Multimedia Content Delivery inMillimeter Wave Home Networks

Bojiang Ma, Student Member, IEEE, Hamed Shah-Mansouri Member, IEEE,and Vincent W.S. Wong, Fellow, IEEE

Abstract—Millimeter wave (mm-wave) communication is apromising technology for short range communications and highspeed services. It provides potential solutions for multimediacontent delivery in home networks. However, approaches forresource allocation in traditional wireless networks may not be ef-ficient for multimedia data transmissions in mm-wave networks.This is due to the very wide bandwidth and highly directionaltransmissions, which bring challenges as well as opportunities tothe resource allocation of mm-wave transmissions. In this paper,we first characterize different usage scenarios of multimediacontent delivery by introducing a set of utility functions. We thenformulate a joint power and channel allocation problem based ona network utility maximization framework, which captures thespatial and frequency reuse of mm-wave communications. Theformulated problem is a non-convex mixed integer programming(MIP) problem. We reformulate the problem into a convex MIPproblem and propose a resource allocation algorithm basedon outer approximation (OA) method. We further develop anefficient heuristic algorithm which has a lower complexity thanthe OA based algorithm. Simulation results present the tradeoffsbetween the OA based and heuristic algorithms for differentscenarios and show that our proposed algorithms substantiallyoutperform recently proposed schemes in the literature.

Index Terms—millimeter wave technology, smart home net-works, spatial and spectrum reuse.

I. INTRODUCTION

Home networks, which facilitate communications amongdevices inside a home, can improve the quality of life of theresidents [1]. With the popularity of devices such as smarthigh-definition television (HDTV), tablets, and smartphones,multimedia content delivery has been a major source of datatraffic in home networks. However, the number of devices andtheir traffic demand are increasing. It is important to improvethe spectrum efficiency to better utilize the limited spectrumresources and meet the quality of service (QoS) requirement atthe same time. The recently developed millimeter wave (mm-wave) band technology shows the potential to provide highdata rate transmissions as well as high spectrum efficiency [2],[3]. The mm-wave technology can provide over 1 Gbps datarate for short range communication [4], which is promising

Manuscript received on Sept. 19, 2015; revised on Jan. 5, 2016; andaccepted Mar. 13, 2016. This work was supported by the Natural Sciencesand Engineering Research Council (NSERC) of Canada. The review of thispaper was coordinated by Prof. Walid Saad.

Part of this paper was presented at the IEEE Global CommunicationsConference (Globecom14), Austin, TX, Dec. 2014.

B. Ma, H. Shah-Mansouri, and V. W. S. Wong are with the Departmentof Electrical and Computer Engineering, the University of British Columbia,Vancouver, BC, Canada, V6T 1Z4, e-mail: {bojiangm, hshahmansour, vin-centw}@ece.ubc.ca.

for multimedia content delivery [5], [6]. Since the mm-wavesystems utilize directional transmissions [7], they result insmall interfering ranges and can provide a good opportunityfor spectrum reuse in smart home networks.

IEEE released the 802.15.3c [8] and 802.11ad [9] standards1

for the wireless personal area network (WPAN) and wire-less local area network (WLAN) based on mm-wave bandtechnology. Both standards aim to enhance the throughputin the 60 GHz band. The applications include the supportof wireless uncompressed video streaming, super broadbandInternet access, and wireless office space in smart homes[10]. 802.15.3c and 802.11ad standards have similar mediumaccess control (MAC) protocols. They have signalling pe-riod for control purpose, transmission coordination period forscheduling decision announcement, and data transfer interval.They use carrier sense multiple access with collision avoidance(CSMA/CA) for the contention-based access periods and timedivision multiple access (TDMA) for the reservation-basedaccess periods. The IEEE 802.11ay [11], [12] study group isformed in 2015 to extend IEEE 802.11ad and further improvethe throughput and different usage scenarios of mm-wavenetworks. However, the standardization process is still ongoing and stable documents are yet to be released.

Spectrum sharing and scheduling are important issues inresource allocation for mm-wave wireless networks. TDMA,frequency division multiple access (FDMA), and space divi-sion multiple access (SDMA) are three different multi-useraccess methods that schedule users with the shared resources.TDMA and FDMA eliminate interference among users byallocating non-overlapping resources. SDMA improves thesystem throughput by considering spatial reuse under interfer-ence control. TDMA has been used as the scheduling schemefor several industrial standards [8], [9], [13]. It can preventco-channel interference and is simple to be implemented.However, TDMA does not fully exploit the spatial reuseand results in a low spectrum efficiency. Meanwhile, mm-wave technology adopts directional antennas which providea significant opportunity to further utilize FDMA and SDMA.Considering the features of mm-wave, an integrated scheme,which employs SDMA together with FDMA and TDMA, cancombine the benefits of each scheme and improve the spectrumefficiency.

1The IEEE 802.11ac which works on 5 GHz frequency band is also a goodchoice to satisfy the current demand of home networks. It can be regarded asan extension of 802.11a/g in terms of the MAC in 5 GHz band. In this paper,we focus on the mm-wave based home networks which can further satisfythe usage requirements in future home networks.

There are several studies which investigate the wirelessresource allocation problem in home networks. Wu et al.in [5] summarized the challenges of mm-wave multimediacommunication in home networks and developed a QoS-awaremultimedia scheduling scheme which achieves a balancebetween users’ satisfaction and computational complexity.Yiakoumis et al. in [14] proposed a home network slicingcontrol mechanism, which allows different service providersto deploy services using a shared infrastructure. They alsopresented a method to customize the slices for high-qualityservices. A resource reservation-based backoff mechanism isproposed in [15], which reuses time slots for transmission inbackoff cycles to improve QoS for video delivery in homenetworks. In [16], Li et al. designed a distributed powercontrol scheme with different radio access technologies, whichaims to maximize the aggregate data rate of home networks.Sundaresan et al. in [17] developed a detection algorithmto locate the throughput bottlenecks in home networks. Ituses timing and buffer information to accurately detect thebottlenecks in both cable and wireless links. Li et al. in [18]proposed a new rate adaptation scheme to reduce the latencyfor delay-sensitive applications in home networks.

Meanwhile, spatial reuse has been considered for mm-wavetechnology in several studies. Park et al. in [19] investigatedthe potentials for spatial reuse and interference managementin mm-wave wireless networks and developed a simulationmodel to evaluate the spatial reuse performance. In [20], Chenet al. proposed a spatial reuse strategy for mm-wave WPANswith different directional antennas based on beamforminginformation. A scalable heuristic STDMA scheduling (SHSS)algorithm, which allows concurrent transmissions in the sametime slot, is proposed in [21] to enhance the throughput ofmm-wave based networks. In [22], Singh et al. investigatedinterference management for mm-wave mesh networks, andproposed an analytical framework to estimate the impactof antenna pattern and density of concurrent links on theMAC protocol. Qiao et al. in [23] formulated an optimizationproblem to maximize the aggregate throughput of indoormm-wave networks by considering concurrent beamforming.They proposed an iterative beam searching algorithm, whichincreases the throughput and improves the energy efficiencyof the system. Athanasiou et al. in [24] considered multi-user SDMA in client association problem and proposed anassociation algorithm based on subgradient methods.

