Fair Beamwidth Selection and Resource Allocation for Indoor Millimeter-Wave Networks Nima Eshraghi† , Vahid Shah-Mansouri† , and Behrouz Maham‡ †

School of ECE, College of Engineering, University of Tehran, Iran ‡ School of Engineering, Nazarbayev University, Kazakhstan Email: [email protected],[email protected],[email protected]

Abstract— Millimeter-wave (mm-wave) communication is a promising technology for supporting extremely high data rates in the next generation wireless networks. Mm-wave signals experience high path loss and directional transmission is required to compensate the severe channel attenuation. The special characteristics of the mm-wave propagation arise opportunities as well as challenges for the network resource allocation problems. In this paper, a fair user association, beamwidth selection and power allocation problem for indoor mm-wave networks is studied. The objective of the optimization problem is to maximize the minimum user throughput to provide a fair resource distribution among the users. In our model, we take into account the unique mm-wave communications features, namely beam alignment procedure and directional transmission. Simulation results confirm the superior performance of the proposed solution compared to the existing approaches.

I. I NTRODUCTION To accommodate the growing surge of high data rates in wireless communication networks, the system capacity has been enhanced using advanced modulation and signal processing techniques. Nonetheless, the efficiency of these schemes is restricted because of the narrow bandwidth of the legacy networks. Hence, the millimeter-wave (mm-wave) technology is a promising choice to abate the imminent spectrum scarcity and boost the network capacity. In this respect, there is an increasing effort devoted to the area of the mm-wave communications. However, there are some technical challenges in the development of communication networks based on the mm-wave technology. The channel path loss in the mm-wave bands is generally higher than that of traditional microwave frequencies. Moreover, due to inherent propagation characteristics, mm-wave signals are more sensitive to blockage compared to the conventional bands. Furthermore, the immense amount of available bandwidth leads to significantly higher accumulated noise power at the receiver. Nevertheless, the small wavelength at the mm-wave bands allows the implementation of vast number of antenna elements in the current size network devices. Thus, beamforming techniques are adopted to overcome the severe path loss. Directional transmission is also beneficial for reducing the interference level. To fully exploit the directivity gain, transmitter and receiver beams should be carefully aligned. To this end, in the recent IEEE standards [1] and [2], firstly a sector-level sweep is performed, followed by the beam-level searching process. The beam training procedure incurs an alignment overhead,

which depends on the operating beamwidths, and this affects the resource allocation policy. There are several studies in the literature that scrutinize directional transmission in mm-wave communications. A concurrent beamforming protocol for optimally exploiting the directionality in mm-wave networks is presented in [3]. Authors in [4] address the joint beam searching and transmission scheduling problem to further improve spatial resource reuse. Moreover, a standard-compliant protocol for the interferenceaware scenario is introduced. In [5], joint association control and relay selection problem in mm-wave network is formulated as an optimization problem. Then, a distributed auction-based solution is presented for the multi-assignment class problem. The authors in [6] discuss the key MAC layer issues in cellular networks, such as random access procedures, frequent handover, scheduling and user association problems. In this paper, we study the problem of user association, beamwidth selection and power allocation for an indoor mmwave network. We first capture the interaction between the beam-alignment overhead and the achievable throughput of a mm-wave communication link. Then, we formulate the beamwidth selection and resource allocation as an optimization problem. The target of the considered problem is to maximize the minimum user throughput to attain a fair solution and provide a uniform QoS guarantee throughout the network. The considered problem is combinatorial and non-convex. Regarding the special mm-wave communication features, namely directional transmissions and limited ability to support different transmit beams, a low-complexity algorithm for the user association and beamwidth selection is presented. Then, the power allocation problem is solved using primal-dual subgradient method. Finally, the simulation results demonstrate the superiority of the proposed scheme to the adopted approach in the existing mm-wave standards. The remainder of the paper is organized as follows. In Section II, the network model and beam alignment procedure are described. In Section III, the problem is formulated as an optimization problem and the solution approach is proposed. Simulation results and remarks are presented in Section IV and conclusion is drawn in Section V. II. S YSTEM M ODEL AND S CENARIO D ESCRIPTION Consider an indoor mm-wave network consisting of a set of access points (APs), N = {1, . . . , N }, and a set of wireless

each AP is restricted to the number of RF chains implemented in the AP, i.e., X aik ≤ Zi , ∀i ∈ N , (3)

