On the User Association and Resource Allocation in HetNets with mmwave Base Stations

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1 On the User Association and Resource Allocation in HetNets with mmwave Base Stations Cirine Chaieb, Zoubeir Mlika, Fatma Abdelkefi and Wessam Ajib Department of Applied Mathematics, Signals, and Communications, Higher School of Communications of Tunis {cirine.chaieb, Department of Computer Science, University of Quebec at Montreal Abstract Combining millimeter wave (mmwave) with sub-6 GHz communications is a promising solution for future heterogeneous cellular networks (HetNets) to improve coverage and capacity. This paper studies the user-base station association problem in HetNets with the existence of both sub-6 GHz and mmwave base stations (BSs) where each BS has a limited number of resource blocks (RBs). Motivated by the observation that traditional user- BS association methods may not be effective in such hybrid HetNet, an optimization problem is formulated in order to maximize the number of associated users and to ensure an efficient resource utilization by minimizing simultaneously the number of used RBs. Since the formulated problem is proved to be NP-hard, a heuristic algorithm is proposed. Simulation results show that the proposed algorithm approaches the optimal one with a significant reduction in computational complexity. I. INTRODUCTION The mobile data traffic is expected to grow 53 percent from 2015 to 2020 and the global number of mobileconnected devices will exceed 50 billion in 2020 [1]. To cope with this rapid growth, new technology deployments is necessary for 5G cellular networks. Among them, massive multiple-input multiple-output (MIMO), millimeter wave (mmwave) communication, and dense heterogeneous networks (HetNets). In this paper, we are interested in the integration of HetNet and mmwave. MmWave communication is expected to support data rates of many gigabits per second. However, employing mmwave bands requires dealing with the high rain attenuation, high oxygen absorption and high propagation loss [2]. To achieve robustness using mmwave communication, solutions to these propagation problems have been considered in recent studies. To overcome the high atmospheric attenuation and absorption as well as to imporve capacity and coverage, reducing the cell size less than 200 meters becomes a promising solution [3]. Previous works proved that steerable directional antennas, with high gain in the transmitter and receiver, limits the effects of multi-path and path-loss in mmwave /17/$31.00 c 2017 IEEE communication. Moreover, due to the short wavelengths, mmwave antenna size can be very small, which facilitates the integration of MIMO technique and mmwave. This paper focuses on the user-base station association (UA) problem, called hereinafter UAP, in a hybrid Het- Net, where a macro-cell base station (MBS) is overlaid with small-cell base stations (SBSs) sharing mmwave and sub-6 GHz frequency bands. Several related works study UAP in hybrid HetNets. In [4], a low complexity distributed UA algorithm is proposed to maximize throughput in a massive MIMO hybrid HetNet powered by renewable energy. The authors prove that mmwave communication can ensure significant enhancements compared to massive MIMO. In [5], UA in hybrid HetNet is considered. The authors prove that mmwave communication can improve the rate compared to low frequencies communication. The work in [6] study UA in a sub-6 GHz HetNet with a limited number of time-frequency resource blocks (RBs) to maximize the number of satisfied users. To find a close-to-optimal UA solution, a two-phase method based on a semidefinite relaxation approach is proposed. In [7], the authors maximize the number of satisfied users under signal to interference-plus-noise ratio (SINR) constraints in sub-6 GHz HetNet. They prove that the problem is NP-hard and propose heuristic algorithms to solve it efficiently. Note that, in both [6], [7], the authors do not consider mmwave communication. Traditional UA methods, such as max-sinr, are not effective in HetNets as well as in hybrid HetNets. Hence novel UA algorithms are needed in such networks to overcome the mmwave propagation problems. We propose in this paper a novel UA method for the down-link data transmission. Our main objectives are: (i) maximizing the number of associated users under quality-of-service (QoS) constraints, and (ii) ensuring an efficient resource exploitation. The rest of this paper is organized as follows. Section II presents the system model. Section III formulates

