Mobility-Aware User Association in HetNets withMillimeter Wave Base Stations

Cirine Chaieb∗, Zoubeir Mlika†, Fatma Abdelkefi∗ ‡ and Wessam Ajib†

∗Department of Applied Mathematics, Signals, and Communications, Higher School of Communications of Tunis†Department of Computer Science, University of Quebec at Montreal

‡ IMT Atlantique, UMR CNRS 6285 Lab-STIC, University of Brittany Loire, F-29238 Brest, France∗{cirine.chaieb, fatma.abdelkefi}@supcom.tn

† mlika.zoubeir@courrier.uqam.ca, † ajib.wessam@uqam.ca

Abstract—As sub-6 GHz spectrum is becoming increasinglyscarce, millimeter wave (mmWave) bands are considered as oneof the key technologies for future cellular networks. Motivatedby the rapid growth of the data rate demands and the numberof wirelessly-connected devices, this paper considers a hybrid(sub-6 GHz and mmWave) heterogeneous network with a limitednumber of time-frequency resource blocks (RBs). To overcomethe mmWave propagation problems and the need of frequentupdate of association due to mobility, a novel mobility-awareuser-base station association strategy based on Markov chainis proposed. Simulation results validate the performance of theproposed strategy by reducing the need of frequent handoversbetween mmWave base stations in the network.

Keywords—User-base station association, millimeter wave, mo-bility, Markov chain, handover.

I. INTRODUCTION

Combining heterogeneous and small-cell networks withmillimeter wave (mmWave) communications seems to be aperspective solution for next generations of cellular networksto overcome the explosive growth of the data rate demandsand the number of wirelessly-connected devices.

Different from sub-6 GHz bands, mmWave band, whichis the band of spectrum between 30 GHz and 300 GHz, isexpected to provide a high data rate of the order of multi-gigabits per second. However, due to the short wavelengthof extra-high frequencies and the highly dynamic behavior ofthe mmWave channel, mmWave communications suffer from asignificant sensitivity to blockage and a high penetration loss.Recent studies have shown that reducing the coverage radiusof cells less than 200 meters and incorporating mmWave com-munications with sub-6 GHz communications are consideredas a promising solution to cope with the mmWave propaga-tion problems [1]. Moreover, with the help of directionnelantennas and beam-forming techniques in the transmitter andthe receiver, interference among different mmWave links isgreatly reduced and consequently mmWave communicationsare considered as noise-limited [2].

This paper studies the user-base station association problem(UAP) in a hybrid HetNet operating on both mmWave andsub-6 GHz frequency bands. In an urban environment, theexistence of mmWave line-of-sight (LOS) path, which isrequired for successful and reliable transmission, is not alwaysavailable and it can be dynamically intermittent due to various

factors such as user motion and other obstacles. Therefore,the performance of mmWave communications are severelyaffected by the propagation environment and the density ofobstacles. To avoid the need of frequent update of associationand to ensure an efficient resource utilization, in this paper,a novel user-base station association (UA) strategy for mobileusers in a hybrid HetNet is studied.

