Green Downlink Radio Management Based Cognitive Radio LTE HetNets

Transcription

1 Green Downlink Radio Manageent Based Cognitive Radio LTE HetNets Ahad Alsharoa, Ahed E. Kaal Departent of Electrical and Coputer Engineering, Iowa State University (ISU), Aes, Iowa, USA, Eail: {alsharoa, Abstract In this paper, the proble of radio and power resource anageent in underlay cognitive radio heterogeneous networks is investigated, where acro and pico Base Stations (BSs) are considered as priary BSs while feto BSs are considered as secondary BSs. The goal is to iniize the total priary power consuption and axiize the secondary utility of the network while satisfying the priary user quality of service deterined by target data rate and interference constraints. Furtherore, a green counication algorith is ipleented based on a sleeping strategy. Siulations study investigates the perforance of the proposed schee and shows an iportant saving in ters of total power consuption. Index Ters Cognitive radio, heterogeneous networks, sleeping strategy. I. INTRODUCTION Green counications and energy efficiency in wireless counication networks has attracted the interest of researchers recently [1]. In fact, downlink counication in cellular networks accounts for over 7% of the total energy consuption in the network [2]. Several schees were proposed to save the energy consuption using dynaic Base Stations (BSs) switching-on/off saving strategies. The proposed schees in the literature tried to reduce the downlink power consuption by switching off BSs during their off-peak hours when data traffic is low [3]. The work presented by Koudouridis et. al in [4] proposed a siulated annealing-based algorith to turn on-off BSs in a Heterogeneous Networks (HetNets). The authors in [5] introduced two node switching odes which operate on an interediate and fast tie scale in order to exploit short/long idle periods of the BSs. Two heuristic switching ON/OFF approaches were proposed in [6], where equal power distribution is considered. Since ost of the wireless data traffic takes place in indoor environents, obile users ay have difficulty in receiving high data rates fro Macrocell Base Stations (MBSs) due to the penetration loss. Sallcell technology, including Pico Base Stations (PBSs) and Feto Base Stations (FBSs), which is short range and low cost is designed to handle the high aount of traffic with a low power consuption. However, all aforeentioned green techniques did not consider crossinterference in their syste odel. In addition to that they are liited to the sleeping strategies without optiizing neither the transitted power nor the resource allocation. On the other hand, Cognitive Radio (CR) has been proposed recently to solve the spectru scarcity proble. The concept of the CR is that the secondary users are allowed to allocate soe priary spectru opportunistically [7]. Few schees in the literature cobine the CR concept with HetNets by considering the FBSs and their corresponding users as a secondary network [8], [9]. For instance, the work in [8] assued overlay CR, where the priary users ay release soe bandwidth for the secondary transission. Thus, the interference between priary and secondary networks is negligible. In [9], the authors assued underlay CR, where secondary users access the spectru siultaneously with the priary users under soe interference liitation constraints to aintain a certain Quality-of-Service (QoS) of the priary transission, and they proposed an iterative algorith to solve the resource allocation proble for the uplink transission. However, to the best of the authors knowledge, the downlink proble of priary and secondary resource and power anageent for HetNets including priary BSs eploying sleeping strategy and secondary BSs has not been discussed so far, which is what we address in this paper. Therefore, our contributions in this paper can be suarized as follows: (i) Forulating a downlink optiization proble for CR-HetNets that ais to iniize the total priary power consuption of the network and axiize the secondary rate utility, taking into account the BSs power budget, the QoS for each priary user, and the interference between priary and secondary BSs; (ii) Ipleenting a green counication algorith for priary BSs based on a sleeping strategy; (iii) Proposing a two step allocation coputationally efficient procedure for resource allocation; and (iv) Deriving closed for expressions for the priary and secondary BSs power where three different secondary utility functions are considered depending on the level of fairness aong the secondary users. The reinder of the paper is organized as follows. Section II investigates the CR-HetNets syste odel. The priary proble forulation and solution is given in Section III. Section IV gives the secondary proble forulation and solution. The nuerical results are discussed in Section V. Finally, the paper is concluded in Section VI. II. SYSTEM MODEL We consider a cognitive Long-Ter Evolution (LTE) CR- HetNets syste odel, where the secondary FBSs share the spectru with the priary MBSs and PBSs. The geographical area of interest is subdivided to M hexagonal cells of equal sizes. It is assued that at each hexagonal cell,, one MBS is placed in the center of cell and L PBSs are distributed at the edges as shown in Fig. 1. Also, we assue F FBSs are distributed uniforly inside the cell. Let us define the total nuber of priary and secondary users as U tot and K tot, respectively, where U tot = M =1 U and K tot = M =1 K. U and K are the nuber of priary and secondary users per cell, respectively.