2 the UA problem and studies its NP-hardness. Section IV describes the proposed solutions. Section V presents simulation results and finally the conclusions are given in Section VI. II. SYSTEM MODEL This paper considers a two-tier hybrid HetNet composed of one MBS and a set of SBSs. The MBS uses only the sub-6 GHz frequency bands to ensure a large coverage area. The set of SBSs is devised in two sub-sets, the first consists of sub-6-ghz-sbss (SSBSs) sharing the same frequency bands as the MBS, and the second consists of mmwave-sbss (MSBSs) operating at 60 GHz. In addition, we consider two types of users: Figure 1. An example of a two-tier hybrid HetNet macro-cell users (MUs) and small-cell users (SUs). An example of the system model is given in Fig. 1. The MBS and the MUs are indexed by 0. Let M = {1, 2,..., M}, N = {1, 2,..., N} and K = {1, 2,..., K} denote the sets of MSBSs, SSBSs and SUs, respectively. We assume that every MSBS is equipped with M mmw directional antennas and the SUs use mmwave frequency bands when there is no blockage and switch to sub-6 GHz frequency bands otherwise. We denote the transmit power of the MBS, MSBS m and SSBS n by P 0, P m and P n, respectively. Finally, to model UAP as an integer linear program (ILP), two binary variables are introduced as follows: x km = 1 if and only if the kth SU is associated to the mth MSBS and x kn = 1 if and only if the kth SU is associated to the nth SSBS. Let X = [x km ] and X = [x kn ] denote the matrices representation of the variables x km and x kn, respectively. Since the MBS and the SSBSs operate on the same frequency bands, their communication will interfere with each other. Hence, when the kth user is associated to the nth SSBS, the received SINR can be calculated as: γ n g kn SINR kn = 1 +, (1) n N {0} γ n g kn n n where γ n = P n /σ 2 is the transmit signal to noise ratio (SNR) of BS n and σ 2 is the thermal noise power level for sub-6 GHz. The channel gain between the kth user and the nth SSBS g kn is given by: g kn = h kn K 0 ( Rkn d 0 ) α 2, (2) where K 0 is a constant capturing the system and transmission effects, d 0 is the reference distance, R kn is the distance between the kth user and the nth SSBS, α is the path-loss exponent, and h kn is a Gaussian random variable with zero mean and unit variance. Note that the computation of the interference is based on the worstcase scenario when all sub-6 GHz BSs are transmitting as in [8]. It is well-known that mmwave communication is noise-limited [9]. Hence, SNR is considered instead of SINR. Thus, the received SNR, γ km, between the kth user and the mth MSBS is given by: γ km = P mg km P L 1 (R km ) σm 2, (3) where P L 1 (R km ) denotes the path-loss between the kth SU and the mth MSBS that are within a distance of R km from each other. The propagation model used to calculate the path-loss is given by [3]: P L(R km ) = ψ + 10κ log 10 (R km ) + ξ, ξ N(0, υ 2 ), (4) where ψ and κ are the least square fits of floating intercept and slope over the measured distances, and ξ is the log-normal shadowing with variance υ 2. We assume that each MSBS uses analog beamforming with phase shifters. We consider an uniform planar square antenna, and the effective antenna gain for each MSBS with the beamwidth θ = 2π/ M mmw, which is the relative power radiated by the mth MSBS in the direction of the user. The antenna gain between the kth user and the mth MSBS is given by [4]: g km = { MmmW, with probability θ/2π 1 / ( ) sin 2 3π 2, with probability 1 θ/2π M mmw For simplicity of derivation, the antenna gain g km is assumed to be equal to M mmw. The achievable rate from the kth SU to the mth MSBS and to the nth SSBS can be calculated using Shannon theorem, respectively, as follows: (5) R km = log 2 (1 + SNR km ), R kn = log 2 (1 + SINR kn ). (6) In practice, each BS allocates a certain number of RBs to its associated users. The number of RBs allocated to each SU depends on its required QoS and the corresponding associated SBS. Thus, the minimum number of RBs.