User q

AP j

k∈M

where Zi indicates the ability of AP i to support different transmit beams. However, due to the complexity and cost limitations for a mobile device, according to the recent IEEE standards [1] and [2], each user is able to make only one directed beam, i.e., X aik ≤ 1, ∀k ∈ M. (4)

AP i User k

Fig. 1.

An example of a mm-wave wireless network.

i∈N

devices, M = {1, . . . , M }, distributed uniformly within the room area. An example of the network is indicated in Fig.1. Since at the physical layer of mm-wave communications blockage is a paramount problem, we place several APs at different locations to increase the probability of finding lineof-sight APs to the user devices. The network elements (APs and users) are assumed to be equipped with the mm-wave transceivers, so that they can direct their beams to transmit or receive the data packets. The APs control the transmit power for data transmission to the users at the physical layer. Note that the antenna size in the mm-wave bands is in the order of several millimeters. Thus, thanks to the small wavelength, a large number of antenna elements can be fabricated in the network devices used these days. Therefore, using array processing techniques and narrow beams, the APs are enabled to direct different transmit powers towards separate user destinations. We denote pik as the allocated transmit power of AP i directed towards user k. In addition, we define the binary variable aik as the user association indicator, where aik = 1 if user k is associated to AP i, and aik = 0 otherwise. Thereby, AP i does not allocate power for user k, unless the mobile user device is associated to the AP, i.e., 0 ≤ pik ≤ aik Pmax ,

∀i ∈ N , ∀k ∈ M,

(1)

where Pmax is the maximum transmit power of the AP. Moreover, since the total transmit power of each transmitter is restricted to Pmax , we have X pik ≤ Pmax , ∀i ∈ N . (2) k∈M

The propagation features at the mm-wave 60 GHz band are rather different from the traditional 2.4 and 5 GHz microwave frequencies. One notable difference is that according to the Friss law, due to shifting to a higher carrier frequencies, the omni-directional path loss increases at the mm-wave bands. Therefore, the beamforming techniques are exploited to combat the severe path loss. It should be noted that since a specific number of antenna elements are involved to produce a directed beam, each AP can support a limited number of transmit beams. Besides, each transmit beam is directed towards a user device, and hence the number of supported user devices by

Directional transmission at the mm-wave bands not only can alleviate the severe path loss but also is beneficial for lowering the interference level. A. Beam Alignment Procedure Next, we explain the beam alignment procedure and the role of beamwidth selection in our model. Note that the directionality is required at both transmitter and receiver sides to establish a mm-wave communication link. Although the antenna gain of the main lobe of the beam pattern considerably improves the link budget, the transmitter and receiver nodes suffer from a time-consuming beam alignment procedure to form a sufficiently good mm-wave link. In the current mmwave based network technical standards, the communicating devices begin with finding the best sector-level beams through a sequence of pilot signal transmissions. Then, the corresponding nodes search to find the optimal beams within the selected sector area. Obviously, achieving a higher link budget requires utilizing narrower beams, which in turn incurs an excessive beam-training overhead. It is shown in [7] that the sectorlevel beam-training overhead can be substantially mitigated by tracking the devices over time. Therefore, without loss of generality, we assume that the network elements are aware of at which sector the associated devices are located, prior to the beam alignment phase. This assumption is valid for the scenarios with low-mobility wireless devices (e.g., pedestrian users) as it is expected in an indoor network environment. During the beam alignment phase, the corresponding nodes search over all possible beam vector combinations using a set of pilot signal transmission to align their beams. Let Tp represent the required time for a single pilot transmission, which has to be performed for each combination. Hence, using the exhaustive search approach adopted by the existing mm-wave standards [1] [2], the overall time duration of the alignment phase between AP i and user k, denoted by τik , can be expressed by [8] τik = Tp