2 Fig. 1: Priary heterogeneous network. MBS PBS Macro FP Pico FP 1 Pico FP 2 Pico FP log 1 d ou in, log 1 d in in +.3d in + L ow ), where d ou in is the distance traveled outdoor between the outdoor user and the building external wall, d in is the indoor traveled distance between the building wall and FBS, and L ow is an outdoor-indoor penetration loss. 3) Outdoor-outdoor pathloss: The pathloss in db between an outdoor user and its MBS or PBS is given by PL = log 1 d ou ou, where d ou ou is the outdoor distance between the outdoor user and its corresponding MBS or PBS. 4) Indoor-outdoor-indoor pathloss: The pathloss in db between an indoor user and a FBS that is not serving it is given by PL = ax( log 1 d ou in, log 1 d in in +.3d in + L ow +.3d in,1 +.3d in,2 + 2L ow ), where d inf is the indoor traveled distance between the building wall and FBS f. The channel gain, which is the ration between the user u and the BS over n, can be expressed as: In LTE, orthogonal frequency division ultiple access (OFDMA) is the access schee for the downlink. The available spectru is divided into Resource Blocks (s) consisting of 12 adjacent subcarriers. Each has a bandwidth of B = 18 KHz while each subcarrier has a bandwidth of 15 KHz [1]. We denote by N (BS) the nuber of available s at the BS. It is assued that each FBS is equipped with two transceivers: one for priary spectru sensing to detect the spectru holes in order to utilize the and the other transceiver is for the cognitive data counication. Hence, FBSs use the latter transceiver for underlay cognitive transission. Finally, we ake the following assuptions: (i) A user is served by at ost one BS (either MBS, PBS, or FBS) with a unique. (ii) Using the Frequency Partitions (FP) technique shown in Fig. 1, there is no inter-tier interference on the downlinks of MBSs and PBSs as they are using different sets of orthogonal s. (iii) The reaining interference can be categorize as: 1) inter-tier interference between secondary BSs and priary BSs that are using the sae sets of s; 2) intra-tier interference between PBSs and neighboring PBSs that are in the sae cell and using the sae sets of s. As will be shown in the sequel, the forer interference can be solved by respecting a certain priary interference threshold I th [11]. The latter interference issue can be solved using resource allocation algorith. In our fraework, we assue that the priary and secondary proble are solved for different phases and repeated every tie slot. Also, it is assued that the channel gains are constant during the coherence tie. A. Pathloss and Channel Model Different pathloss odels are eployed in our syste odel and given as follows (assuing that all the distances in this paper are given in eters) [12] 1) Indoor-indoor pathloss: The pathloss in db between an indoor user and its serving FBS is given by PL = log 1 d in in +.3d in in, where d in in is the indoor distance between indoor user and its corresponding FBS. 2) Outdoor-indoor pathloss: The pathloss in db between an outdoor user and its FBS is given by PL = ax( h n,bs,u = 1 P L BS,u ξ BS,u +1 log 1 F n,bs,u 1, (1) where ξ BS,u captures log-noral shadowing with zero-ean and a standard deviation σ ξ. F n,bs,u corresponds to Rayleigh fading power between user u and the BS over n, with a Rayleigh paraeter a such that E{ a 2 } = 1. Fast Rayleigh fading is assued to be approxiately constant over the subcarriers of a given, and independent identically distributed over s. B. Base Station Power Model We consider that only MBSs and PBSs can be set in active or sleep ode. While FBSs are always considered to be in the active ode. In the active ode, the BS is serving a certain nuber of users connected to the network. The power consuption of a BS corresponding to this ode, noted P BS, can be coputed as follows: P BS = a BS P tx BS + b BS, (2) where a BS corresponds to the power consuption that scales with the radiated power due to aplifier and feeder losses and b BS odels an offset of site power which is consued independently of the average transit power and is due to signal processing, battery backup, and cooling. In (2), P tx BS = (BS) N n=1 P n,bs, denotes the radiated power of the BS, which corresponds to the su of the radiated power over the s P n,bs, n = 1,, N (BS) and depends on the state. The value of P n,bs greater than if n of the BS is allocated to a certain user and otherwise. Note that a BS and b BS differ fro one BS to another depending on the type of the BS. III. PRIMARY PROBLEM FORMULATION AND SOLUTION We assue that the priary BS forces the received crosstier interference to not exceed a fixed interference threshold. Therefore, the achievable data rate of user u served by a priary BS over n in cell can be given as R n,j,u = B log 2 (1 + SINR n,j,u), (3)