Several related works study UAP for mobile users. In [3],a mobility aware mathematical model, within a stochasticgeometry framework, is proposed. The authors study the effectof mobility on coupled and decoupled uplink and downlinkUA strategies in a two tier cellular network. For mobile users,they prove that the decoupled UA association strategy imposeshigher handover rate compared to the coupled strategy, whichis based on received signal strength (RSS). In [4], a mobilityaware UA rule in mmWave networks is proposed in orderto overcome the limitations of the conventional RSS basedassociation. The authors prove that taking into account the usermobility, especially in an urban environment, can overcomeoverly frequent re-association, and thus the need of frequenthandovers between base stations (BSs). To tackle the mobilitychallenges in 5G cellular networks, the work in [5] proposesa multi-connectivity concept for a cloud radio access network.The authors prove that with multi-connectivity the number ofmobility failures can considerably decrease without degradingthe users throughput. Furthermore, in [6], a meta-heuristicassociation approach based on a distributed auction algorithmin dynamic mmWave networks is proposed with the objectiveof optimizing the network throughput and ensuring fairnessamong users. Moreover, the effect of mobility on the systemperformance is shown in [7]–[9]. To cope with the intermittentmmWave transmission, authors in [10] propose a Markovdecision process framework for mmWave networks that aimsto minimize the signalling overhead caused by suboptimal cellselection and subsequent re-association. Note that our previouswork [11] studies UAP in a hybrid HetNet under a limitednumber of time-frequency resource blocks (RBs) only forstationary users. In contrast to the existing literature, this paperincorporates UA and RBs allocation problems for mobile usersin a hybrid HetNet with consideration of the erratic nature ofthe mmWave channel.

Throughout this paper, d.e refers to the ceiling functionand upper-case (resp. lower-case) bold letters denotes matrices(resp. vectors) where the ith row (resp. ith column) of matrix

978-1-5386-2070-0/18/$31.00 ©2018 IEEE 153

A is denoted by Ai (resp. Ai).

The rest of this paper is organized as follows. Section II in-troduces the system model. Section III describes the proposedUA strategy for mobile users. Section IV presents simulationresults and finally section V concludes this paper.

II. SYSTEM MODEL

We consider a two-tier hybrid HetNet composed of onesub-6 GHz macro-cell BS and two sets of small-cell basestations (SBSs), the first is mmWave SBSs (mmWSBSs)operating at 60 GHz and the second is sub-6 GHz SBSs(SSBSs) operating at sub-6 GHz. For an illustration, see Fig. 1.

Figure 1. An example of a two-tier hybrid HetNet

This paper considers downlink data transmission. Notethat the macro-cell BS, which is indexed by 0, operates atsub-6 GHz frequency band to provide basic coverage. Weuse subBS to denote the sub-6 GHz macro-cell BS or aSSBS. To facilitate our analysis, let M = {1, 2, . . . ,M},N = {1, . . . , N} and K = {1, 2, . . . ,K} denote mmWSBSs,SSBSs and users, respectively. Finally, we define xkm (resp.x′kn) as the association binary variable which is equal to 1 ifand only if the kth user is associated to the mth mmWSBS(resp. to the nth SSBS). Note that, in this paper we study UAto SBSs when each user can be associated to only one BS inthe network.

For mmWave links, we consider, as in [12], the signal-to-noise-ratio (SNR) instead of the signal to interference-plus-noise ratio (SINR). The achievable rate per unit bandwidthfrom the kth user to the mth mmWSBS can be calculated asfollows:

Rkm = log2

(1 +

PmgkmPL−1(dkm)

σ2m

), (1)

where Pm is the transmit power of the mth mmWSBS, gkm isthe mmWave channel gain, PL(dkm) is the path-loss betweenthe kth user and the mth mmWSBS within a distance dkm andfinally σ2

m is the mmWave thermal noise power. In this paper,we use the mmWave path loss model proposed in [1] which

takes into account the quality of link between the user and themmWSBS.

Contrary to mmWSBSs, the communication between sub-BSs will interfere with one another since they share the samesub-6 GHz frequency band. Consequently, the correspondingachievable rate per unit bandwidth between the kth user andthe nth SSBS can be expressed as:

R′kn = log2

1 +γn|g′kn|2

1 +∑

n′∈N∪{0}n′ 6=n

γn′ |g′kn′ |2

, (2)

where γn is the transmit SNR of subBS n and g′kn is thechannel gain between the kth user and the nth subBS.

