Joint User Association and Energy-Efficient Resource Allocation with ...

2013 IEEE 24th International Symposium on Personal, Indoor and Mobile Radio Communications: MAC and Cross-Layer Design Track

Joint User Association and Energy-Efficient Resource Allocation with Minimum-Rate Constraints in Two-Tier HetNets Haris Pervaiz, Leila Musavian and Qiang Ni School of Computing and Communications, InfoLab 21, Lancaster University, UK Email: {h.pervaiz, l.musavian, q.ni}@lancaster.ac.uk Abstract—This paper proposes joint user association and energy- efficient resource allocation in the uplink of multi-user two-tier Orthogonal Frequency Division Multiplexing (OFDM) Heterogeneous Networks (HetNets) subject to user’s maximum transmission power and minimum-rate constraints. The proposed scheme aims at achieving high rates at low powers satisfying the user’s quality-of-service (QoS) constraints (in terms of minimumrate requirements) by offloading the users with low signal to noise ratio (SNR) from macrocell to the pico base station (BS). A channel-to-noise-ratio (CNR)-based rate proportional resource allocation approach is proposed to transform the minimumrate constraint into a minimum required transmission power constraint on each subcarrier. The single-user single-carrier and multi-user multi-carrier energy efficiency (EE) maximization problems are then solved under maximum and minimum power constraints using Karush-Kuhn-Tucker (KKT) conditions. The impact of users’ maximum transmission power and minimumrate requirements on EE and throughput are investigated through illustrative results. The rate-proportional approach is evaluated against the equal rate allocation approach for different user associations and various numbers of users, maximum transmission power, and circuit powers. Significant gains in EE can be achieved for the HetNets if the path loss based user association is combined with the proposed CNR rate proportional mechanism. Index Terms—Energy efficiency (EE), user association, resource allocation, Heterogeneous Networks (HetNets).

I. I NTRODUCTION The HetNets includes low-power overlaid BSs (or small cells), e.g., microcell, picocells, and femtocells, within the macrocell geographical area, deployed by either user or the network operator who shares the same spectrum with the macrocells [1]. The purpose of HetNet is to allow the user equipments (UEs) to access small cells that overlap geographical coverage areas even though the UEs are within the donor macrocell [2]. The deployment of small cells has a great potential to improve the spatial reuse of radio resource and also to enhance the transmit power efficiency [3], and in turn, the energy efficiency (EE) of the network. EE is, in fact, one of the key performance indicators for the next generation wireless communications systems. The motivation behind the EE arises due to the current energy This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under Grant No EP/K011693/1.

978-1-4577-1348-4/13/$31.00 ©2013 IEEE

cost payable by operators for running their access networks as a significant factor of their operational expenditures (OPEX) and the feasibility of cooperative management of wireless access networks in sharing resources among the end users. Hence green networking paradigm, which focuses on the means to reduce the energy consumption in the wireless access networks, has received big attention [4] [5]. Recently, several works have considered throughput maximization to measure the performance in the OFDM systems for downlink [6], uplink [7] [8] [9] and joint uplinkdownlink [10] transmission schemes. On the other hand, when EE is the considered performance metric, [11] proposes an EE-maximization link adaptation and resource allocation technique for an OFDMA system considering fixed circuit and transmit power by improving the mobile EE for the flat-fading OFDMA channels. A low complexity time-sharing bandwidth allocation approach to maximize the EE of a downlink flatfading channel is proposed in [12]. Further, energy-efficient channel and power allocation problem in the uplink of an OFDM system is considered subject to maximum transmit power constraint, based on the assumption that each user can transmit at one channel in [4], wherein two different energy scheduling algorithms were proposed. In [13], the authors investigate the tradeoff between spectral and energy efficiencies as a function of the circuit power, power amplifier (PA) efficiency and channel power gain in time-varying Rayleigh fading point-to-point channels. These works, however, do not consider the impact of users’ minimum-rate requirements and the use of HetNets on EE in OFDM systems. In [14], the authors proposed a dynamic network selection mechanism in cooperative heterogeneous wireless networks considering both network and user perspective in order to optimise the user’s perceived QoS using evolutionary game theory. The major contribution of this paper is to propose a joint subcarrier and power allocation technique for maximizing EE within HetNets, based on the user association when user’s minimum-rate requirements are to be satisfied. Specifically, we consider the pico-BS-first user association to offload the users from macrocell to pico BS to enhance EE. Further, we propose a rate-proportional mechanism to divide the user’s

