =10◦, αmax = 30◦). In addition to evaluating the performance ofDNN-based BM-IC, we also propose another two alternativesas a comparison:

1) SNR maximization-based association between STA andAP (i.e., Max-SNR in Fig. 9);

2) random association between STA and AP (i.e., Randomin Fig. 9).

As can be seen from Fig. 9, the sum-rate ratio of DNN-based BM-IC is higher than that of the BM-IC with SNRmaximization-based association and random association. Sur-prisingly, when the number of APs and STAs is 3 and 6, respec-tively, the sum-rate ratio of DNN-based BM-IC can achieveabout 97% of Algorithm 1’s. When there are 3 APs with 12STAs, which means the mmWave network becomes denser, thesum-rate ratio of DNN-based BM-IC can reach about 90% ofAlgorithm 1’s. When there are 7 APs with 14 STAs, whichmeans the mmWave network becomes larger, the sum-rate

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Fig. 10. The computation time ratio (compared to Algorithm 1) required byDNN in different mmWave network scenarios.

ratio of DNN-based BM-IC can be about 88% of Algorithm1’s. Even if there are 7 APs with 28 STAs, the sum-rate ratioof DNN-based BM-IC can still achieve about 77% of Algo-rithm 1’s. For the SNR maximization-based BM-IC, the sum-rate ratio can just achieve about 78% of Algorithm 1’s in sparsescenarios, for example, there are 3 APs with 6 STAs and thereare 7 APs with 14 STAs. However, in dense mmWave networkscenarios, the sum-rate ratio decreases obviously, for example,the sum-rate ratio turns to 60% of Algorithm 1’s when there are3 APs with 12 STAs. What’s worse, when there are 7 APs with28 STAs, the sum-rate ratio decays to 45% of Algorithm 1’s.This is because the denser the mmWave network is, the more se-rious the interference will be. SNR maximization-based BM-ICignores the inter-beam interference during communication, thusthe sum-rate of the entire mmWave network is reduced. Fig. 9also shows that the performance of random association-basedBM-IC is always the worst. The sum-rate ratios achieved in allthe four scenarios are below 50%. The reason lies on the factthat random association-based BM-IC neither guarantees higherthroughput of itself, nor ensures less interference to other STAsand APs. Thus, its performance will be the worst.

The superiority of DNN-based BIMC is that, oncethe DNN model is trained, it can achieve comparableperformance to that of the traditional BM-IC algorithm(e.g., Algorithm 1) with much less computation time.The computation time ratios of DNN-based BIMC method(i.e., computationtimeof DN N−basedBIM C method

computationtimeof Algorithm1 ) in the fourmmWave network scenarios are shown in Fig. 10. It is obviousthat the computation time ratios of DNN-based BIMC methodare lower than 7% when compared to Algorithm 1. When thenumber of STAs and APs is small, for example, there are 3 APswith 6 STAs, the computation time ratio of DNN-based BIMCmethod is about 6.8% of Algorithm 1’s. Jointly taking the resultsin Fig. 9 into account, we can conclude that DNN-based BM-ICmethod can achieve about 97% of the sum-rate with 6.8% of thecomputation time. There is a fact that, when there are a largenumber of APs and STAs, the computation time of Algorithm 1will increase significantly. Although the time to train the DNNwill also increase with the increasing number of STAs and APs,once the DNN model is trained, the time required for DNNto perform BM-IC will not significantly increase, because the

calculations in DNN are relatively simple and fast [22], [23],[28]. Therefore, when the number of APs and STAs increases,the computation time ratio of DNN will decrease. For example,when there are 3 APs with 12 STAs, or there are 7 APs with 14or 28 STAs, the computation time ratio reduces to 2% ∼ 4%.

Jointly taking the results of Fig. 9 and Fig. 10 into account,we can know that DNN-based BM-IC can achieve considerablesum-rate with relatively less computing time. The traditionalBI-MC algorithm needs too many complicated computationsand iterations, making it challenging for practical applications.For the DNN-based BM-IC method, however, an accurate DNNmodel can be obtained through offline training to approximatethe traditional BI-MC mechanism. Therefore, a considerablesum-rate can be obtained online with much less computationtime. This is very important for performance promotion in densemmWave network.