3 served by the mth MSBS or by the nth SSBS to the kth SU is given, respectively, by: Qk b km =, b Qk kn = W R km W R kn, (7) where W and W denote the bandwidth of mmwave and sub-6 GHz RB, respectively, Q k is the required data rate of the kth SU, and. refers to the ceiling function. For an efficient resource allocation, the demand of each SU must be at most the achievable rate from its associated SBS. Thus, the QoS constraint of the kth SU when it is associated to the mth MSBS or to the nth SSBS can be expressed, respectively, as: Q k x km R km, k K, m M, (8) Q k x kn R kn, k K, n N. (9) The total number of RBs used is the sum of all allocated RBs by the MSBSs and the SSBSs, which is equal to: b knx kn. (10) m M b km x km + n N The main notations are summarized in Table I. III. USER ASSOCIATION PROBLEM This section starts by formulating UAP and then studying its NP-hardness. A. Problem Formulation The objective of UAP is to maximize the number of associated SUs as well as to minimize the number of used RBs. This objective is studied in [6], [7], [10] where hybrid communications are not considered. UAP can be formulated as the following ILP: maximize X,X ρ x km (1 ρ) b km x km m M m M + ρ x kn (1 ρ ) n N n N (P1a) b knx kn subject to x km, x kn {0, 1}, k K, m M, n N, (P1b) b km x km t m, m M, (P1c) b knx kn t n, n N, x km + m M n N x km S, m M, x kn S, n N. x kn 1, k K, (P1d) (P1e) (P1f) (P1g) where ρ and ρ are two tuning factors that belong to the interval [0, 1]. Constraints (P1c) and (P1d) ensure that the total number of RBs used by the mth MSBS and by the nth SSBS does not exceed given RB thresholds t m and t n, respectively. Constraints (P1e) ensure that each SU is associated exactly to one SBS, and finally constraints (P1f) and (P1g) indicate that the maximum number of SUs that can be associated to the MSBS and SSBS does not exceed given values S and S, respectively. Note that ρ and ρ guarantee a certain balance between the number of expanded RBs and the number of associated SUs. More specifically, when ρ and ρ are close to 1 (resp. to 0), the objective is to maximize the number of SUs associated to the SBSs (resp. to minimize the number of mmwave and sub-6 GHz RBs used). From [10], the optimal values of these tuning factors are given by: ρ opt [ m M t m 1 + m M t, 1 m B. NP-hardness ], ρ opt [ n N t n 1 +, 1 n N t n ]. (11) In this subsection, we prove that UAP is NP-hard by showing that a special case of it is NP-hard. Lemma 1: UAP is NP-hard. Proof: We prove that UAP is NP-hard by restriction, that is, we reduce the generalized assignment problem (GAP) [11] to a special case of UAP in polynomial-time. In GAP, we are given a set of items and a set of bins where each bin j has capacity c j and for each item i and bin j, there is a weight w ij. The objective of GAP is to assign the maximum possible number of items to the bins such that each bin does not exceed its capacity. An instance of UAP can be constructed as follows: Let S = N, S = 0, ρ = 0, M =, and ρ = 1. Under this restriction, UAP is equivalent to maximizing the number of associated users to the SSBSs subject to the capacity constraint of each SSBS. Hence, by analogy, if the SSBSs represent the bins and the users represent the items, UAP becomes equivalent to GAP. This proves the lemma. Since UAP is NP-hard, it is unlikely to find an optimal polynomial-time algorithm to solve it. Moreover, solving the corresponding ILP in (P1) using branch-and-bound approaches is computationally infeasible. Consequently, to alleviate the computational complexity, a heuristic UA algorithm (HUA) is proposed. Note that HUA is compared to the optimal algorithm (OPT) obtained by solving (P1) using IBM ILOG CPLEX solver under MATLAB. IV. PROPOSED HEURISTIC ALGORITHM In the following, we present HUA. The notations used in the algorithm are as follows. We use upper-case bold letters to denote matrices. The ith row (resp. ith column) of matrix A is denoted by A i (resp. A i ). Lower-case bold letters are used to denote vectors. The main idea of HUA is to start by associating the users to the SBSs that have the minimum number