Special characteristics of mm-wave communications (e.g.,directional transmission via beamforming, low multiuser in-terference) have been utilized to improve various performancemetrics. From the perspective of mm-wave local area net-works, in [25], Shokri-Ghadikolaei et al. investigated theimportant challenges of MAC design in short range mm-wave networks. They showed that collision-aware MAC canimprove the efficiency of mm-wave networks. In [26], Son etal. developed a directional MAC protocol to allow concurrenttransmissions to exploit spatial reuse in mm-wave WPANs.Kim et al. in [27] considered the video transmission in asport stadium using mm-wave technology and formulated arelay selection and coding rate adaption problem to maxi-mize the video quality. From the perspective of mm-wave

cellular networks, Zheng et al. in [28] studied the challengesand protocols in 5G mm-wave based cellular system. Theirsimulation results show the potential of achieving a very highcapacity in the future mm-wave cellular systems. In [29], DiRenzo introduced a novel analysis framework using stochasticgeometry for mm-wave cellular networks. The analysis andsimulation showed that the noise-limited approximation isaccurate for typical cellular network densities.

D2D communication based on mm-wave technology is anemerging topic and has great potentials in future mm-wavehome networks. Niu et al. in [30] proposed a schedulingscheme for D2D transmissions to exploit spatial reuse inmm-wave heterogeneous cellular systems. In [31], Qiao etal. proposed a TDMA-based MAC structure and a resourcesharing scheme for D2D communications in mm-wave basednetworks. Rehman et al. in [32] proposed a scheduling al-gorithm for mm-wave D2D networks using vertex coloringapproach. Their method improved the aggregate throughputby scheduling the conflicting flows with different priority.Besides, the measurement results for mm-wave home networksare provided in [33]–[36].

Millimeter wave based technology is being regarded asa promising candidate for multimedia content delivery inhome networks in the foreseeable future. However, the studiesfor multimedia transmission using mm-wave is limited. Theexisting resource allocation schemes in mm-wave networksdo not capture the characteristics of various applications inmm-wave multimedia home networks. Although optimizationframework has frequently been used to tackle the resourceallocation problem for indoor wireless networks, there areseveral differences for the scheduling and power allocationproblem using mm-wave. First, the propagation features ofmm-wave transmission, such as high attenuation and sensi-tivity to blockage, makes it possible to utilize spatial reuseto further improve the spectrum efficiency. Second, the mul-tiuser interference in directional communication in mm-wavetransmission is substantially less than that in omnidirectionalsystems. Third, the characteristics of mm-wave create thespecific constraints for the resource allocation, such as possiblechannel bonding. Moreover, the existing works do not fullyexploit the diversity of frequency division, which can furtherimprove the energy efficiency and channel utilization.

It is essential to design a novel scheduling mechanism tobetter utilize the special features of mm-wave communications(such as wide bandwidth, directional communication, smallinterfering range), and satisfy the new requirements for varioustypes of multimedia content delivery (such as high data ratefor uncompressed HD video transmission and flexible data ratefor file downloading). It is also important to consider energyefficiency for growing number of battery-powered portabledevices in home networks.

In this paper, we study the scheduling and power allocationproblem in the emerging smart home networks based on mm-wave technology. We adopt directional antennas for practicalmm-wave communications. We consider potential concurrenttransmissions in the network, which deliver various typesof multimedia content (e.g., uncompressed video). The maincontributions of this paper are as follows:

• We introduce utility functions to characterize differentusage scenarios and types of multimedia services in thesmart home networks.

• We propose a novel integrated TDMA/FDMA/SDMAscheduling scheme that allows concurrent transmissionsusing directional antenna for mm-wave home networkto fully exploit the potential of spatial reuse and furtherincrease the spectrum efficiency.

• We formulate a channel and power allocation problem,which considers QoS and energy efficiency requirementsof users, and maximizes the aggregate network utility.The formulated problem is a non-convex mixed integerprogramming (MIP) problem. We reformulate the non-convex problem into a convex MIP problem and designan algorithm based on the outer approximation (OA)method to obtain the optimal solution of the reformulatedproblem. We further propose a heuristic algorithm, whichhas a lower computational complexity than the OA basedalgorithm.

• Through extensive numerical studies, we evaluate theperformance of our proposed algorithms in terms ofaggregate utility and throughput for different home net-works. We further compare both proposed algorithmswith recently proposed scheduling algorithms [21] and[32]. Results show a substantial improvement in termsof aggregate throughput and utility compared with theproposed algorithms in [21] and [32].

The key differences between our work and [21] are asfollows. In [21], the authors aimed to improve the systemthroughput. In this paper, we formulate a utility maximizationproblem to better characterize different application scenariosof multimedia content delivery in mm-wave networks. Fur-thermore, we consider the minimum data rate requirementand energy efficiency as the practical constraints in our for-mulation. The authors in [21] proposed a heuristic STDMAscheduling scheme, while we introduce an OA method to ob-tain the solution of the resource allocation problem. We furtherpropose a greedy algorithm which has a lower complexity thanthe OA method. Results show that both of our algorithmsoutperform the one proposed in [21]. More importantly, weintroduce channelization and possible channel bonding of 60GHz bands to bring another dimension to further improve thespectrum efficiency of the mm-wave systems.

We extend the work in [37] from several aspects. In [37],we studied the resource allocation problem for multimediacontent delivery using omni-directional mm-wave communi-cation without spatial reuse. In this paper, we improve thespatial reuse by allowing concurrent transmissions in the samechannel. We further consider more practical directional anten-nas for mm-wave communication instead of omni-directionalantennas. We utilize the small interfering range feature of di-rectional mm-wave communications and design an integratedscheduling scheme, which significantly improves the spectrumefficiency. We design a new algorithm based on the OAmethod, which has a lower computational complexity than thegeneralized Benders decomposition method used in [37]. Wealso propose a heuristic algorithm which is computationally

Fig. 1. An example of a smart home wireless network. Solid arrowsrepresent the multimedia content delivery links. Dashed lines illustrate thecontrol message exchange links. The access point also acts as a coordinatorto schedule the transmissions among the device pairs.

less complex than the OA method.The rest of this paper is organized as follows: In Section

II, we present the system model. We formulate the resourceallocation problem in Section III, and propose a schedulingalgorithm in Section IV. We develop a low complexity heuris-tic algorithm in Section V. Simulation results are presentedin Section VI. Conclusions are given in Section VII. The keynotations and variables used in this paper are listed in TableI.

II. SYSTEM MODEL

We consider a smart home network as shown in Fig. 1.The network devices are equipped with mm-wave technology.The list of devices includes smart HDTV, TV set-top box,laptops, HD projector, and wireless display. The devices arecoordinated by the access point via the control links. Themultimedia content is delivered via the data links. Each datalink consists a transmitting device and a receiving device. Wedenote the set of data links by Q, where each data link servesa different pair of users. We assume the multimedia contents,such as videos for wireless display and files to be shared, areavailable at the transmitting devices. Short control messagesneed to be exchanged between the access point and devices forresource allocation purpose. Note that the network setting issimilar to the IEEE 802.15.3c and 802.11ad standards, whichonly allow one radio frequency (RF) chain between a pair oftransmitter and receiver. If multiple RF chains are required formultimedia content sharing, the spatial gain can be limited bythe number of RF chains that one device can create.