V. CONCLUSIONS

Due to the directional transmission and dense network de-ployment, complexity of BM-IC in mmWave communicationsystems becomes a serious challenge. By leveraging deeplearning techniques, this paper proposes a DNN-based BM-IC method to reduce the interference and improve the sum-rateof dense mmWave network. We first propose an efficient BFTmechanism to establish the directional links between MAP andSAPs as well as between APs and STAs. Simulation resultsverified the high efficiency of our proposed BFT mechanism.Secondly, we formulate the BI-MC in dense mmWave networkas an optimization problem, and then we design a BFT informa-tion aided algorithm to generate the training data for DNN-basedBM-IC method. In addition, the proposed algorithm is also re-garded as the baseline for evaluating the performance of DNN-based BI-MC method. Finally, the simulation results show thefeasibility and advantage of DNN-based BI-MC method. Thisstudy shows that DNN-based BM-IC can achieve considerablesum-rate with relatively less computing time in dense mmWavenetwork, which greatly reduces the overhead for computationability in actual applications.

APPENDIX APROOF OF EQUATION (2) AND (3)

Assume the number of beams of AP and STA can generate isbAP and bSTA, respectively. According to [19], [21], [36], whenMAP performs BFT with the n SAPs, for both the BFT in IEEE82.11ad/ay and our proposed efficient BFT mechanism, the pro-cesses are the same. That is, MAP should transmit bAP trainingframes in its bAP beams to complete ISS phase. While in RSSphase, each of the n SAPs should transmit bAP training frames.Then, MAP should transmit n “FB” frames to the n SAPs.Therefore, for both the BFT in IEEE 802.11ad/ay and our pro-posed efficient BFT mechanism, there are (bAP + n · bAP + n)training frames required for completing Step 1 in Section II-B.

For Step 2 in Section II-B, we assume each AP performsBFT one by one with STAs to avoid the collision problem whenadopting the BFT in IEEE 802.11ad/ay. Similar to the processesin Step 1, there are (bAP + s · bSTA + s) training frames requiredfor an AP. Then the other n APs will repeat the above processes,so the total number of training frames required for the BFT inIEEE 802.11ad/ay when completing all the BFT processes isbad/ay = (bAP + n · bAP + n) + (bAP + s · bSTA + s) · (n + 1).

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602 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 68, NO. 1, JANUARY 2019

However, for Step 2 in our proposed efficient BFT mech-anism, each of the n + 1 APs should transmit bAP trainingframes one by one to complete ISS phase. For RSS phase,each of the s STAs should transmit bSTA training frames one byone. Then, the n SAPs should transmit n “SAP FB” frames toMAP. Soon afterwards, MAP transmits n “MAP FB” framesto the n SAPs. Finally, the selected SAP (based on the SNRmaximization) will transmit “FB” frames to STAs. There-fore, the s STAs require s · (bSTA + 2n + 1) training framesto complete RSS phase in total. Therefore, the total numberof training frames required for our proposed efficient BFTmechanism when completing all the BFT processes is bpro =(bAP + n · bAP + n) + bAP · (n + 1) + s · (bSTA + 2n + 1). �

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Pei Zhou received the B.E. degree in communi-cation engineering from Southwest Jiaotong Uni-versity, Chengdu, China, in 2015. He is currentlyworking toward the Ph.D. degree with the KeyLaboratory of Information Coding and Transmis-sion, School of Information Science and Technol-ogy, Southwest Jiaotong University, Chengdu, China.His research interests include radio resource man-agement for mmWave wireless networks, machinelearning, etc.