3 where SINR n,j,u is signal-to-interference-plus-noise-ratio and is given by SINR n,j,u = ɛ n,j,u P n,j hn,j,u I th +N. Pn,j is the priary BS j transitted power allocated to n in cell, while ɛ n,j,u is a binary variable that is equal to 1 if priary user u is allocated the n of BS j in cell and otherwise. N = N B is the background noise power, where N is the noise power density. The rate in (3) is considered to be the worst case scenario or a lower bound of the priary rate as the interference threshold, I th, ay not be reached by the secondary BSs. Consequently, the actual priary user achieved rate is greater or equal to this lower bound and it is ainly derived by considering the actual secondary interference instead of I th. Therefore, our optiization proble OP 1 that ais to iniize the total power consuption using the sleeping strategy, while satisfying a certain priary QoS is forulated as follows OP 1: M L U N (j) iniize πj a j ɛ n,j,upn,j + b j π,ɛ,p U subject to: N (j) u=1 n=1 N L (j) U u=1 j= n=1 ɛ n,j,u 1, =1 j= u=1 n=1 (4) ɛ n,j,up n,j P j, = 1,.., M, j =,.., L, (5) R n,j,u R th, u = 1,.., U, = 1,.., M, (6) = 1,.., M, j =,.., L, n = 1,.., N (j), where (5) and (6) represent the priary peak power and priary iniu user rate constraints, respectively. Equation (7) ensures that each priary user is served by at ost one BS with a unique. Note that index j represents the MBS if j = and the PBS otherwise. πj is a binary variable that is equal to if the BS j in cell is turned off; otherwise, πj = 1. The forulated OP 1 given in (4)-(7) is a nonconvex proble and considered as NP-hard proble due to the existence of the binary variables, hence, we propose to solve it in three steps. Firstly, we start with a feasible power and switching binary variable vector (i.e., π) to find the s allocation iteratively. We then derive closed-for expressions of the optial priary powers allocation. Finally, greedy sleeping algorith is applied. A. Allocation Given feasible powers and switching binary variables, the allocation proble can be solved heuristically in polynoial tie since the objective function is onotonically increasing with the SINR. We can find a solution by assigning ɛ n,j,u (op) = 1 to user with the axiu SINR n,j,u, and ɛ n,j,u (op) = for all other users in cell and eliinate the n. This process is repeated for all users and all cells until all priary users assigned to a unique n or no ore s are available. Algorith 1 suarizes the -user allocation at each cell to obtain the optial ɛ n,j,u (op). (7) Algorith 1 to User Allocation at Each cell 1: Initialization: Set ɛ n,j,u =, = 1,.., M, j =,.., L, n = 1,.., N (j) 2: Allocation: 3: for u = 1,, U ( do ) 4: u(op) = argax SINR n,j,u. u 5: ɛ n,j,u(op) = 1. 6: end for B. Power Allocation. We can solve our convex power optiization proble for fixed binary variables (i.e.,π, ɛ) by exploiting its strong duality [13] by finding the Lagrangian ultipliers that axiize the dual proble as follows axiize λ,µ iniize P L(λ, µ), (8) where L(λ, µ) is the Lagrangian function. λ and µ are Lagrangian vectors that contain the Lagrangian ultipliers associated with constraints (5) and (6), respectively. Hence, by solving (8), the optial power Pn,j (op) can be given as follows P n,j(op) = [ µ u B (a j + λ j ) ln 2 I th + N h n,j,u ] +, (9) where [x] + = ax(, x). We can eploy the subgradient ethod to find their optial values and thus the optial solution of the proble, see [14] for ore details. C. Sleeping Algorith Let us define the total QoS threshold as the ratio between the nuber of priary users in outage divided by the