A. Channel Model

We consider the mm-wave transmissions operate in thefrequency band from 57 GHz to 64 GHz. This band is usedin 802.15.3c [8], 802.11ad [9], and 802.11ay [11]. There arethree channels in this frequency range according to the mm-wave band channelization. Each channel has a bandwidth of2160 MHz. The channel model at the 60 GHz band is quitedifferent from that for 2.4 or 5 GHz bands. One important dif-ference is that the 60 GHz communication requires directionalantenna. We adopt the wireless channel model in the 60 GHz

TABLE ILIST OF KEY NOTATIONS AND VARIABLES USED IN THIS PAPER

Symbols MeaningB Bandwidth of each channelC Set of available channelsG0 Antenna gain of a pair of communicating devicesGi,j Antenna gain between transmitter i and receiver jht,ci,j Channel gain between transmitter i and receiver j

in time slot t on channel cImaxi Estimated maximum interference received by

receiver iIt,ci Interference received by receiver i in time slot t

on channel cLslot Length of each time slotLsp Length of scheduling periodLa Length of alignment periodLb Length of beacon periodLc Length of control periodN0 Background noise powerpt,ci Transmission power at transmitter i in time slot t

on channel cpmax Maximum transmission powerp Power allocation vectorQ Set of data linksV Set of data links with battery-powered transmitting

devicesZ Set of data links with minimum data rate

requirementri Effective throughput of link iri Effective throughput of link i when interference is

limited to Imaxi

rmini Minimum data rate requirement for link i

S1, S2, S3 Usage scenariosT Set of time slotsUi Utility of user iUi Utility of user i when interference is limited

to Imaxi

xt,ci Time slot and channel allocation variable for linki in time slot t on channel c

x Time slot and channel allocation vectorη Efficiency of transceiverξ Threshold of energy efficiencyΘ3dB Beam-level beam widthΨst Sector-level beam width for transmitterΨsr Sector-level beam width for receiver

indoor situation [35], which is proposed specifically for mm-wave communication. Each transmitting antenna distributesthe power in the main lobe and several side lobes. In this paper,we consider the large scale channel characterizations. Specif-ically, we consider the impact of blockage and reflectionsfor both line-of-sight (LOS) and non-line-of-sight (NLOS)cases. If the LOS is blocked, we consider possible NLOScommunications. This is because the first order reflection inmm-wave networks can be significant [38] and makes NLOScommunication possible. The shadowing and multipath effectscaused by blockage and reflections of mm-wave signals areincluded in the channel model [35, pp. 7] [36, pp. 141]. Inthe mm-wave channel model, the channel gain between thetransmitter of link i and receiver of link j (i, j ∈ Q) isrepresented as hi,j = 1

PL(di,j) , where di,j is the distancebetween the corresponding transmitter and receiver. The path

loss is given by [35]

PL(d)[dB]

=

ALOS + 10nLOS log10 ( ddbp

) +XσLOS

+ 20 log10

(4πfcdbp

s

), if LOS exists,

ANLOS + 10nNLOS log10 ( ddbp

) +XσNLOS

+ 20 log10

(4πfcdbp

s

), if LOS is blocked,

(1)where ALOS and ANLOS are the attenuation in LOS and NLOSsignals, nLOS and nNLOS are the path loss exponents, and XσLOS

and XσNLOS are zero-mean Gaussian random variables withstandard deviation σLOS and σNLOS that model the shadowingeffects of LOS and NLOS environments, respectively. Inaddition, fc is the carrier frequency, dbp is the referencedistance, and s is the speed of light. Channel estimation helpsto determine the aforementioned parameters. It is performedperiodically by the transmitter and receiver via transmittingand analyzing orthogonal pilot sequences [39].

In mm-wave technology, directional antenna is used toimprove the antenna gain. A directional transmitting antennamodel is proposed in [40]. In this model, the transmittingantenna achieves a high gain in the main lobe and an averagedlow gain in the side lobes. The antenna gain in differentdirections is given as follows [40]:

Gtx(Θtx)

=

{Gtx

0 10−1.204(Θtx/Θ3dB)2 , if 0◦ ≤ Θtx < Θml/2,

Gtxsl , if Θml/2 ≤ Θtx ≤ 180◦,

(2)where Gtx

0 and Gtxsl represent the maximum transmitting an-

tenna gain and the average side lobe gain, respectively. Thetransmitting angle is denoted as Θtx. Θ3dB is the angle ofthe half-power beam width, and Θml is the angle of themain lobe. In addition, Gtx

0 = 100.9602−2 ln sin(Θ3dB/2), Gtxsl =

10−0.04111 ln Θ3dB−1.0597, and Θml = 2.6Θ3dB.We consider the network devices are equipped with di-

rectional receiving antennas where the antenna models arethe same as transmitting ones. The receiving antenna gain isdenoted by Grx(Θrx). The receiving angle is denoted as Θrx,which is the angle between the line from the signal source tothe receiving antenna and the pointing direction of the antenna.The antenna gain for directional receiving antenna is given asfollows:

Grx(Θrx)

=

{Grx

0 10−1.204(Θrx/Θ3dB)2 , if 0◦ ≤ Θrx < Θrr/2,

Grxsl , if Θrr/2 ≤ Θrx ≤ 180◦,

(3)where Grx

0 and Grxsl represent the maximum receiving gain and

the average side lobe gain, respectively, and Θrr is the angleof receiving range.

In Fig. 2, we show the transmission pattern using direc-tional transmitting and receiving antennas. The directionalbeams of transmitters and receivers are shown by the oval-like shapes. Different grids represent the communication indifferent frequency bands. The antenna gain of each pair ofcommunicating devices is denoted by G0 = Gtx(0)Grx(0). We

Fig. 2. An example of transmission pattern using directional transmitting andreceiving antennas. The antenna patterns illustrate gains in different directions.The obstacles have different sizes and are located randomly. Frequency band1 is allocated to link m to avoid possible interference with links i and j.Frequency band 2 is allocated to links i and j to improve spatial reuse.

denote the angle between lines from transmitter j to receiversi and j by Θtx

j,i. Similarly, we denote the angle betweenlines from receiver i to transmitters j and i by Θrx

j,i. Theantenna gain between transmitter j and receiver i is denotedas Gj,i = Gtx(Θtx

j,i)Grx(Θrx

j,i).

B. Integrated TDMA/FDMA/SDMA Scheduling for SmartHome Networks

In home networks, the access point also acts as the co-ordinator (similar to the piconet coordinator in WPAN andpersonal basic service set central point in WLAN). We proposean integrated scheduling scheme based on a scheduling periodstructure. Each scheduling period begins with a beacon periodfor network synchronization. It is followed by the controlmessage exchanging period. During this period, transmitterscan send the transmission request messages and the coor-dinator broadcasts the scheduling decision. The remainingtime of the scheduling period is the data transfer interval.The multimedia content delivery usually has different QoSrequirements. Therefore, QoS-constrained multimedia contentis usually scheduled in the contention-free periods according tothe standards. We assume all multimedia content is transferredusing the reservation-based time slots in the data transfer in-terval. Each time slot starts with an alignment period, followedby the data transmission period. In both IEEE 802.15.3c and802.11ad standards, TDMA is used during the reservation-based period, which only allows one transmission pair in atime slot. To further explore the spectral reuse for mm-wavetechnology, we allow co-channel concurrent transmissions inthe same time slot using SDMA. To meet the QoS require-ments of different services, such as wireless display or videogaming, the reservation-based period is centrally scheduled bythe coordinator for each transmission pair.