4 Algorithm 1 HUA algorithm Require: t = [t 1,..., t m ], t = [t 1,..., t n], B = [b km ], B = [b kn ], K, M, N, S, S 1: X 0, X 0 2: i 0 3: repeat 4: i i + 1 5: v sort B i in ascending order 6: v sort B i in ascending order 7: n 1, m 1, a 0 8: while n N and m M and a = 0 do 9: w find(b i = v m ), w find(b i = v n) 10: repeat 11: m 0 w 1, n 0 w 1 12: if v m v n and t m0 b im0 and sum(x m0 ) + 1 S then 13: x im0 1 14: t m0 t m0 b im0 15: a 1, break 16: else if t n 0 b in 0 and sum(x n 0 ) + 1 S then 17: y in0 1 18: t n 0 t n 0 b in 0 19: a 1, break 20: else 21: remove w 1 and w 1 from w and w, respectively. 22: end if 23: until w = [ ] and w = [ ] 24: n n + 1, m m : end( while 26: until t = 0 and t = 0 ) ( or (i = K) or sum(x) = S and sum(x ) = S ) 27: return X, X of required RBs and giving more priority to mmwave communications. In lines 1 2, HUA sets the association matrices X and X to the empty matrices, and the counter i, which counts the number of associated users so far, to 0. Next, in line 3, the repeat loop starts the association procedure between SUs and SBSs. In lines 5 6, HUA sorts in ascending order the minimum number of required RBs of each SSBS and MSBS. In other words, HUA starts associating the users that require the least number of RBs and iterates the SBSs as long as there is no association yet (see the while loop in line 8). The two vectors w and w, in line 9, contain the indexes of MSBSs and SSBSs which have the same number of required RBs, respectively. To minimize the number of used RBs, HUA starts using the minimum number of required RBs and it checks if the available RBs are sufficient and the maximum number of associated SUs is not yet reached (see line 12). After each association, the remaining RBs and the total number of associated Table I NOTATION AND VALUE PARAMETERS Notation Parameter Value γ0, γn Transmit SNR of MBS and SSBS, resp. 40 db, 30 db, resp. W, W Bandwidth of sub-6 GHz and mmwave RB, resp. 180 khz, 2 W, resp. MmmW Number of antennas of MSBS 4 Wm mmwave bandwidth 1 GHz S, S Maximum number of SUs per MSBS and SSBS, resp. 8, 8, resp. tm, t n Total number of RBs for MSBS m and SSBS n, resp. 50 RBs, 50 RBs, resp. Pm MSBS s transmit power 30 dbm d0 Reference distance 1 m α Path-Loss exponent 4 σm 2 Thermal noise power for mmwave 174 dbm/hz+10 log 10 Wm + 10 db Model parameter (f = 73 GHz) NLOS LOS ψ = 86.6, κ = 2.45 and υ = 8 db [3] ψ=69.8, κ=2 and υ=5.8 db [3] SUs are updated. The while loop terminates either when HUA finds a possible association, or it does not find an available SBS any more. HUA continues in the same way and it halts when: (1) there are no more available RBs, (2) all the SUs in the network are associated, or (3) the maximum number of associated SUs is reached. The computational complexity of the proposed heuristic algorithm is O((K + 2M 2 )M 2 ) in the worst case when N = M. V. SIMULATION NUMERICAL RESULTS In this section, we present simulation results by using Monte Carlo simulations to evaluate the performance of HUA. The results are calculated over 10 4 channel realizations and averaged out. We consider a two-tier HetNet composed of one MBS, three MSBSs and three SSBSs. The location of the MBS is assumed to be in the center of a circle of radius 300 meters, whereas the locations of the SUs and the SBSs are generated uniformly at random within the circle. Unless otherwise specified, the constant K 0 is set to 10 3 and the QoS demand of each user is set to 1 Mbps. Other important simulation parameters are shown in Table I. The tuning factors ρ opt-min and ρ opt-min are given, respectively, by m M t m/(1 + m M t m) and n N t n/(1 + n N t n). The performance of HUA is compared to the performance of OPT, an optimal algorithm provided by solving the ILP in (P1) using IBM ILOG CPLEX solver. Fig. 2 shows the percentage of associated SUs versus the total number of SUs. We can observe that when K is small (less than 25), HUA is tightly close to OPT with an important reduction in the computational complexity. As K increases, the percentage of the associated SUs of both HUA and OPT decreases. It is important to note that the performance of HUA is always close to OPT even for large values of K. For instance, the gap between the two algorithms is less than 10 % for K = 100. This is due to the limited number of associated SUs to each SBSs and to the limited number of RBs in the network as can be seen from the constraints (P1c), (P1d), (P1f) and (P1g). Fig. 2 shows also that the mmwave association in