ψa ψu , φaik φuk

(5)

where φuk and φaik are, respectively, the beamwidth of the user k, and the beamwidth of AP i for data transmission to user k. Moreover, ψ indicates the sector-level beamwidths, and for simplicity, we use superscript a to specify parameters related to APs and u for user devices. Upon accomplishment

of the beam alignment procedure, the optimal directions for data transmission and reception are discovered and the mmwave communication link can be established to start the data transmission phase. Note that the alignment time duration cannot surpass the time slot duration T , and thus the feasible region is constrained by Tp ≤ φaik φuk , ∀i ∈ N , ∀k ∈ M. (6) T Furthermore, because the beam alignment occurs within the sector-level beamwidths, we have aik ψ a ψ u

φumin ≤ φuk ≤ ψ u , aik φamin

≤

φaik

a

≤ aik ψ ,

∀k ∈ M,

(7)

∀k ∈ M, ∀i ∈ N ,

(8)

where φumin and φamin are the minimum possible operating beamwidth for user devices and APs, and they depend on the number of antenna elements implemented in the devices and the antenna configurations. Note that in (8), we multiplied the lower bound and upper bound by the corresponding user association variable aik , so that if user k is not associated to AP i, the corresponding beamwidth is forced to take the value of zero. B. Effective Throughput In the mm-wave communications, the total power gain between an AP and a user is composed of three main terms, namely the wireless channel power gain, and the AP and user device’s antenna directivity gains. To make the model analytically tractable, similar to [6] and [9], we approximate the actual beam pattern by a sectored model, where the power gains are constant inside the main lobe for all angles, and a i be the observing small value  for the side lobe gain. Let αkq angle between the users k and q from the point of view of AP i. k Similarly, let βij be the angle between AP i and AP j from a the user k standing point (see Fig.1). We denote by gik and u gik the AP i and user k antenna gains on the link connecting the nodes to each other, i.e.,  2π/φa , if aik = 1    P ik φa a i a 2π/φiq , if aiq = 1 and αkq ≤ 2iq gik = q∈M    , otherwise

P P and user k, the term j∈N q∈M,q6=k pjq Gjk represents the interference perceived by user k, and σ is the noise power. Note that the effective throughput depends on the transmit power, operating beamwidths, and the network topology. Additionally, the narrower beamwidths for data transmission and reception enhance the level of signal-to-interference-plusnoise-ratio (SINR). Nevertheless, the gain is achieved at the expense of increased alignment overhead and consequently leaves less time for data packet transmission. This captures a trade-off between the effective throughput and the time specified for the beam alignment procedure. III. FAIR B EAMWIDTH S ELECTION AND R ESOURCE A LLOCATION A. Problem Formulation In this paper, we consider the problem of joint user association, beamwidth selection and power allocation for an indoor mm-wave network. The target of the optimization problem is to maximize the minimum user throughput. Maximizing the minimum throughput yields a fair resource allocation among the users, thus a more uniform QoS can be guaranteed throughout the mm-wave network. Hence, the optimization problem can be formulated as ( ) X maximize min rik (10a) {a,φ,p}

subject to

k∈M

aik φamin ≤ φuq φuk 2

+

2

φaik

i ∈ N , k ∈ M, (10d) i ∈ N , k ∈ M, (10e) k ∈ M, (10f) a

≤ aik ψ , i ∈ N , k ∈ M, (10g)

i ≤ αkq + (2 − aik − aiq )ψ u ,

i ∈ N , k, q ∈ M, (10h) X

aik ≤ Zi ,

i ∈ N , (10i)

k∈M

aik ≤ 1, aik ∈ {0, 1},

k ∈ M, (10j)

i∈N

if ajk

if aik = 1 φu k = 1 and βij ≤ 2k otherwise

Moreover, the effective throughput of the link connecting AP i to user k in bps/Hz (i.e., normalized by the channel bandwidth) is denoted by rik and can be expressed as rik = (1 −

i ∈ N , (10c)