In Fig. 3, we illustrate the structure of a scheduling periodwith the proposed integrated TDMA/FDMA/SDMA scheme.The scheduling period consists of the beacon, control, and datatransfer interval. We use Lb, Lc, Lslot, and Lsp to denote thelength of the beacon period, control period, time slot, and thescheduling period, respectively. In each time slot, we use La to

Fig. 3. Structure of the proposed integrated TDMA/FDMA/SDMA schedul-ing scheme for mm-wave home networks.

represent the duration of the alignment period. According tothe standard [9, pp. 300], during the alignment period in datatransfer interval, the beamforming refinement protocol (BRP)is executed for the alignment. Exhaustive search is used tofind the refined beams. We define the sector-level beam widthfor the transmitter and receiver as Ψst and Ψsr, respectively.We also denote the time required to transmit pilot sequencesas Tp. The overhead of the alignment can be modeled as La =

d Ψst

Θ3dBedΨsr

Θ3dBeTp [41], where d·e is the ceiling function. Note

that the beam-level beam width is Θ3dB.In the data transfer interval, each device is allocated differ-

ent channel and time slot. Different from WPAN/WLAN spec-ifications 802.15.3c and 802.11ad, we allow different devicesto occupy the same frequency band within the same time slot(e.g., users u1 and u4 in the first time slot and first frequencyband) based on SDMA. FDMA is also integrated in schedulingmechanism by dividing the whole frequency band into threeseparate channels according to [8]. By integrating FDMA,more flexibility is provided for the scheduling mechanism toimprove the channel utilization.

The coordinator is responsible for allocating the resourceblocks to all links to optimize the network performance.We denote T as the set of time slots, and C as the set ofavailable mm-wave frequency bands. We further denote pt,ciand ht,ci,i as the transmission power at the transmitting deviceof link i and the corresponding channel gain of the link onchannel c ∈ C in time slot t ∈ T , respectively. We usepi = (p1,1

i , · · · , p1,|C|i , · · · , p|T |,1i , · · · , p|T |,|C|i ) to denote the

power allocation decision vector for the transmitting device oflink i, and p = (p1, · · · ,pi, · · · ,p|Q|) to denote the powerallocation vector for all links. The effective throughput ri forlink i can be modeled as

ri(p) = ηBLslot − La

Lsp

∑t∈T

∑c∈C

log2

(1 +

pt,ci G0ht,ci,i

N0 + It,ci

), (4)

where B is the bandwidth of each channel, η ∈ [0, 1] isthe efficiency of the transceiver, and N0 is the noise power.In addition, It,ci =

∑j∈Q\{i} p

t,cj Gj,ih

t,cj,i is the received

interference power of link i on channel c in time slot t.

C. Utility Functions

Utility is considered as an important metric to efficientlyallocate resource blocks to heterogeneous multimedia traffic.

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2

2.5

Effective Throughput (Gbps)

Uti

lity

Scenario 1

Scenario 2

Scenario 3

Fig. 4. An example of utility versus effective throughput for differentscenarios.

The utility reflects the relative satisfaction level of a userregarding the allocated resources. We define utility functionsto characterize the users’ experience for different types ofmultimedia content delivery. We consider the following usagescenarios for mm-wave applications: S1) Uncompressed videostreaming: HDTV signal transmission with adaptive modu-lation coding; S2) Workstation desktop and conference ad-hoc: transmissions between computer devices or in an ad-hocmanner; S3) Kiosk file downloading: video and music sharingon portable devices.

We define S1, S2, and S3 as the sets of users that useservices under usage scenarios S1, S2 and S3, respectively.Some services in scenarios S1 and S2, such as video streamingor conference ad-hoc, have a minimum data rate requirement.Since each transmission link serves a corresponding user, weuse set Q to represent the set of the users as well as thelinks. In the remaining parts of the paper, we use the termslink and user interchangeably. We use the following quasi-concave function to characterize the satisfaction level of useri ∈ S1 ∪ S2 with respect to effective throughput:

Ui(ri(p))

=

{0, ri(p) < rmin

i ,

K1i ln(1 +K2

i ln(1 + (ri(p)− rmini )), ri(p) ≥ rmin

i ,(5)

where coefficients K1i and K2

i are application dependentparameters, and rmin

i is the minimum data rate requirement foruser i under specific usage scenario. The satisfaction of user iincreases quickly at the beginning when rmin

i is achieved andthen the marginal increment becomes smaller as the data rateincreases. This type of function is widely used for applicationswith minimum data rate requirement. The services in scenarioS3, such as file downloading, do not have a minimum datarate requirement (i.e., rmin

i = 0, i ∈ S3). Moreover, the utilityincreases linearly with respect to the effective throughput. Forthese services, we use the following linear utility function [42]for user i ∈ S3 as follows:

Ui(ri(p)) = K3i ri(p), (6)

where K3i is an application dependent parameter. Examples of

utility functions for different scenarios are shown in Fig. 4.

III. PROBLEM FORMULATION

The use of directional antenna can allow more concurrenttransmissions. However, only a proper scheduling scheme canfully exploit the potentials of the spatial reuse. Therefore, wepropose an integrated TDMA/FDMA/SDMA scheme, whichconsiders spatial reuse of directional antenna and co-channelinterference management in order to improve the spectrumefficiency of the home networks.

Apart from the benefits, the high power consumption ofmm-wave communication brings a challenge to the battery-powered devices such as smartphones and tablets. Therefore,energy efficiency becomes a critical challenge for mm-wavebased systems. We define the energy efficiency of user i as theratio between the amount of data transmitted and the energyconsumed, which is

Lspri(p)

(Lslot − La)∑t∈T

∑c∈C

pt,ci, (7)

where (Lslot − La)∑t∈T

∑c∈C p

t,ci represents the energy

consumed by user i to transmit Lspri(p) amount of data. Weuse V ⊂ Q to denote the set of links with battery-poweredtransmitting devices. We consider a threshold of the energyefficiency for these links in set V .

To formulate the problem, we define binary variables xt,ci ∈{0, 1}, t ∈ T , c ∈ C, where xt,ci = 1 if time slot t inchannel c is allocated to link i. Otherwise, xt,ci = 0. Wealso define time slot and channel allocation vector xi =(x1,1i , · · · , x1,|C|

i , · · · , x|T |,1i , · · · , x|T |,|C|i ) for user i, and vec-tor x = (x1, · · · ,xi, · · · ,x|Q|) for all users. We consider theaggregate network utility as the performance criterion. Theoptimal resource allocation decision depends on the allocatedresource blocks and the transmission power of the transmittingdevices. We denote the maximum transmission power as pmax.The threshold of energy efficiency is denoted by ξ. To find theoptimal resource allocation decision, the utility maximizationproblem is formulated as follows:

maximizex, p

∑i∈Q

Ui (ri(p)) (8a)

subject to ri(p) ≥ rmini , i ∈ Q, (8b)

ri(p) ≥ ξLslot − La

Lsp

∑t∈T

∑c∈C

pt,ci , i ∈ V, (8c)

0 ≤ pt,ci ≤ xt,ci pmax, i ∈ Q, t ∈ T , c ∈ C, (8d)∑

c∈Cxt,ci ≤ 3, i ∈ Q, t ∈ T , (8e)

xt,ci ∈ {0, 1}, i ∈ Q, t ∈ T , c ∈ C, (8f)

where constraint (8b) ensures that the minimum throughputrequirement is satisfied for each user. Constraint (8c) impliesthat the ratio between the effective throughput and powerconsumption is greater than the minimum threshold ξ. Con-straint (8d) guarantees that the transmission power of link i isnot greater than pmax. According to the latest standardizationprogress of mm-wave networks (i.e., IEEE 802.11ay [11]),channel bonding is considered to allow each transmission pairto use up to three mm-wave channels in a time slot. Therefore,

we consider constraint (8e) to indicate that each link can utilizeno more than three bonded channels during a time slot.