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minimum-rate requirements in between its associated subcarriers based on the subcarriers CNRs. Specifically, when CNR of a subcarrier is higher, higher minimum-rate will be allocated to that subcarrier, and vice versa. This proposed approach is compared to the equal rate allocation approach, wherein the user’s minimum-rate requirement is equally allocated among all the subcarriers [6] [10]. The minimum-rate constraint for single-user and multi-user cases is transformed into minimum power constraints on each subcarrier. The power allocation using Karush-Kuhn-Tucker (KKT) conditions are then used to compute the instantaneous subcarriers transmit powers while not violating the users’ maximum transmit power constraints. Simulation results indicate that the proposed rate proportional approach enhances the EE in the order of 10.2% as compared to the equal rate approach. Our study also reveals that EE increases with the maximum transmission power (Pmax ) while on the other hand, the EE decreases with increase in minimumrate required by the users. The EE increases with the number of users and decreases with the distance from their connecting BS. II. S YSTEM M ODEL AND P ROBLEM D ESCRIPTION We consider an uplink two-tier HetNets composed of one macrocell overlaid with one pico BS. The pico BS is connected to the macrocell via a high capacity wired backhaul. The frequency resource is equally divided into K subcarriers, each with bandwidth W, which is utilized by a set of N users. We further assume that the channel state information (CSI) corresponding to each subcarrier is perfectly known to the UEs transmitters. At this stage, the effect of the interference from adjacent cells is not taken into consideration. The cochannel interference between pico BS and macrocell is catered assuming that each of them communicates the usage of subcarrier with each other using Almost Blank Frame (ABF). We consider an orthogonal subcarrier selection scheme, introduced in [15], that assigns each subcarrier exclusively to  either pico BS (PB) or macrocell at any time, such that KPB KM = ∅ with KM and KPB indicating the set of subcarriers assigned (k) to the macrocell and pico BS, respectively. Let cPBn and (k) cMn denote the subcarrier allocation indices for pico BS and macrocell, respectively. If the subcarrier k ∈ KPB , for k = {1, · · · , K}, is allocated to user n, for n = {1 · · · N }, (k) (k) then cPBn = 1, and otherwise cPBn = 0. Similarly, if the (k) subcarrier k ∈ KM is allocated to user n, cMn = 1, and (k) otherwise, cMn = 0. To maintain the QoS requirements, each user has a minimum-rate constraint. We assume that the minimum-rate requirement of all users are identical and is referred by Rmin . The achievable rate on each subcarrier k by user n using Shannon capacity for macrocell and pico BS are then given by:   (k) (k) (k) (k) RMn = cMn × W log2 1 + γMn × pMn , (1a)   (k) (k) (k) (k) (1b) RPBn = cPBn × W log2 1 + γPBn × pPBn ,

(k)

(k)

where n = {1, · · · , N }, and k = {1, · · · , K}. pPBn and pMn indicate the power allocated to the subcarrier k for user n in (k) (k) the pico BS and macrocell, respectively. γMn and γPBn refer to the CNR of user n on subcarrier k in the macrocell and pico BS, respectively. Similarly, the rate of user n using subcarrier (k) k choosing macrocell or pico BS is represented by RMn and (k) RPBn , respectively. The overall rate of HetNets is composed of two components; the first component is the total rate of users choosing macrocell and the second one is the total rate of users choosing pico BS, formulated as NM   NPB       (k) (k) R= RMn + RPBn , (2) n=1 k∈KM

n=1 k∈KPB

The transmission power can now be represented as a function of data transmission rate for macrocell and pico BS as follow:   (k) (k) (k) (k) (k) pMn (RMn ) = 2(RM n /W ×cM n ) − 1 /γM n ,  (k)  (k) (k) (k) (k) pPBn (RPBn ) = 2(RP Bn /W ×cP Bn ) − 1 /γP Bn ,