η pik ≤ rik , Tp ≤ φaik φuk , aik ψ a ψ u T φumin ≤ φuk ≤ ψ u ,

and u gik

i ∈ N , k ∈ M, (10b)

k∈M

X  u   2π/φk , = 2π/φuk ,   ,

i∈N

0 ≤ pik ≤ aik Pmax , X pik ≤ Pmax ,

τik p G P ikPik ) log2 (1 + ), T σ+ pjq Gjk

(9)

j∈N q∈M,q6=k a c u c where Gik = gik gik gik is the overall power gain and gik is the wireless channel power gain on the link between AP i

where the main optimization parameters are transmit powers, beamwidths and the binary user association variables. Constraint (10b) enforces the directed transmit power to an unassociated user to be zero, and the constraint in (10c) is the power budget limit. Furthermore, the constraint expressed in (10d) implies that the ratio between the effective throughput and the power consumption should be greater than the minimum energy efficiency threshold, denoted by η. In addition, constraint (10e) ensures that the searching time for the beam alignment phase is less than the time slot duration. Moreover, the constraint stated in (10f) limits the range of user device’s beamwidths, and the one in (10g) guarantees that an AP

only directs beams to its associated users. Constraint (10h) ensures that if two user devices are associated to the same AP, their beamwidths should not intersect with each other. Also, constraints (10i) and (10j) imply that the ability of supporting separate transmit beams is restricted by the number of RF chains implemented in the wireless device. The optimization problem in (10) is a non-convex mixedinteger programming problem whose feasible set is not convex, and thus it is hard to solve in general. In addition to the combinatorial variables and the interference term involved in the rate formula, the channel gains resulted from the beamwidth selection contribute to the non-convexity in the considered mm-wave network problem. Particularly, the channel gains not only are functions of beamwidths, but they also depend on the user association decisions and the network topology. Hence, the complexity of finding the optimal solution is not affordable even for a small size network. Therefore, the problem solution will be accomplished in two phases. In the first phase, we will perform the user association and specify the beamwidths, and in the second phase, we solve the power allocation problem.

Algorithm 1 User Association and Beamwidth Selection 1: Given the set of APs N , users M and channel gains G 2: For all the AP-user links find the closest mobile device (from angle view) to the user i Qik = argminq∈M/k (αkq ) 3: Compute the metric value for all available channels c c i γik = (gik /giQ ) log(1 + αkQ ) ik ik 4: Set H := G 5: while H 6= ∅ 6: Find the AP with the largest metric value for each user Ik = argmax(γik )

B. User Association and Beamwidth Selection

11: 12:

In this section, to circumvent the challenges in problem (10), we propose a low-complexity and suboptimal algorithm for the user association and beamwidth selection phase. It is beneficial that for each AP-user communication link, we first identify the closest (from angle view) mobile device to the user by i Qik = argminq∈M/k (αkq ). Then, for all AP-user links, we define the user association and beamwidth selection metric c c i as γik = (gik /giQ ). Note that the angle ) log(1 + αkQ ik ik i αkQik is the smallest angle that AP i observes the neighbor nodes to user k. We adopt the logarithmic function for angles because if the closest neighbor node is located outside the sector-level beamwidth, the AP beam to the desired user destination does not intersect with the neighbor device. Thus, after a certain angle threshold, the metric improves less for distant nodes. Additionally, the constant term in the logarithm argument is added to ensure that all metrics have a positive value. The idea of this metric is to prioritize the wireless links with higher gains and users with farther proximate nodes. In this way, in addition to expending less power by APs for supporting high data rates, a larger range for the beamwidths of the users and APs are provided for the selected links. Then, the channel links related to each user are sorted in a decreasing order, according to their metric value. We then find the user whose largest metric is smaller than other user devices. In other words, we try to maximize the minimum user throughput. By differentiating from the estimated data rate for the corresponding communication link, we obtain the optimal value of Φ∗ik = φaik φuk . Based on the optimal value for the multiplication of the beamwidths, the new lower and upper bounds for the user device beamwidth are introduced. Finally, according to the constraint (10h), if there are feasible solutions for the selected AP and user beamwidths, the corresponding user is associated to that AP and the beamwidths are determined. Particularly, we set the upper bound to the

i∈N

7:

Find the user which has the minimum largest metric K = argmin(Ik )

8:

Obtain the optimal Φ∗IK K = φaIK K φuK by differentiating from the  estimated data rate    P gIK K (2π)2 ψ a ψ u T /T log2 1 + max RIK K = 1 − ΦI Kp (σ+I)ΦIK K K i h i h Φ∗ Φ∗ IK K u Set LB=max φmin , ψa and UB=min ψ u , φIaK K min Set ϑ as the largest value in the range [LB, U B] that does not violate constraint (10h) if ϑ 6= ∅ then aIK K = 1 Set the user device beamwidth as φuK = (ϑ + LB)/2, and the AP beamwidth φaIK K = Φ∗IK K /φuK Remove all the channels related to user K from H if AP IK is fully occupied by its limit on the number of supported beams then remove AP IK from the set of APs else remove channel gIK K from the set of available channels end while

k∈M

9: 10:

13: 14: 15: 16:

maximum value in the feasible region for the user beamwidth that does not violate the constraint (10h). Note that a wide user beamwidth means that the user observes other APs by its main lobe and the harmful interference from other APs is boosted by the main lobe gain. It also should be noted that since the multiplication of the user device and the AP beamwidths is determined and is fixed to Φ∗ik , choosing a very small user beamwidth leads to a wider AP beamwidth, which causes detrimental interference for other users. Therefore, we properly select the user beamwidth to be the average of lower and upper bounds. Moreover, if a user or an AP reaches its limit on the supported transmit beams, all the channels related to that device will be removed from the set of available channels. The process continues until no channel link remains available. The entire procedure is summarized in Algorithm 1. C. Power Allocation Given the user association and beam angles, the beamforming gains are specified, and consequently, the overall channel gains among the network entities (APs and mobile devices) are determined. Nevertheless, owing to the interference term in the rate formula, problem (10) is still non-convex. To reformulate the problem, we impose a proper threshold on the harmful interference level perceived by the users. Note that by

pik Gik τik ) log2 (1 + ). rf ik = (1 − T σ + Imax

4 3.5

Minimum User Throghput (bps/Hz)

leveraging the directional transmissions in mm-wave networks, the level of interference is significantly alleviated compared to the omni-directional communication. The mm-wave communication networks illustrate a transitional behavior from the interference-limited to the noise-limited regime [10], where unlike the traditional wireless networks the interference is not a major concern. Hence, similar to the approaches used in [10] and [11], we denote Imax as the maximum allowable interference level, and we define

3 2.5 2 1.5 1 Proposed Scheme RssMaxTh Policy RndMaxMin Policy

0.5

(11)

0 4

Then, the epigraph form of the problem can be stated as t

maximize {t,p}

i ∈ N , k ∈ M, (12b) i ∈ N , (12c)

k∈M

η pik ≤ rf i ∈ N , k ∈ M, (12d) ik , X X piq Gik ≤ Imax , k ∈ M, (12e) X i∈N

where Πik = a∗ik Pmax , and a∗ik is the user association decision. To provide a closed-form solution for the power allocation problem (12), we utilize an effective iterative method such as primal-dual subgradient method [12]. Therefore, the Lagrange function can be formed as X X X X L= t+ λi (Pmax − pik ) + ωik (rf ik − η pik ) i∈N

+

X

i∈N k∈M

k∈M

νk (Imax −

X X

(13)

where {λ}, {ω} and {ν} are the non-negative dual variables corresponding to the constraints (12c), (12d), and (12e), respectively. By applying KKT optimality conditions to (13), we have Υik / ln(2) ∂L = − λi + ωik ζik − ηωik ∂pik 1 + pik Υik X X − νk Giq = 0,

(14)

i∈N q∈M/k

where ζik = (1 − τik /T ) and Υik = Gik /(σ + Imax ). Thereby, the optimal power allocation and the optimal primal variable t∗ are given by  Πik  p∗ik = 