Note that the objective function in (8a) is non-convex dueto the interference term It,ci in (4). Moreover, the time slot andchannel allocation variables x are binary. Thus, problem (8) isa non-convex MIP problem, which is in general hard to solve.However, we can reformulate the problem and obtain a subop-timal solution. To reformulate problem (8), we first evaluatethe potential interference received by each link. Due to thedirectional communication of mm-wave networks, multiuserinterference is greatly reduced compared with omni-directionalsystems. The mm-wave systems show a transitional behaviorfrom interference-limited to noise-limited regime, dependingon several factors such as density of transmitters and operatingbeam width [43]. The interference observed by different linksmay be completely different. In this paper, we estimate theinterference for each link by assuming all links transmit inthe same channel with maximum transmission power pmax. Theestimated interference of link i is denoted as Imax

i . A similaridea is used in [41], which provides a conservative estimationof the interference. We define

ri (pi) , ηBLslot − La

Lsp

∑t∈T

∑c∈C

log2

(1 +

pt,ci G0ht,ci,i

N0 + Imaxi

),

(9)and

Ui (pi)

,

{K1i ln

(1 +K2

i ln(1 +

(ri (pi)− rmin

i

))), i ∈ S1 ∪ S2,

K3i ri (pi) , i ∈ S3.

(10)We then reformulate the non-convex MIP problem into thefollowing minimization problem.

minimizex, p

−∑i∈Q

Ui (pi) (11a)

subject to∑

j∈Q\{i}

pt,cj Gj,iht,cj,i ≤ I

maxi , i ∈ Q, t ∈ T , c ∈ C,

(11b)

ri(pi) ≥ rmini , i ∈ Q, (11c)

ri(pi) ≥ ξLslot − La

Lsp

∑t∈T

∑c∈C

pt,ci , i ∈ V, (11d)

constraints (8d)–(8f).

Problem (11) is an MIP problem with convex objective func-tion. Compared with problem (8), the new constraint (11b)ensures that for each user, the received interference poweris less than the estimated maximum interference. Constraints(11c) and (11d) are transformed into convex constraints witha smaller feasible region.

IV. OUTER APPROXIMATION BASED POWER ANDCHANNEL ALLOCATION ALGORITHM

To solve problem (11), we use the OA method, whichis a standard technique to solve convex MIP problems andprovides their optimal solution [44], [45]. The convergence ofOA method has been proven in [44]. The OA method solves

the convex MIP problem iteratively. Two problems, namelythe subproblem and master problem, are involved in eachiteration. The subproblem is a convex nonlinear programming(NLP) problem and the master problem is a mixed-integerlinear programming (MILP) problem. The NLP subproblemis obtained from the original convex MIP problem by fixingthe value of integer variables. The NLP subproblem providesan upper bound of the optimal value of the original convexMIP problem. The MILP master problem uses the solution ofthe NLP subproblem as an input, and provides a lower boundof the optimal value of the original convex MIP problem. Weiteratively solve the subproblem and master problem until theirsolutions converge.

To use the OA method, we first transform problem (11) intoa standard MIP format by simplifying the notation. We define

f(p) = −∑i∈Q

Ui (pi) ,

φt,ci (p) =∑

j∈Q\{i}

pt,cj Gj,iht,cj,i − I

maxi , i ∈ Q, t ∈ T , c ∈ C,

ψ1i (pi) = rmin

i − ri(pi), i ∈ Q,

ψ2i (pi) = ξ

Lslot − La

Lsp

∑t∈T

∑c∈C

pt,ci − ri(pi), i ∈ V.

Then, problem (11) can be rewritten in the standard form as:minimize

x, pf(p) (12a)

subject to φt,ci (p) ≤ 0, i ∈ Q, t ∈ T , c ∈ C, (12b)

ψ1i (pi) ≤ 0, i ∈ Q, (12c)

ψ2i (pi) ≤ 0, i ∈ V, (12d)

constraints (8d)–(8f).

After transforming the original problem into the standardform, we can formulate the NLP subproblem and MILP masterproblem in each iteration. We denote k as the index of eachiteration.

1) NLP subproblem (kth iteration): The NLP subproblemis obtained by fixing the value of binary variables x. Bydoing so, the problem only consists of the continuous variablesp. In iteration k, given x(k) as a constant vector, the NLPsubproblem is as follows:

minimizep

f(p) (13a)

subject to 0 ≤ pt,ci ≤ xt,c(k)i pmax, i ∈ Q, t ∈ T , c ∈ C,

(13b)constraints (12b)–(12d).

Constraint (13b) is similar to (8d), where xt,c(k)i is given as

a constant. In problem (13), the objective function and theconstraints are all convex. Therefore, it is a convex problemwhich can be solved by using convex optimization solverssuch as CVX [46]. We denote the optimal solution of problem(13) by p∗. It is clear that the optimal value f(p∗) obtainedfrom problem (13) is an upper bound of the optimal value ofproblem (12). In order to find a lower bound of the originalproblem, we formulate the master problem.

2) MILP master problem (kth iteration): Both the objectivefunction and the constraints in the master problem are based

on outer linearization [45]. If the value f(p∗) obtained bysolving the NLP subproblem is the tightest upper bound amongall iterations, we use p∗ as the input p(k) to formulate themaster problem. We introduce ϕ as an auxiliary variableto formulate the MILP problem. The solution of the MILPproblem provides a lower bound of the original convex MIPproblem [45, pp. 8]. The MILP master problem in iteration kis

minimizex, p, ϕ

ϕ (14a)

subject to f(p(k)) +∇f(p(k))(p− p(k))T ≤ ϕ,k = 1, ..., k, (14b)

φt,ci (p(k)) +∇φt,ci (p(k))(p− p(k))T ≤ 0,

i ∈ Q, t ∈ T , c ∈ C, k = 1, ..., k, (14c)

ψ1i (p

(k)i ) +∇ψ1

i (p(k)i )(pi − p

(k)i )T ≤ 0,

i ∈ Q, k = 1, ..., k, (14d)

ψ2i (p

(k)i ) +∇ψ2

i (p(k)i )(pi − p

(k)i )T ≤ 0,

i ∈ V, k = 1, ..., k, (14e)constraints (8d)–(8f).