(3a) (3b)

Assume R is the total achieved rate and Ptotal is the total power consumed(represented as a function of R) of HetNets (including macrocell and pico BS)respectively. Since the circuit power (PC ) is related to the UE handsets, we assume PCM = PCP = PC . The system EE (η) is defined as the amount of data transferred per unit energy consumed by the system (usually measured in b/J/Hz) and is defined as η = R/(PC + Ptotal ),

(4)

III. J OINT U SER A SSOCIATION AND E NERGY-E FFICIENT R ESOURCE A LLOCATION A. User Association In order to avoid frequent vertical handoffs in HetNets, user association rules are defined for wireless transmission [16]. In traditional homogeneous cellular networks, the user association is based on the received signal strength [17]. One of the key issues is that all BSs within the same tier should have identical biasing factor. In this paper, we propose uplink path loss based association in which the user associates to the BS with the lowest path loss. The motivation behind using the pico-BS first [17] (or path loss) association is to associate the users with the closest BS which can help in maximizing the overall EE of the system. Unique association of users with the macrocell or pico BS is assumed. Specifically, each user can only be associated with one BS. Define the user association index for pico BS by IPB,n which is equal to 1 if the user n is associated to the pico Bs and 0, otherwise. Similarly, we can define the user association index for macrocell by IM,n = (1 − IPB,n )1 . It is assumed that a subcarrier can only be assigned to one user in a scheduling interval. Hence, the (k)

1 For the sake of clarity,c M N indicates the allocation of subcarrier k ∈ KM to user n whereas IM n indicates the association of user n with macrocell.

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to (8) as derived in [4] 











log2 (1 + γp∗ ) (1 + γp∗ ) − PC = 0. γ















(8)








The EE for SU-SC case can then be computed as R(popt ) η ∗ = PC +p . opt



























C. Single User Multi Carrier (SU-MC) Case







































(a) Pico BS First
































(b) Macrocell only

Fig. 1: User Association Rules

achieved rates and power for user n on subcarrier k denoted (k) (k) by Rn and pn can be defined as Rn(k)

= IMn ×

p(k) n

= IMn ×

(k) (k) RMn + IPBn × RPBn , (k) (k) pMn + IPBn × pPBn ,

Similarly, for a case of single-user with K subcarriers, the EE-maximization problem can be formulated as: K (k) max ( k=1 Rn (p)) η (p) = max  (k) K p P +( sm C k=1 pn (p)) s.t. K 

(5a) (5b)

Different user association schemes for the uplink of HetNet with N = 25 are shown in Fig. 1. Fig. 1 depicts that picoBS-first associates more users with pico BS as compared to the other user association techniques. B. Single User Single Carrier (SU-SC) Case Improving the EE can result in reduction of the user achieved rate, and hence degrading the user’s QoS [11]. In this paper, we consider the UE minimum-rate requirement along with its maximum transmit power constraint in order to investigate the tradeoff between the achieved EE and QoS requirements. The EE-optimization problem for a case where N=1 and K=1 can be formulated as: R (p) ηsmax (p) = max , (6) p PC + p s.t.

(k) p(k) n ≤ Pmax , pn ≥ 0, ∀k ∈ {1, · · · , K}

k=1 K 

Rn(k) ≥ Rmin , ∀n ∈ {1, · · · , N }

k=1 max where ηsm is the maximum achievable EE for SU-MC. In order to convert the minimum-rate requirement into subcarrier minimum transmit power constraints, we use two different approaches namely, equal and CNR-based rate proportional allocations. In equal rate allocation approach [1] [7], Rmin is divided equally among the sub-carriers allocated to the user as follows: Rmin Rmin = , (n) countsc

p(k) n (Rmin ) =

2

Rmin W

−1

(k) γn

, ∀k = 1, 2, · · · , K,

(9)