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 thePh.D. degree in communication engineering in1999 from Southwest Jiaotong University, Chengdu,China. He was a Faculty Member with the Depart-ment of Electrical Engineering, Tongji University,Shanghai, China, in September 1984. He then joinedthe School of Information Science and Technology,Southwest Jiaotong University, Chengdu, where hehas been a Professor since 2001, and the Chair of the

Department of Communication Engineering since 2006. He held visiting posi-tions with the Institute of Railway Technology, Technical University at Berlin,Berlin, Germany, in 1998 and 1999, and with the Center for Advanced Telecom-munication Systems and Services, University of Texas at Dallas, Richardson,TX, USA, in 2000 and 2001. He has, to his credit, around 200 high-qualityresearch papers in journals and conference publications. He has authored orcoauthored five books or textbooks. His research interests include wirelessbroadband access control, radio resource management, multihop relay networks,and broadband wireless access for high speed railway. He is the Chair of theIEEE Vehicular Technology Society of Chengdu Chapter, and an Editor of theIEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.

Xianbin Wang (S’98–M’99–SM’06–F’17) receivedthe Ph.D. degree in electrical and computer en-gineering from National University of Singapore,Singapore, in 2001. He is currently a Professor andthe Tier-I Canada Research Chair at Western Uni-versity, London, ON, Canada. Prior to joining West-ern, he was with Communications Research CentreCanada as a Research Scientist/Senior Research Sci-entist between July 2002 and December 2007. FromJanuary 2001 to July 2002, he was a System Designerat STMicroelectronics. His current research interests

include 5G technologies, Internet-of-Things, communications security, machinelearning, and locationing technologies. He has more than 350 peer-reviewedjournal and conference papers, in addition to 29 granted and pending patentsand several standard contributions.

Dr. Wang is a Fellow of Canadian Academy of Engineering and an IEEE Dis-tinguished Lecturer. He has received many awards and recognitions, includingCanada Research Chair, CRC President’s Excellence Award, Canadian FederalGovernment Public Service Award, Ontario Early Researcher Award, and sixIEEE Best Paper Awards. He currently serves as an Editor/Associate Editorfor the IEEE TRANSACTIONS ON COMMUNICATIONS, the IEEE TRANSACTIONS

ON BROADCASTING, and the IEEE TRANSACTIONS ON VEHICULAR TECHNOL-OGY. He was also an Associate Editor for IEEE TRANSACTIONS ON WIRELESS

COMMUNICATIONS between 2007 and 2011, and the IEEE WIRELESS COMMU-NICATIONS LETTERS between 2011 and 2016. He was involved in many IEEEconferences including GLOBECOM, ICC, VTC, PIMRC, WCNC, and CWIT,in different roles such as Symposium Chair, Tutorial Instructor, Track Chair,Session Chair, and TPC Co-Chair.

Yan Long (M’16) received the B.E. degree in elec-trical and information engineering in 2009, and thePh.D. degree in communication and information sys-tems from Xidian University, Xi’an, China, in 2015.From September 2011 to March 2013, she was a visit-ing student in the Department of Electrical and Com-puter Engineering, University of Florida, Gainesville,FL, USA. She is currently a Lecturer with the Schoolof Information Science and Technology, SouthwestJiaotong University, Chengdu, China. Her researchinterests include millimeter wave wireless communi-

cations, internet of things, 5G cellular networks, cognitive radio networks, andwireless resource optimization.

Rong He received the B.E. degree in automationcontrol in 1997, the M.E. degree in communicationinformation engineering and control in 2002, andthe Ph.D. degree in computer application technol-ogy from Southwest Jiaotong University, Chengdu,China, in 2011. She joined the School of InformationScience and Technology, Southwest Jiaotong Univer-sity, in 1997, where she has been an Associate Pro-fessor since 2009. She held visiting position with theDepartment of Electrical and Computer Engineering,University of Waterloo, ON, Canada, from 2014 to

2015. She has published more than 30 research papers in journals and confer-ences. Her research interests include wireless broadband access control, radioresource management, next generation Wi-Fi.

Xiao Han received the B.E. degree in electrical en-gineering from Sichuan University, Chengdu, China,in 2008, the Ph.D. degree in communication engi-neering from Zhejiang University, Hangzhou, China,in 2013. He was a Postdoctoral Research Fellowwith the National University of Singapore, Singapore,from 2013 to 2014. He then joined Huawei Technolo-gies, Shenzhen, where he has been a Senior ResearchEngineer since 2014. His research interests includewireless channel access, radio resource management,MAC layer of IEEE 802.11.