For practical considerations, the number of RBs that mustbe allocated to each user depends on its required quality-of-service (QoS). More precisely, a higher number of allocatedRBs are needed for a higher QoS demand. To this end, let Qkdenotes the required data rate of the kth user and W (resp.W ′ ) denotes the bandwidth of each mmWave (resp. sub-6GHz) RBs. Using this notations, the minimum number of RBsserved by the mth mmWSBS or by the nth SSBS to the kthuser is given, respectively, by:

bkm =

⌈Qk

WRkm

⌉, (3)

b′kn =

⌈Qk

W ′R′kn

⌉. (4)

Unlike sub-6 GHz communications, mmWave communicationsare highly susceptible to user motion and obstacles, thus, amobility aware UA strategy is proposed in the following.

The main notations are presented in Table I.

III. MOBILITY-AWARE USER ASSOCIATION

This section describes the random way point (RWP) mobil-ity model, that is used in this paper to model the users mobility,and then presents the mobility-aware UA strategy.

A. Random Way Point Mobility Model

In this model, the movement of users is generated asfollows: each user resides in a way-point for a random pausetime and then moves randomly to another way-point. Note thatthe velocity, the mobility direction and the walk interval areall chosen randomly and independently of other users [13]. Toguarantee a constant number of users in the system, when auser leaves the simulation area, he will be replaced by anotheruser generated randomly.

B. User Association Based on Markov Chain

Since mobility affects directly the quality of a communi-cation link, taking into account the mobility in UA decision isrequired in order to overcome the need of frequent update ofassociation and thus the need of frequent handovers betweenBSs. In the considered system model, three types of handoverscan be defined: (i) handover between two different mmWSBSs,(ii) handover between two different subBSs and (iii) handoverbetween one mmWSBS and one subBS.

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The proposed UA strategy is based essentially on estimat-ing the state of each mmWave link, which can be in one ofthree conditions:

• Outage (OUT), denoted by state 0: the link betweenthe user and the mmWSBS is not available.

• Non-line of sight (NLOS), denoted by state 1: thelink between the user and the mmWSBS is partiallyavailable (e.g., due to blockage).

• Line of sight (LOS), denoted by state 2: the linkbetween the user and the mmWSBS is fully available.

UA strategy associates each user according to the linkstate. Precisely, if the probability of OUT is smaller thanthe probability of LOS or NLOS, UA strategy associates thecorresponding user to the mmWSBS. Otherwise, the user isassociated to the subBS. We summarize the UA strategy asfollow:

• Step 1: Calculate the probabilities of the state of eachlink. The state of the link between the kth user and themth mmWSBS depends on the distance dkm. Hence,the probabilities for being in one of the three states(0, 1, and 2) are given, respectively, by [1]:

P0 = max {0, 1− exp(−a0dkm + b0)} , (5)P1 = 1− P0 − P2, (6)P2 = (1− P0) exp(−a2dkm), (7)

where a0, a2 and b0 are constants given in [1]. Thestate probability vectors of the link between the kthuser and the mth mmWSBS is denoted by skm =[P0, P1, P2]. Let S = [skm] be the state probabilityvector of all links (k,m).

• Step 2: Based on Markov chains, calculate the transi-tion probabilities and make approximations of the linkstates. Let S = {0, 1, 2} denotes the set of states. Thetransition probability of going from state i to state j,pi,j , is defined as:

pi,j = Pr[s′ = j | s = i], i, j ∈ S, (8)

where s (resp. s′) denotes the current state (resp. thenext state). The transition probability matrix, T, usedto model the mmWave link states is given by:

T =

[p0,0 p0,1 p0,2p1,0 p1,1 p1,2p2,0 p2,1 p2,2

].

The state transition diagram is shown in Fig. 2.

• Step 3: Given the current state probability vector skmbetween user k and mmWSBS m and the transitionprobability matrix T, we can calculate the next stateprobability vector as skmT. The final state probabilityvector will be used to associate user k to mmWSBSm in order to provide robust and reliable communica-tions.