ωik ζik / ln(2) 1  P P −  λi + η ωik + νk Giq Υik i∈N q∈M/k

∗

t = min

k∈M

X i∈N

k∈M

∗

rf ik (p ),

νkc+1

h  i+ c = ωik − δ2c ζik log2 (1 + p∗ik Υik ) − η p∗ik , (17b)   + X X = νkc − δ3c Imax − p∗iq Gik  , (17c) i∈N q∈M/k

where δcl , l ∈ {1, 2, 3}, denotes the step sizes at the c-th iteration. In the primal-dual optimization approach, the optimal primal variables and optimal power allocation are obtained by (15) and (16). Then, the dual variables will be updated accordingly and the process continues till the iterates converge. IV. S IMULATION R ESULTS

piq Gik ),

i∈N q∈M/k

k∈M

20

where [a]b0 = min{max{0, a}, b}. The dual variables updates using the subgradient method can be obtained as " !#+ X c+1 c c ∗ λi = λi − δ1 Pmax − pik , (17a)

k ∈ M, (12f)

rf ik ,

16

Fig. 2. Minimum user throughput vs the number of users, where M/N = 2.

c+1 ωik

i∈N q∈M/k

t≤

12

Number of Users, M

(12a)

subject to 0 ≤ pik ≤ Πik , X pik ≤ Pmax ,

8

, (15)

0

(16)

In this section, we present the simulation results to evaluate the performance of the proposed scheme for an indoor mmwave network with 50 × 50 m2 area. Wireless channel gains are composed of path loss and shadowing effects, and the path loss model and parameters are adopted from IEEE 802.15.3c standard [1]. Moreover, similar to [1], the maximum transmit power is considered as Pmax = 10 mW. The APs are able to support Zi = 3 different transmit beams concurrently. We evaluate the network performance over 1000 different network topologies. We further compare the performance of the proposed scheme to RSSI-based user association with fixed beamwidth for maximizing network throughput (RssMaxTh) policy, which is the adopted approach in the current mm-wave standards, and random user association with fixed beamwidth for Max-Min objective (RndMaxMin). Fig.2 depicts the minimum user throughput versus the number of mobile devices, where the ratio M/N = 2 is kept fixed. It is observed that the proposed scheme achieves a higher minimum data rate than RssMaxTh and RndMaxMin policies. Furthermore, the minimum data rate declines as the number of network devices increases for RssMaxTh and RndMaxMin policies, however, it remains almost unchanged

1 Proposed Scheme RssMaxTh Policy RndMaxMin Policy

90

0.9

70

Jain Index

Network Throughput (bps/Hz)

110

50

30

0.8

0.7 Proposed Scheme RssMaxTh Policy RndMaxMin Policy

0.6

10

0.5 4

8

12

16

20

4

Number of Users, M

Fig. 3.

Network throughput comparison for the three schemes.

for the proposed scheme . The reason is that the by RSSI-based user association, the mobile devices are associated to APs mainly based on the AP-user distance. However, for mm-wave communications, the location of the other nodes and angles to other users must be considered as well and the beamwidth should be determined adaptively. As it is illustrated in Fig.3, the proposed scheme shows relatively close performance to RssMaxTh policy in terms of overall network throughput. This is because of the fact that in the RssMaxTh policy, the objective directly involves the network throughput. Nevertheless, the proposed scheme maximizes minimum throughput. Therefore, in our scheme by sacrificing a little network throughput we can enhance the minimum data rate drastically. The weak random channel selection in the RndMaxMin policy leads to the poor network throughput performance. To compare the fairness of the schemes, we utilize the Jain Index, defined as  P 2 rk k∈M P 2. J= M rk k∈M