0 ≤ p ≤ Pmax

The sum of the achievable rate on each sub-carrier allocated to user n should be at least equal to its minimum-rate requirement according to

Rn(k) (p) ≥ Rmin

Rn(1) + Rn(2) + · · · + Rn(K) ≥ Rmin ,

where ηsmax is the maximum achievable EE for SU-SC and R(p) indicates the rate of the user as a function of its power. The minimum transmit power required to achieve minimumrate can be computed by solving (3) using Rmin , yielding

In CNR-based rate proportional mechanism, the minimum-rate constraint is distributed among the sub-carriers k ∈ 1, · · · , K, proportional to their respective γ  s as

p(k) n (Rmin ) =

2

Rmin W

−1

(k)

γn

,

(7)

Rn(1) : Rn(2) : · · · : Rn(K) = γn(1) : γn(2) : · · · : γn(K) ,

p

(1)

Rn

(1)

γn

R (p) , PC + p

(11)

which can be transformed into

The optimization problem can then be updated as: ηsmax (p) = max

(10)

(2)

=

Rn

(2)

γn

(K−1)

= ··· =

Rn

(K−1)

γn

(K)

=

Rn

(K)

γn

.

(12)

Now, by substituting (12) into (10), we get = R(K) n

s.t. p(k) n (Rmin ) ≤ p ≤ Pmax The  optimal power  is popt =  min Pmax , max p∗ , pkn (Rmin ) where p∗ is the solution

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R(i) n =

Rmin (1)

γn (K) γn (i) γn (i+1) γn

+

(2)

γn (K) γn

+ ··· +

(K)

γn (K) γn

,

× Rn(i+1) , i = 1, 2, · · · , K − 1,

(13a)

(13b)

  (k) (k) Similarly, pn Rn , ∀k ∈ {1, · · · , K}, allocated to user n using KKT conditions according to:  can be computed using (7). The EE-maximization problem, is d(ηn,k )  = 0. iteratively solved in a suboptimal way for each subcarrier k dp pk =pk ∗ n n allocated to the user n. Consider a case where all the subcarri

ers k < kref are already taken into account. We now formulate Set A=[N R(n)] and B= N P (n) , then n=1 n=1 the optimization problem for subcarrier kref , considering the      ∗ rate and power that already allocated to subcarriers k < kref , A + log 1 + γpk ∗ 1 + γpkn 2 n as   −B −KP C = 0. (17) (k) K γ max k=1 R(k) + Rn η (p) = max   (14) Hence, the  optimal power is popt = (k) K p sm   ∗ PC + k=1 P (k) + pn min Pmax , max pkn , pkn (Rmin ) . s.t. K  Consider a case when K=3 sub carriers are allocated to the (k) pn ≤ Pmax , ∀k ∈ {1, · · · , K} nth user in MU-MC case. The minimum-rate requirement on (1) (2) (3) k=1 each sub-carrier, i.e., Rn , Rn and Rn can be computed (1) (2) (3) (k) (k) using (13a) or (13b). Similarly, p(Rn ), p(Rn ) and p(Rn ) pn (Rmin ) ≤ pn ≤ Pmax , ∀k ∈ {1, · · · , K} ∗ can be computed using (7). Subsequently, optimal power pkn pn(k) ≥ 0, ∀k ∈ {1, · · · , K} for each (n, k) combination can be calculated such that it does In (14), R(k) and P(k) are the achieved rate and power not violate the maximum transmission power constraint. The consumption of all subcarriers before  considering