The gradient vectors in problem (14) are as follows:

∇f(p(k)) =− ηB(Lslot − La)

Lsp ln 2

(C1,1

1 , · · · , Ct,ci , · · · ,

C|T |,|C||S1∪S2|, C

1,11 , · · · , Ct,c

j , · · · , C|T |,|C||S3|

),

(15)

where Ct,ci , i ∈ S1 ∪ S2, t ∈ T , c ∈ C, is

Ct,ci =

(1 +K2

i ln

(1 +

(ηB

Lslot − La

Lsp

∑t∈T

∑c∈C

log2

(1 +

G0ht,ci,ip

t,c(k)i

N0 + Imaxi

)− rmin

i

)))−1(1 +

(ηB

Lslot − La

Lsp

×∑t∈T

∑c∈C

log2

(1 +

G0ht,ci,ip

t,c(k)i

N0 + Imaxi

)− rmin

i

))−1

×K1iK

2i G0h

t,ci,i

N0 + Imaxi +G0h

t,ci,ip

t,c(k)i

,

(16)and Ct,c

j , j ∈ S3, t ∈ T , c ∈ C, is

Ct,cj =

K3jG0h

t,cj,j

N0 + Imaxj +G0h

t,cj,jp

t,c(k)j

. (17)

In addition,

∇φt,ci (p(k)) =

(Gt,c1,iht,c1,i, · · ·G

t,ci−1,ih

t,ci−1,i, 0, G

t,ci+1,ih

t,ci+1,i, · · · , G

t,c|Q|,ih

t,c|Q|,i),

(18)and

∇ψ1i (p

(k)i ) =

−ηB(Lslot − La)G0

Lsp ln 2

(C1i , · · · , Ct

i , · · · , C|T |i

),

(19)

where Cti , i ∈ Q, t ∈ T , is defined as the tth component in

the gradient vector, and

Cti =

(ht,1i,i

N0 + Imaxi +G0h

t,1i,i p

t,1(k)i

, · · · ,

ht,|C|i,i

N0 + Imaxi +G0h

t,|C|i,i p

t,|C|(k)i

).

(20)

The gradient vector ∇ψ2i (p

(k)i ) is

∇ψ2i (p

(k)i ) =

(C1i , · · · , Ct

i , · · · , C|T |i

), (21)

in which Cti , i ∈ V, t ∈ T , is defined as the tth component in

the gradient vector, and

Cti =

Lslot − La

Lsp

(ξ −

ηBG0ht,1i,i

ln 2(N0 + Imax

i +G0ht,1i,i p

t,1(k)i

) ,· · · , ξ −

ηBG0ht,|C|i,i

ln 2(N0 + Imax

i +G0ht,|C|i,i p

t,|C|(k)i

)).(22)

Note that the MILP master problem can be solved usingstandard optimization solvers such as MOSEK [47]. The MILPmaster problem has more constraints (i.e., the constraintsadded in the kth iteration) compared to the one formulated inthe previous iteration as shown in (14b)–(14e). Therefore, thelower bound of the optimal value of the convex MIP problem,which is obtained by solving the master problem, is tightenedin each iteration. Similarly, by solving the subproblem andthe master problem iteratively, the gap between the lowerand upper bounds decreases. When the gap is smaller thana threshold, the solution of (12) is obtained.

The OA based scheduling and power allocation algorithm isshown in Algorithm 1. The proposed algorithm contains foursteps. In the first step, we initialize the scheduling variablesand power variables, the initial upper bound UB, and theinitial lower bound LB, respectively (as shown in Line 1).In the second step, we solve NLP subproblem (13) to obtainsolution p. We update the current upper bound UB to be theminimum value of the previous UB and f(p) (as shown inLine 4). We then set the value of p(k) as p (as shown in Line5). In the third step, we solve MILP master problem (14). Weupdate the lower bound by setting it as ϕ and set the valueof x(k+1) as x (as shown in Lines 7 and 8). Then, we setk := k + 1. In the fourth step, we evaluate the differencebetween the current upper bound UB and lower bound LB.If UB − LB ≤ ε, the algorithm returns the optimal solutionx∗ and p∗. Otherwise, it returns to the second step (Line 3).

Compared with the generalized Benders decompositionmethod used in [37], although OA based algorithm has re-duced the computational complexity of MIP problem (11), thecomplexity of Algorithm 1 is still very high due to the MILPproblem in each iteration. MILP problems are generally NP-hard [48]. In particular, the worst-case complexity increasesexponentially with the number of binary variables. The worst-case complexity of each iteration in the OA based algorithm

Algorithm 1: Integrated TDMA/FDMA/SDMA ResourceManagement based on OA Method

1 Initialize x(1), p(0), k := 1, UB := +∞, LB := −∞2 while UB − LB > ε do3 Solve problem (13) to obtain solution p4 UB := min

(UB, f(p)

)5 p(k) := p6 Solve problem (14) to obtain solution x and optimal

value ϕ7 LB := ϕ8 x(k+1) := x9 Set k := k + 1

10 end11 output Scheduling decision x∗ = x(k) and optimal

power p∗ = p(k−1)

is O(2|Q||T ||C|), which is the complexity of solving problem(14) in worst case. Thus, OA based algorithm is too complexfor the real-time scheduling.

V. GREEDY BASED HEURISTIC ALGORITHM

To overcome the computational complexity of the OA basedalgorithm, we propose a greedy based heuristic channel andpower allocation algorithm in this section. The proposedheuristic greedy algorithm is shown in Algorithm 2. In thisalgorithm, Z denotes the subset of links which require aminimum data rate. In the algorithm, we consider each timeslot in a certain channel as a resource block (RB). We denote∆ri(xi, x

t,ci ) as the estimated potential rate increment for link

i if time slot t in channel c is allocated to it and maximumtransmission power pmax is used. We also define ∆Ui(xi, x

t,ci )

as the estimated potential utility increment for link i.The proposed algorithm separates the channel allocation

and power allocation, which can reduce the computationalcomplexity. There are three major steps in the algorithm. Inthe first step, we allocate the RBs to guarantee the minimumdata rate requirements of the links, assuming the maximumpower is used at the transmitting devices (Lines 2 to 14).Due to the directional communication, an RB can be sharedby different links if the SINR requirements of all links aresatisfied. Therefore, we find the link with the largest estimatedrate increment and allocate the corresponding RB slot to thatlink (Lines 5 to 7). Specifically, we form set W of indexesi, t, and c, subject to the conditions that RB t, c has notbeen allocated to link i, the interference requirement will besatisfied if RB t, c is allocated to this link, and no other channelis allocated in the same time slot (Line 3). Then, we sort thepotential rate increment for different links and RBs in a non-increasing order (Line 5), and record i, t, c corresponding tothe largest element of the sorted list (Line 6). In the secondstep, we allocate the RBs to all links by considering the utilityincrement (Lines 15 to 22). In each iteration, we allocate anRB to that link which results in the largest estimated networkutility increment (Lines 17 to 21). The selection of the RBs

Algorithm 2: Integrated TDMA/FDMA/SDMA ResourceManagement based on Greedy Algorithm

1 Initialize pi := (pmax, . . . , pmax), i ∈ Q, xt,ci := 0,i ∈ Q, t ∈ T , c ∈ C

2 while Z 6= ∅ do3 W :=

{(i, t, c) ∈ {Z, T , C} | xt,ci = 0,∑

j∈Z\{i}pmaxGj,ih

t,cj,i ≤ Imax

i ,∑c∈C

xt,ci ≤ 3}

4 if W 6= ∅ then5 Sort ∆ri(xi, x

t,ci ), (i, t, c) ∈ W in a

non-increasing order6 Select the first element of the sorted list and

record i, t, c7 Set xt,ci := 18 if ri(pi) ≥ rmin

i then9 Z := Z \ {i}

10 end11 else12 Return infeasible13 end14 end15 do16 W :=

{(i, t, c) ∈ {Q, T , C} | xt,ci = 0,∑

j∈Q\{i}pmaxGj,ih

t,cj,i ≤ Imax

i ,∑c∈C

xt,ci ≤ 3,

∆Ui(xi, xt,ci ) > 0

}17 if W 6= ∅ then18 Sort ∆Ui(xi, x

t,ci ), (i, t, c) ∈ W in a

non-increasing order19 Select the first element of the sorted list and

record i, t, c20 Set xt,ci := 121 end22 while W 6= ∅23 Given Q,V , and x∗ = (xt,ci )i∈Q,t∈T ,c∈C , solve problem