Algorithm 1 presents the pseudo-code of the proposedUA strategy. More precisely, to take advantage of the largemmWave bandwidth, the proposed UA strategy associates auser to a mmWSBS that requires the minimum number of

0 1

2

p0,2

p0,0

p0,1

p1,0

p1,1

p1,2

p2,2

p2,1

p2,0

Figure 2. A state transition diagram.

Algorithm 1 UA strategyRequire: t, t′,S,B,B′,T,K,M,N, Y, Y ′

1: X← 0, X′ ← 02: k ← 03: repeat4: k ← k + 15: rb← sort in ascending order Bk

6: rb′ ← sort in ascending order B′k7: n← 1, m← 1, a← false8: while n ≤ N and m ≤M and a = false do9: w← find(Bk = rbm), w′ ← find(B′k = rb′n)

10: repeat11: m0 ← w1, n0 ← w′112: skm0

= skm0T

13: if rbm ≤ rb′n and (P2 > P0 or P1 > P0) andtm0≥ bkm0

and 1 +∑i xim0

≤ Ym0then

14: xkm0← 1

15: tm0← tm0

− bkm0

16: a← true, break17: else if t′n0

≥ b′kn0and 1 +

∑i x′in0≤ Y ′n0

then18: x′kn0

← 119: t′n0

← t′n0− b′kn0

20: a← true, break21: else22: remove w1 and w′1 from w and w′, respectively.23: end if24: until w = [ ] and w′ = [ ]25: n← n+ 1, m← m+ 126: end while27: until

(t = 0 and t′ = 0

)or (k = K) or

(∑i xim =

Ym,∀m and∑in x′in = Y ′n,∀n

)28: return X = [xkm],X′ = [x′kn]

RBs and has a probability of outage that is less than the prob-ability of LOS or NLOS. We denote by t = [t1, t2, . . . , tM ]

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(resp. t′ = [t′1, . . . , t′N ]) the RBs thresholds of each mmWSBS

(resp. each SSBS). The maximum numbers of users that canbe associated to mmWSBS m and to SSBS n are given,respectively, by Ym and Y ′n. To ensure an efficient RBsutilization, the proposed algorithm sorts in ascending order,in lines 5–6, the required number of RBs for each mmWSBSand SSBS. The results of these sorting operations are given bythe indexes of the SBSs and are stored in rb and rb′. Then, therepeat loop starts the association procedure between users andSBSs under either no more available RBs, all the users in thenetwork are associated, or the maximum number of associatedusers is reached. After each association, the algorithm, in lines14–15 and 18–19, updates the number of associated users andthe number of remaining RBs in the network.

The computational complexity of the proposed algorithm,for N =M , is O(KM2) in the worst case.

IV. SIMULATION RESULTS

In this section, we validate the performance of the proposedUA strategy for mobile users using Monto Carlo simulations.Simulations consider a two-tier HetNet where the macro-cellBS is located at the center of a circle of radius 300 meterswhereas the SBSs and the users are deployed randomly anduniformly within the circle. The channel sub-6 GHz gains

are modeled as g′kn = hkn

√K0 (dkn/d0)

−α where K0 is aconstant capturing the system and transmission effects, d0 isthe reference distance, dkn is the distance between the kth userand the nth subBS, α is the path-loss exponent, and finallyhkn is a complex Gaussian random variable with zero meanand unit variance. For simplicity of derivation, the mmWavechannel gain gkm is assumed to be equal to the numberof antennas in the mmWSBS denoted by MmmW [14]. Thepropagation model, used to calculate the path-loss is givenby PL(dkm) = ψ + 10κ log10(dkm) + ξ, ξ −→ N(0, υ2),where ψ and κ are the least square fits of floating interceptand slope over the measured distances, and ξ is the log-normal shadowing with variance υ2 [1]. The transition matrixT is calculated based on the user’s motion by counting thenumber of transition between states. Note that, the conditionalprobabilities are averaged over a large number of independentruns. Unless otherwise specified, the QoS demand of each useris set to 1 Mbps. The values used in simulations for the mainparameters are given in Table I.