subcarrier vector C and D can be updated as C = C + R(k) and D = K K ∗ kref . Let C=[ k=1 R(k)] and D= k=1 P (k) , then (14) D+pkn where R(k) is the achieved rate for user n on sub∗ can be solved using KKT conditions yielding carrier k at optimal power pkn . In order to find the sub-carriers      ∗ ∗ for the next user nref > n using (16), C and D from the nth 1 + γpkn C + log2 1 + γpkn − D − PC = 0. (15) user will be added to the A and B, respectively. γ Here, we propose a joint user association and energyHence, the optimal power is p = efficient subcarrier allocation algorithm. The proposed algoopt    ∗ rithm consists of two parts: subcarrier allocation and power . min Pmax , max pkn , pkn (Rmin ) allocation. In order to maximize the EE, each subcarrier D. Multi User Multi Carrier (MU-MC) Case should be allocated to the user that can maximize the achieved Here, we consider the case of a MU-MC scenario with N rate with the minimal transmit power while satisfying the UEs and K subcarriers in HetNets. In an uplink scenario, mul- minimum-rate and maximum transmit power constraints. In tiple users transmit data towards a BS so each communication the uplink, the subcarrier and the power allocation phases are link between user and BS introduces an individual PC [11]. interlinked so both these phases need to be performed together in order to increase EE. Hence, the EE maximization problem can be formulated as:   N k IV. S IMULATION R ESULTS n=1 R(n) + Rn (16) ηn,k (S, R) = max N We consider a two-tier HetNets environment with a single K × P C + ( n=1 P (n)) + pkn macrocell with 500m radius overlaid with a pico BS with a s.t. radius of 125m. For EE measurements, the bandwidth of each K  cell is 1 MHz and the bandwidth of each subcarrier is 180 kHz. k (Snk ×pn ) ≤ Pmax , ∀n ∈ {1, · · · , N } The minimum-rate requirement for each user is considered as k=1 0.42b/s/Hz. The maximum transmission power of macrocell pkn (Rmin ) ≤ pkn ≤ Pmax , ∀n ∈ {1, · · · , N } and pico BS are 20W and 200mW respectively whereas the N value of circuit power is PC = 100mW . We assume that the  Snk = 1, ∀k ∈ {1, · · · , K} total number of users N = 25 are uniformly distributed within n=1 the simulated scenario. The path-loss model for macrocell k and pico BS are given as PL(dB) = 34 + 40 log10 (dn ) pn ≥ 0, snk ∈ {0, 1} , ∀n, k and PL(dB) = 37 + 30 log10 (dn ) [16], where dn is the is Here, S is an N × K matrix with each element snk indicating the distance of a user n from the BS in km and therefore, P (P LM the allocation of subcarrier k to user n. Similarly, P is an N×K P LM n (dB)/10) and P LP = 10(P Ln (dB)/10) . The n n = 10 k matrix with each element pn representing the allocated power noise spectral density is assumed to be N0 = −141dBm/Hz. to sub-carrier k associated with user n. In similar manner,R We investigate the effects of the proposed CNR-based rate is an N×K matrix with Rnk representing the allocated rate to proportional allocation as opposed to the equal rate allocation sub-carrier k associated with user n. Initially ∀n,R(n) and P(n) on EE in MU-MC case with N = 25 and K = 5 in Fig. 2. are set to zero. At this point, the solution to (16) can be found Fig. 2 shows that the EE increases with the number of users

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Joint User Association and Energy-Efficient Resource Allocation Algorithm Initialization of variables: N = Number of users K = number of sub-carriers in the system NT otal : Total number of schedulable users in the system hM n,k : indicates the channel gain of user n for subcarrier k in macrocell B : indicates the channel gain of user n for subcarrier k hP n,k in pico BS A = {1, 2, · · · , K} ∀n = 1 to N, Cn = ∅, Pn = 0, Rn = 0 Step 1: 2 2 |hP B | | hM (k) (k) n,k | Compute γP Bn = P LPn,k B N B and γM n = P LM N B 0 0 n n Step 2: For n = 1 : N (k)

(k)

(k)

γn = IP B,n γ P Bn + I M,n γM n , ∀k ∈ A (k)

Sort N users on the basis of γn (k) n∗ = maxn γn , ∀k ∈ A

for given k as follow:

Cn = Cn ∪ {k} A = A − {k} (n)

countsc = size (Cn ) , ∀n (n)

If countsc = 1, (k) Compute pn (Rmin ) using (7) Compute optimal power p∗ satisfying the power constraint using (8) (k) If p∗ < pn (Rmin )