(23) to obtain p∗ as the power allocation24 output Channel and power allocation decision x∗ and p∗

and the links should also satisfy the constraint that a linkcannot utilize multiple channels simultaneously. The secondstep terminates when W = ∅. Now, we have allocated thechannels and obtained channel allocation result x. In the thirdstep, we obtain the power of each transmitter by solvingthe following problem based on the obtained x. The powerallocation problem is as follows:

maximizep

∑i∈Q

Ui (pi) (23a)

subject to ri(pi) ≥ rmini , i ∈ Q, (23b)

ri(pi) ≥ ξLslot − La

Lsp

∑t∈T

∑c∈C

pt,ci , i ∈ V, (23c)

0 ≤ pt,ci ≤ xt,ci pmax, i ∈ Q, t ∈ T , c ∈ C. (23d)

Problem (23) is a convex optimization problem and can be

TABLE IISIMULATION SETTINGS [8], [9], [35]

Parameter ValueFrequency band 57.05 - 64.00 GHzBandwidth of each channel B 2.160 GHzNoise power spectrum density N0/B −174 dBm/HzMaximum transmission power pmax 10 dBmCarrier frequency fc1, fc2, fc3 58.32, 60.48, 62.64 GHzPath loss reference distance dbp 1 mAttenuation of signals ALOS, ANLOS 7.1, 18 dBPath loss exponent nLOS, nNLOS 2.0, 2.5Shadowing standard deviation σLOS, σNLOS 1.5, 3.4Length of scheduling period Lsp 65 msLength of beacon period Lb 0.3 msLength of control period Lc 5 msPilots transmission duration Tp 655 nsSector level beam width Ψsr, Ψst 90o

solved by using convex optimization solvers. The optimalsolution of this problem is denoted by p∗. Finally, Algorithm2 returns the channel and power allocation decision (Line 24).

In the following, we provide the complexity analysis of thegreedy algorithm. In the first step of the algorithm from Lines1 to 14, the number of iterations mainly depends on the sizeof set W . Given |W|, the complexity of sorting in Line 5is O (|W| log(|W|)), which is O (|Z||T ||C| log(|Z||T ||C|)) inworst case. Since the time required for executing the linesin the first step except Line 5 is constant, and the number ofiterations executing the first step is O(|W|), the complexity ofthe first step is O

(|W|2 log(|W|)

). Similarly, the complexity

of the second step (Lines 15 to 22) is O(|W|2 log(|W|)

).

Note that the convex problem (23) can be solved in polynomialtime. Due to the fact that Z ⊆ Q and |W| ≥ |W|, theoverall complexity of the algorithm is O

(|W|2 log(|W|)

),

i.e., O((|Q||T ||C|)2 log(|Q||T ||C|)

). It can be seen that the

complexity of the greedy algorithm is reduced compared tothe OA based algorithm, which significantly improves itsapplicability for the real-time scheduling.

VI. PERFORMANCE EVALUATION

In this section, we evaluate the performance of the proposedOA based and the greedy algorithms. We further compare bothof the proposed algorithms with scalable heuristic STDMAscheduling (SHSS) algorithm [21] and vertex multi-coloringconcurrent transmission (VMCCT) algorithm [32]. This isbecause [21] and [32] also focus on the spatial reuse inindoor mm-wave networks. The key differences between ouralgorithms and the algorithm proposed in [21] and [32] arethat we further utilize mm-wave channelization and proposean OA based scheduling algorithm to maximize the aggregateutility for multimedia content delivery in mm-wave networks.We consider the transmitting devices are randomly located inthe home with a uniform distribution. The receiving devicesare randomly located with an average distance of 2 m aroundthe transmitting devices. A random number of transmittingdevices operate on battery. Their links form set V . Theservice requested by each link is randomly selected fromS1, S2, and S3. The parameters for the utility function are

2 4 6 8 10 12 14 160

10

20

30

40

50

60

Number of links

Aggre

gat

e T

hro

ughput

(Gbps)

OA based Algorithm

Greedy Algorithm

VMCCT Algorithm

SHSS Algorithm

Fig. 5. Aggregate throughput versus number of links with the home area of10 m × 10 m and Θ3dB = 15o.

K1i = 1,K2

i = 0.7, rmini = 0.95 Gbps, i ∈ S1; K1

i =1.5,K2

i = 1, rmini = 1.54 Gbps, i ∈ S2; and K3

i = 0.15,i ∈ S3 [8]. The energy efficiency threshold ξ is 105 bit/joule[49]. The length of each time slot Lslot is (Lsp−Lb−Lc)/|T |.Note that the number of time slots is equal to the numberof links in the network2. Other simulation parameters aresummarized in Table II [8], [9], [35]. We repeat the experimentusing Monte Carlo simulations for each network setting, andcalculate the average value of the performance metrics overdifferent network settings.

We first compare the performance of our proposed al-gorithms with SHSS and VMCCT algorithms. Since SHSSand VMCCT algorithms aim to improve the throughput ofthe network using spatial reuse, we compare the algorithmsin terms of throughput. In Fig. 5, we plot the aggregatethroughput of the proposed OA based, greedy, SHSS, and VM-CCT algorithms for different number of links in the network.Note that each link represents a pair of devices. Althoughthe proposed algorithms aim to increase the network utility,they both achieve a higher aggregate throughput comparedto the SHSS and VMCCT algorithms. This is because SHSSalgorithm randomly selects the concurrent transmitting devicesbased on aggregate interference. However, we improve thespatial reuse by allocating the channels while consideringthe throughput and utility increment of each link. Moreover,VMCCT algorithm has a fixed exclusive region to forbidconcurrent transmissions while we consider all possible con-current transmissions to improve the spatial reuse.

In Fig. 6, we compare the aggregate throughput of ourproposed algorithms with SHSS and VMCCT algorithms fordifferent half power beam width Θ3dB to show the impact ofalignment overhead. When the beam width is very narrow,the alignment overhead is dominant and reduces the overall

2According to the IEEE 802.15.3c and 802.11ad standards, the duration ofa time slot can vary [35, pp. 26] [9, pp. 151, 178]. The duration of a time slotis determined based on transmission requests of active links. In our system,we assume all devices are active during the scheduling period and the totalnumber of time slots is equal to the number of links. Since the duration ofdata transfer interval is the product of the duration of each time slot and thenumber of time slots, the duration of a time slot depends on the number ofactive links in the network.

0 10 20 30 40 50 600

5

10

15

20

25

30

35

40

45

Half Power Beam Width Θ3dB

( o )

Aggre

gat

e T

hro

ughput

(Gbps)

OA based Algorithm

Greedy Algorithm

VMCCT Algorithm

SHSS Algorithm

Fig. 6. Aggregate throughput versus half power beam width with the homearea of 10 m × 10 m. The number of links |Q| = 10.

throughput. However, OA based and greedy algorithms alwaysoutperform SHSS and VMCCT algorithms.