total nuber of users for all cells (i.e., Uout U tot γ out ) [6], where γ out denotes the tolerated priary outage threshold. The basic idea of the algorith is to eliinate redundant MBSs and/or PBSs without affecting the priary QoS. Firstly, at each iteration, the algorith switches off one priary BS of the total priary BSs in the network and then verify whether the total QoS threshold is satisfied or not. If it is satisfied, the priary BS can be eliinated. Then, the algorith finds the eliinated BS that provided the lowest total power consuption and eliinate it. This procedure is repeated until no change can be ade. The priary resource allocation with sleeping strategy algorith can be suarized in Algorith 2. IV. SECONDARY PROBLEM FORMULATION AND SOLUTION Let us assue that the nuber of feto users are less than or equal to the total nuber of the available s in cell (i.e., K N () ). Thus, the achievable data rate of secondary user k served by FBS f over n can be given as R n,f,k = B log 2 ( 1 + SINR n,f,k ), (1) where SINR n,f,k = κ n,f,k P n,f h n,f,k I, I n,j +N n,j is the cross-tier interference fro the priary network to the secondary network and given by In,j = U u=1 ɛ n,j,u (op)p n,j (op)h n,j,u. is a binary variable that is equal to 1 if secondary user κ n,f,k

4 Algorith 2 Priary Resource Allocation with Sleeping Strategy Algorith 1: Initially, all the priary BSs (MBS and PBSs) in all the cells are assued to be switched on where S contains all priary BSs and L tot is the total nuber of priary BS in the network. 2: while Not converge do 3: Apply Algorith 1 to find the user- allocation. 4: Find the optial power allocation using (9) to calculate the total optial power P using (4). 5: end while 6: Set S = S P tot = P. 7: for l = 1,.., L tot do 8: Eliinate BS l fro S. 9: Repeat Step 2- Step 5 to find P tot,l. 1: if Uout U tot γ out then 11: BS l can be eliinated. 12: else 13: BS l can not be eliinated. 14: end if 15: end for 16: Find the eliinated BS l that provided the lowest total power, i.e.,p tot,l = in(p tot,l ). 17: if P tot,l P tot then 18: BS l is eliinated. 19: P tot = P tot,l. 2: S S\{l }. 21: else 22: No ore changes can be ade. 23: end if 24: The final optial BS set is S, the final iniu total power is P tot. k is allocated the n of FBS f in cell and otherwise. Let Γ(Rn,f,k ) denote the rate utility of the secondary network in cell. By assuing that FBSs can serve the secondary users only (i.e., working as open ode BSs for secondary users and close ode BSs for priary users), the optiization proble of secondary fetocells that axiize the rate utility while satisfying specific power budget and interference threshold constraints can be divided to parallel optiization probles at each cell and forulated as OP 2: axiize κ,p s subject to: K N () k=1 n=1 F K N () f=1 k=1 n=1 F f=1 Γ ( Rn,f,k ) (11) κ n,f,kp n,f P f, f =,.., F, (12) κ n,f,kpn,f 1 I th, δ + U (13) ɛ n,j,u (op) u=1 κ n,f,k 1, f = 1,.., F, n = 1,.., N (), (14) where (12) and (13) represent the secondary power budget and( cross-tier interference ) constraints. In (13), the factor 1/ δ + U ɛ n,j,u (op) is equal to 1 if the n is occupied u=1 by any priary user, and very high value (i.e., neglected constraint) otherwise, where δ is a very sall nuber. Equation (14) is to ensure that each feto user is served by at ost one FBS with a unique in cell. A. Utility Selection In this section, we investigate different utility etrics that will be eployed in our secondary optiization proble. Max C/I Utility: The utility of this etric is equivalent ( ) to the su data rate of the cognitive network Γ = K k=1 R n,f,k Rn,f,k. This approach is known in the literature as Max C/I [15] as it prootes users with favorable channel and interference conditions by allocating to the ost of the resources. Max-Min Utility: Due to the unfairness of Max C/I resource allocation, the need for ore fair utility etrics arises. Max- Min utilities are a faily of utility functions attepting ( ) to axiize the iniu data rate in the network Γ Rn,f,k = in(rn,f,k ) [16]. By increasing the priority of users having k lower rates, Max-Min utilities lead to ore fairness in the network. In order to siplify the proble for