5 HUA converges quickly to OPT whereas the sub-6 GHz association approaches OPT only as K increases. Fig. 3 illustrates the percentage of the associated SUs for different values of ρ and ρ when K = 100. It validates the theoretical result for the values of tuning factors ρ and ρ shown in (11). In fact, as long as ρ and ρ are in the intervals given by (11), OPT does not change. Also, note the significant improvement resulted from HUA even for ρ = ρ = 1. Fig. 4 shows the impact of the tuning factors ρ and ρ in terms of the percentage of expended RBs. We can see that when ρ = ρ = 1, i.e., we do not optimize the number of used RBs, HUA slightly outperforms OPT as the former uses less number of RBs especially when K is not large. Moreover, when ρ and ρ are chosen optimally, OPT uses efficiently the available RBs. Fig. 3 and Fig. 4 confirm the effectiveness of ρ and ρ on both minimizing the utilization of RBs and maximizing the number of satisfied SUs. VI. CONCLUSION In this paper, we investigated the user-base station association and the resource allocation problem in a hybrid HetNet with sub-6 GHz and mmwave communications. The formulated problem targeted to maximize the number of associated users under an efficient utilization of resources in the network. Since this problem is NP-hard, we proposed an efficient heuristic algorithm to solve it in a polynomial-time. Numerical results highlighted that the proposed algorithm gives near-to-optimal performance with a highly alleviated complexity. For future work, we will focus on the beamforming designs and the interference alignment techniques for MIMO systems to reduce the mmwave propagation problems. Figure 2. SUs. Figure 3. SUs. Percentage of associated SUs versus the total number of Percentage of associated SUs versus the total number of REFERENCES [1] Cisco, Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, , [2] T. S. Rappaport, J. N. Murdock, and F. Gutierrez, State of the Art in 60-GHz Integrated Circuits and Systems for Wireless Communications, Proc. IEEE, vol. 99, no. 8, pp , Aug [3] M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, and E. Erkip, Millimeter Wave Channel Modeling and Cellular Capacity Evaluation, IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp , Jun [4] B. Xu, Y. Chen, M. Elkashlan, T. Zhang, and K.-K. Wong, User Association in Massive MIMO and mmwave Enabled HetNets Powered by Renewable Energy, in Proc. IEEE Wireless Commun. and Netw. Conf. (WCNC), Sept. 2016, pp [5] H. Shimodaira, G. K. Tran, K. Araki, S. Nanba, T. Hayashi, K. Sakaguchi, and S. Konishi, Cell Association Method for Multiband Heterogeneous Networks, in Proc. IEEE Personal Indoor and Mobile Radio Commun. (PIMRC), Sept. 2014, pp [6] H. U. Sokun, R. H. Gohary, and H. Yanikomeroglu, QoS- Guaranteed User Association in HetNets via Semidefinite Relaxation, in Proc. IEEE Veh. Technol. Conf. (VTC Fall), Sept. 2015, pp [7] Z. Mlika, M. Goonewardena, W. Ajib, and H. Elbiaze, User- Base Station Association in HetSNets: Complexity and Efficient Algorithms, IEEE Trans. Veh. Technol., vol. 66, no. 2, pp , Feb Figure 4. Percentage of used RBs versus the total number of SUs. [8] E. Pollakis, R. L. Cavalcante, and S. Stańczak, Base Station Selection for Energy Efficient Network Operation with the Majorization-Minimization Algorithm, in Proc. IEEE Signal Process. Advances in Wireless Commun. (SPAWC), Jun. 2012, pp [9] H. Elshaer, M. N. Kulkarni, F. Boccardi, J. G. Andrews, and M. Dohler, Downlink and Uplink Cell Association with Traditional Macrocells and Millimeter Wave Small Cells, IEEE Trans. Wireless Commun., vol. 15, no. 9, pp , Sept [10] E. Matskani, N. D. Sidiropoulos, Z.-Q. Luo, and L. Tassiulas, Convex Approximation Techniques for Joint Multi-User Downlink Beamforming and Admission Control, IEEE Trans. Wireless Commun., vol. 7, no. 7, pp , Jul [11] C. Chekuri and S. Khanna, A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem, SIAM Journal on Computing, vol. 35, no. 3, pp , 2005.