Note that the fairness index ranges from 1/M (worst case) to 1 (best performance). Fig.4 demonstrates that the proposed scheme significantly outperforms RssMaxTh and RndMaxMin in terms of network fairness. The reason is that the objective in the RssMaxTh policy puts the same value for each unit data rate enhancement. On the other hand, the minimum user throughput improvement has a higher value for the proposed scheme, and thus a more balanced QoS can be ensured throughout the network. Although the objective in RndMaxMin policy is to maximize minimum data rate, fixed beamwidths and poor user association leads to weak channel selection which negatively affects the network performance. V. C ONCLUSION In this paper, the problem of user association, beamwidth selection and power allocation for an indoor mm-wave networks was studied. The effect of the beam alignment procedure on the user throughput was investigated. The objective was to maximize the minimum user throughput to achieve a fair resource distribution among the mobile users. The resulting

8

12

16

20

Number of Users, M

Fig. 4.

Jain fairness index versus the number of users.

optimization problem is combinatorial and non-convex. Considering the transmit beam limits for the network devices, we proposed a low-complexity algorithm for the user association and beamwidth selection. Simulation results indicate the superiority of the proposed scheme to the existing mm-wave based standards in terms of fairness. Thus, our scheme can guarantee a more uniform QoS for the users throughout the network. R EFERENCES [1] IEEE Std 802.15.3c-2009, “IEEE standard for information technologytelecommunications and information exchange between systems-local and metropolitan area networks-specific requirements. Part 15.3: Wireless medium access control and physical layer specifications for high rate wireless personal area networks, amendment 2: Millimeter-wave-based alternative physical layer extension,” Oct. 2009. [2] IEEE 802.11 Working Group, “IEEE standard for information technology-telecommunications and information exchange between systems-local and metropolitan area networks-specific requirements. Part 11: Wireless LAN medium access control and physical layer specifications amendment 3: Enhancements for very high throughput in the 60 GHz band,” IEEE Std 802.11ad-2012, pp. 1 –628, Dec. 2012. [3] J. Qiao, X. Shen, J. Mark and Y. He, “Mac-layer concurrent beamforming protocol for indoor millimeter-wave networks,” IEEE Transactions on Vehicular Technology, vol. 64, pp. 327–338, Jan. 2015. [4] H. Shokri-Ghadikolaei, L. Gkatzikis and C. Fischione, “Beam-searching and transmission scheduling in mm-wave communications,” in IEEE International Conf. on Commun. (ICC), pp. 1292–1297, June 2015. [5] Y. Xu, G. Athanasiou, C. Fischione and L. Tassiulas, “Distributed association control and relaying in millimeter wave wireless networks,” in IEEE International Conf. on Commun. (ICC), pp. 1–6, May 2016. [6] H. Shokri-Ghadikolaei, C. Fischione, G. Fodor, P. Popovski, and M. Zorzi, “Millimeter wave cellular networks: A mac layer perspective,” IEEE Trans. on Commun., vol. 63, pp. 3437–3458, Oct. 2015. [7] T. Nitsche, A. Flores, E. Knightly and J. Widmer, “Steering with eyes closed: mm-wave beam steering without in-band measurement,” in IEEE Conf. on Computer Commun. (INFOCOM), pp. 2416–2424, Apr. 2015. [8] R. Congiu, H. Shokri-Ghadikolaei, C. Fischione and F. Santucci, “On the relay-fallback tradeoff in millimeter wave wireless system,” in IEEE Conf. on Computer Commun. Workshops, pp. 622–627, Apr. 2016. [9] T. Bai and R. W. Heath, “Coverage and rate analysis for millimeterwave cellular networks,” IEEE Trans. Wireless Commun., vol. 14, no. 2, pp. 1100–1114, Oct. 2014. [10] H. Shokri-Ghadikolaei and C. Fischione, “The transitional behavior of interference in mm-wave networks and its impact on medium access control,” IEEE Trans. on Commun., vol. 64, pp. 723–740, Feb. 2016. [11] B. Ma, H. Shah-Mansouri, and V. Wong, “Multimedia content delivery in millimeter wave home networks,” IEEE Transactions on Wireless Communications, vol. 15, no. 7, pp. 4826–4838, July 2016. [12] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, UK: Cambridge Univ. Press, 2004.