this approach, we define a new decision variable R in = in(rn,f,k ). k Therefore, our optiization proble becoes axiize κ,p s,r in R in (15) subject to: Rn,f,k R in k = 1,..., K, (16) (12), (13), (14). Proportional Fair Utility: A tradeoff between the axiization of the su-rate and the axiization of the iniu rate could ( be ) the axiization of the geoetric ean data rate Γ Rn,f,k = ( K k=1 R n,f,k )1/K which is equivalent to ( ) Γ Rn,f,k = K k=1 ln(r n,f,k ) [17]. The proportional fair (PF) etric is fair, since a user with a data rate close to zero will ake the whole product go to zero. Hence, any axiization su-rate algorith would avoid having any user with very low data rate. In addition to this, the etric will reasonably proote users with good wireless channels (capable of achieving high data rates), since a high data rate will contribute in increasing the product. B. Secondary Optiization Proble Solution We can solve our secondary optiization proble in two steps. Firstly find the secondary allocation (i.e., find κ vector) using Algorith 1 by applying it to the FBSs. We can then solve our convex optiization proble for fixed κ n,f,k and iterate until converge. Siilar to the priary power allocation, by exploiting the strong duality the secondary power allocation for the Max C/I, Max-Min, PF utilities can be given respectively as [ Pn,f B (op) = (ζf + ρ ) ln 2 I n,j + N ] +, (17) h n,f,k [ Pn,f η k B (op) = (ζf + ρ ) ln 2 I n,j + N ] +, (18) h n,f,k

5 P n,f (op) = ( B (ζ f + ρ ) ln 2 K q=1 q k Rn,f,q I n,j + N ) +, h n,f,k (19) where ζf and ρ represent the Lagrangian ultipliers related to the peak power budget constraint and interference constraint, respectively. Equation (18) includes also η k the Lagrangian ultiplier related to constraint (16) if the Min- Max utility is used. We can see fro (17) that in Max C/I approach, all resources are allocated to the secondary users with favorable channel and interference conditions. By coparing (18) with (17), we can see that η k values control the priority of the power resource allocation. However, enhancing the worst case channel conditions (i.e., corresponding to the iniu rate achieved) could coe at the expense of users with good channel conditions which leads to ore fairness between the secondary users. In (19), a tradeoff between C/I and Max-Min approaches can be clearly deduced. The FBS transission power depends directly on the product of the other user rates. This approach tries to avoid having any user with very low data rate and axiize the product of the secondary rates siultaneously. V. SIMULATION RESULTS We consider 7 hexagonal LTE cells each with radius equal to 1 k. The priary network consists of one MBS at the center of each hexagonal cell and 6 PBSs distributed at the edges of each cell as shown in Fig. 1. The secondary network consists of 7 FBSs which follow a unifor distribution and are distributed in the area of interest with 3 users inside each FBS, hence, K tot = 21. An orthogonal LTE transission is assued where the bandwidth of each FP is equal to 1 MHz (i.e.,equivalent to 5 orthogonal s) as shown is Fig. 1. By eploying OFDMA with the allocation algorith presented in Algorith 1, we assue that all users connected with a PBS within the cell are protected fro the co-channel interference caused by other PBSs as they are deployed sparsely. The axiu transission power for MBS, PBS, and FBS are equal to 46 db, 3 db, and 2 db, respectively. We set the tolerated priary outage threshold to be γ out =.5 and penetration loss to be L ow = 2 db [12]. We also set a = W and b = W for MBSs and a j = 7.4 W, b j = 71 W for PBSs. The shadowing standard deviation and noise power density are given as σ ξ = 8 db, N = 174 db/hz, respectively. Fig. 2 copares the perforance of the proposed schee with the traditional case when all priary BSs are kept active and with unifor power distribution where equal power transission over the s is assued. It is assued that the priary data rate and the priary interference thresholds are equal to R th = 1 Mbps and I th = 2 db, respectively. For instance, coparing to the traditional case, when all priary BSs are active and optial power allocation is applied, we