The proposed mobility-aware UA strategy is compared tothe UA algorithm proposed in [11] with consideration of thesame mobility model. Note that [11] does not consider anyestimate of mmWave channel states.

In Fig 3 and Fig. 4, the importance of taking into ac-counting the quality of mmWave links on the percentageof handovers is shown. Clearly, our proposed UA strategydecreases the percentage of handovers between the mmWSBSsas well as between the subBSs and the mmWSBSs. We canobserve that when K is between 5 and 50, the performancegap between the two curves in Fig 3 is large and exceeds 5 %.

Fig. 4 shows the percentage of handovers between subBSsand between subBSs and mmWSBSs. We can observe thateven for large values of K, the proposed UA strategy reducesthe need of handovers between subBSs and mmWSBSs. It

can be seen that when the mmWave link constraints are notconsidered and the number of users in the network is lessthan 40, the percentage of sub-6 GHz handovers is slightlylower than the percentage of our proposed UA strategy. This isbecause when the mmWave communications are not available,the percentage of associated users to the subBSs increases andconsequently the percentage of sub-6 GHz handovers becomesmore important.

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

Number of users in the network (K)

Perc

enta

geof

hand

over

s

Between mmWSBSs, proposed strategyBetween mmWSBSs, [11]

Figure 3. Percentage of handovers between mmWSBSs versus the totalnumber of users in the network.

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

Number of users in the network (K)

Perc

enta

geof

hand

over

s

Between SSBSs, proposed strategyBetween SSBSs, [11]Between mmWSBSs and SSBSs, proposed strategyBetween mmWSBSs and SSBSs, [11]

Figure 4. Percentage of handovers versus the total number of users in thenetwork.

V. CONCLUSION

This paper focuses on a two-tier hybrid HetNet withmmWave and sub-6 GHz communications. In order to achievereliable and robust mmWave transmissions, a mobility-awareuser-base station association strategy is proposed where themmWave channel states are estimated by using Markov chain

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Table I. NOTATIONS AND VALUE PARAMETERS

Notations Parameters ValuesN Number of SSBSs 3M Number of mmWSBSs 3γ0 Transmit SNR of the macro-cell BS 40 (dB)γn Transmit SNR of SSBS 30 (dB)Pm mmWSBS’s transmit power 30 (dBm)W ′ Bandwidth of sub-6 GHz RB 180 (kHz)W Bandwidth of mmWave RB 2 ∗W ′Wm mmWave bandwidth 1 (GHz)MmmW mmWSBS’s number of antennas 4Y Maximum number of associated users to each mmWSBS 8Y ′ Maximum number of associated users to each SSBS 8tm Total number of RBs for the mth mmWSBS 50t′n Total number of RBs for the nth SSBS 50d0 Reference distance 1 (m)α Path-Loss exponent 4K0 Constant capturing the system and the transmission effects 103

σ2m Thermal noise power for mmWave −174 dBm/Hz+10 log10Wm + 10 (dB)ψ, κ, υ mmWave parameter for NLOS transmission (f = 73 GHz) [1] ψ = 86.6, κ = 2.45 and υ = 8 (dB)ψ, κ, υ mmWave parameter for LOS transmission (f = 73 GHz) [1] ψ = 69.8, κ = 2 and υ = 5.8 (dB)a0

LOS-NLOS-outage probability [1]1/30 (m−1)

b0 5.2a2 1/67.1 (m−1)[0, Pmax] Pause interval [0, 10] (s)[Vmin, Vmax] Velocity interval [1, 3] (m/s)[wmin, wmax] Walk interval [0, 180] (s)HOperiod Handover measurement period 180 (s)

method. Simulation results validate the performance of the pro-posed strategy by reducing the need of frequent re-associationand thus the need of frequent handovers between mmWaveSBSs in the network.

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