We now evaluate the aggregate utility of OA based, greedy,SHSS, and VMCCT algorithms for different number of linksin the network. As shown in Fig. 7, the aggregate utility ofgreedy algorithm is close to the OA based algorithm. Greedyalgorithm achieves at least 90% of the aggregate utility ofthe OA based algorithm and outperforms VMCCT and SHSSalgorithms by 22% and 39%, respectively, when the numberof links is 16 and home area is 100 m2. We also evaluatethe aggregate utility of the proposed greedy algorithm fordifferent home sizes. We compare the results for two differenthome sizes of 144 m2 and 100 m2, respectively. As shownin this figure, a larger home size results in a slightly higheraggregate utility. This is due to the longer distance betweenthe interfering devices in a larger home area. The highestutility is achieved with home area of 144 m2 with 16 links,which is close to the case of 100 m2. Therefore, the proposedalgorithms perform well in homes of different sizes.

In Fig. 8, we compare the performance of the proposedOA based, greedy, SHSS, and VMCCT algorithms when thereis only one usage scenario in the network. Fig. 8 shows theaggregate network utility for three types of usage scenarios,where we fix the number of links to be 10. It is shown that thegreedy algorithm achieves at least 90% of the aggregate utilitycompared to the OA based algorithm in different scenarios.In usage scenario S3, the aggregate utility of OA based andgreedy algorithms is close to each other. This shows whenthe minimum data rate requirement is zero and the utility isa linear function of the effective throughput for scenario S3,the greedy algorithm is more likely to approach the optimalsolution. Both OA based and greedy algorithms outperform theSHSS and VMCCT algorithms. Although the aggregate utilityobtained by the OA based algorithm is slightly higher thangreedy algorithm, we later present that the running time of thegreedy algorithm is much less than the OA based algorithm.

In Fig. 9, we compare the average running time of OAbased, greedy, SHSS, and VMCCT algorithms. Results showthat the running time of the OA based algorithm is a couple ofhundred seconds for each experiment. This degrades the appli-cability of the OA based algorithm when real-time scheduling

2 4 6 8 10 12 14 160

5

10

15

Number of Links

Aggre

gat

e U

tili

ty

OA based Algorithm with Home Area = 144 m2

OA based Algorithm with Home Area = 100 m2

Greedy Algorithm with Home Area = 144 m2

Greedy Algorithm with Home Area = 100 m2

VMCCT Algorithm with Home Area = 144 m2

VMCCT Algorithm with Home Area = 100 m2

SHSS Algorithm with Home Area = 144 m2

SHSS Algorithm with Home Area = 100 m2

Fig. 7. Aggregate utility versus number of links with the home area of 10m × 10 m and Θ3dB = 15o.

S1 S2 S30

5

10

15

20

Usage Scenario

Aggre

gat

e U

tili

ty

OA based Algorithm

Greedy Algorithm

VMCCT Algorithm

SHSS Algorithm

Fig. 8. Aggregate utility versus usage scenarios with the home area of 10m × 10 m. The number of links |Q| = 10.

is needed. The running time of greedy algorithm is almostthe same as SHSS and VMCCT algorithms, and is negligiblecompared to the running time of OA based algorithm. Thisdemonstrates the efficiency of the proposed greedy algorithm.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1610

−4

10−3

10−2

10−1

100

101

102

103

Number of Links

Aver

age

Runnin

g T

ime

(s)

OA based Algorithm

VMCCT Algorithm

Greedy Algorithm

SHSS Algorithm

2.7×10−3

4.3×10−3

3.6×10−3

Fig. 9. Average running time versus number of links with the home area of10 m × 10 m.

VII. CONCLUSION

In this paper, we studied the resource management problemfor multimedia content delivery in a mm-wave based smarthome network. Specifically, we formulated a non-convex MIPoptimization problem to maximize the aggregate network util-ity. We reformulated the problem into a convex MIP problemand designed an OA based algorithm to find the optimalsolution of the reformulated problem. We further proposeda greedy algorithm with a lower computational complexity.Simulation results showed that both algorithms have substan-tial performance improvement compared to recently proposedalgorithms in the literature. For future work, our work canbe extended in several directions. First, we will considercontention-based transmission as a possible method for QoS-constrained applications with the limitation of guaranteed QoSto further improve the channel utilization when the devicedensity is low. Second, our approach can be applied to othermm-wave based networks, such as future 5G systems. Third,a distributed algorithm can be considered when the number ofdevices is large.

ACKNOWLEDGEMENT

The authors would like to thank Dr. Binglai Niu and Mr.Zehua Wang for their help and comments on simulations inthe conference version of this paper.

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Bojiang Ma (S’13) received the B.Eng. degree fromSoutheast University, Nanjing, JiangSu, China, in2009, and M.A.Sc. degree from University of Vic-toria, Victoria, BC, Canada in 2011. He is currentlyworking towards the Ph.D. degree at the Universityof British Columbia, Vancouver, BC, Canada. Hisresearch interests include interference managementand resource allocation for heterogeneous wirelessnetworks using optimization theory and game theory,with current focus on small cell networks, homewireless networks, and mm-wave communication

systems.

Hamed Shah-Mansouri (S’06-M’14) received theB.Sc., M.Sc., and Ph.D. degrees from Sharif Uni-versity of Technology, Tehran, Iran, in 2005, 2007,and 2012, respectively all in electrical engineering.He ranked first among the graduate students. From2012 to 2013, he was with Parman Co., Tehran,Iran. Currently, Dr. Shah-Mansouri is a post-doctoralresearch and teaching fellow at the University ofBritish Columbia, Vancouver, Canada. His researchinterests are in the area of stochastic analysis, op-timization and game theory and their applications

in economics of cellular networks and mobile cloud computing systems. Hehas served as the publication co-chair for the IEEE Canadian Conferenceon Electrical and Computer Engineering 2016 and as the technical programcommittee (TPC) member for several conferences including the IEEE GlobalCommunications Conference (GLOBECOM) 2015 and the IEEE VehicularTechnology Conference (VTC2016-Fall).

Vincent W.S. Wong (S’94, M’00, SM’07, F’16)received the B.Sc. degree from the University ofManitoba, Winnipeg, MB, Canada, in 1994, theM.A.Sc. degree from the University of Waterloo,Waterloo, ON, Canada, in 1996, and the Ph.D. de-gree from the University of British Columbia (UBC),Vancouver, BC, Canada, in 2000. From 2000 to2001, he worked as a systems engineer at PMC-Sierra Inc. He joined the Department of Electricaland Computer Engineering at UBC in 2002 andis currently a Professor. His research areas include

protocol design, optimization, and resource management of communicationnetworks, with applications to wireless networks, smart grid, and the Internet.Dr. Wong is an Editor of the IEEE Transactions on Communications. Heis a Guest Editor of IEEE Journal on Selected Areas in Communications,special issue on “Emerging Technologies” in 2016. He has served on theeditorial boards of IEEE Transactions on Vehicular Technology and Journalof Communications and Networks. He has served as a Technical Program Co-chair of IEEE SmartGridComm’14, as well as a Symposium Co-chair of IEEESmartGridComm’13 and IEEE Globecom’13. He is the Chair of the IEEECommunications Society Emerging Technical Sub-Committee on Smart GridCommunications and the IEEE Vancouver Joint Communications Chapter. Hereceived the 2014 UBC Killam Faculty Research Fellowship.