can see that the proposed schee offers a significant aount of energy saving by switching off the redundant priary BSs. Indeed, during the low traffic where the nuber of priary users is equal to U tot = 1, the total power consuption Total Priary Power Consued [Watt] Nuber of Active Priary BSs Unifor Power without Sleeping Algorith Optial Power without Sleeping Algorith (a) Without Sleeping Algorith (b) Total Nuber of Priary Users Fig. 2: (a) Total priary power consuption, (b) Nuber of active priary users, versus total nuber of priary users. Total Priary Power Consued [Watt] Nuber of Active Priary BSs (a) Unifor Power without Sleeping Algorith Optial Power without Sleeping Algorith Without Sleeping Algorith (b) Priary Target Rate [Mbps] Fig. 3: (a) Total priary power consuption, (b) Nuber of active priary users, versus priary target data rate. is reduced by around 5.5 ties, while this gap decreases as the traffic becoes heavier (i.e., nuber of users increases). Also, the figure shows that the proposed schee overcoes the unifor power distribution. Fig. 2-b shows that the nuber of active BSs increases as the nuber of users increases in order to satisfy the outage constraints Uout U tot γ out. Siilar observations can be ade fro Fig. 3 when the priary data rate threshold increases. In Fig. 3, we plot the perforance of the proposed schee for different R th values with I th = 2 db and U tot = 4. The figure

6 shows that as the target data rate increases the required power consuption to supply the network increases. It can be shown that the proposed schee activates additional priary BS as R th increases. For instance, for R th = 6 Mbps, the total priary power consuption is reduced by around 5% by going fro around 6 Watt to around 3 Watt using the proposed schee instead of the traditional schee where all BSs are active and eployed optial power allocation. Also, we can deduce that, thanks to the sleeping strategy, the proposed schee can increase the target data rate draatically fro 1 Mbps to 6 Mbps by activating only few BSs (i.e., activate around 27 BSs instead of 14 BSs). Total Secondary Su Rate [bps] Max C/I Max Min 1 with Peak Power Constraint Only with Peak Power and Interference Constraints Interfrence Threshold I th [db] Fig. 4: PF Total secondary su rate as a function of interference threshold I th. Finally, in Fig. 4, we ai to investigate the ipact of the interference threshold constraint on the secondary syste perforance. In this figure, we plot the total secondary data rate versus I th for different secondary utilities (Max C/I, Max-Min, PF) with the case of heavy priary traffic (i.e., U tot = 6) and R th = 1 Mbps. The proposed schee is copared to the case when only the peak power constraint is applied. It can be shown that the proposed optial solution when both constraints are considered (i.e.,power constraint and interference constraint) is upper bounded by the case when only power constraint is applied. It is shown that Max C/I utility leads to the highest secondary data rate in the network. However, this coes at the expense of fairness. The choice of the utility is related to the service used to the secondary users. For exaple, if it consists of a pure cognitive transission without priorities, then Max C/I could be eployed by allocating ost of the resources to the user corresponding to the best channel and interference conditions. However, if the application requires the sae downlink rates, then Max-Min utility can be used. On the other hand, the PF approach axiizes the geoetric ean for all the secondary users by allocating alost the sae power to all secondary users. VI. CONCLUSION In this paper, we proposed and solved a green counication optiization proble for LTE HetNets with underlay CR networks. Since ost of energy is consued by MBSs and PBSs, the objective was based on iniizing the total power consued by priary BS (MBSs and PBSs) and axiizing the secondary data rate utility while satisfying a certain priary target rate and a certain priary interference tolerated threshold. More specifically, we optiized the priary and secondary resource allocation adaptively. 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