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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 5, NO. 6, DECEMBER 2016

Energy-Efficient Power Allocation in OFDMA D2D Communication by Multiobjective Optimization Mohammad Robat Mili, Peyman Tehrani, and Mehdi Bennis, Senior Member, IEEE

Abstract—In this letter, we investigate an energy efficient power control design for resource sharing between cellular and device-to-device (D2D) users in orthogonal frequency division multiple access cellular network assisted D2D communication. To maximize the energy efficiency, we formulate a multiobjective optimization problem that is solved by the method based on the weighting coefficients. In this letter, we investigate the problem of power allocation under full and average intercell interfering channel side information (CSI) made available at the D2D transmitters to discuss the significance of having CSI of the intercell interferers at the D2D transmitters. The performance of the proposed algorithms are investigated via numerical analysis. Index Terms—Device-to-device (D2D) communications, statistical CSI, transmit power.

I. I NTRODUCTION N RECENT years, a significant rise in data traffic of cellular networks has occurred. This ever increasing data traffic gives large pressure on the infrastructure of cellular systems. Recently, D2D communications underlaying cellular networks has brought various benefits toward supporting proximity-based applications that exchange instant data among nearby users. In this approach, cellular base stations and direct D2D communications coexist in the same licensed spectrum. Therefore, due to co-channel interference, D2D communication introduces many new challenges such as resource allocation [1], [2]. Energy consumption and environmental sustainability of wireless systems will become an even more urgent issue in the future, hence, more efficient approaches are required to reduce the energy consumption without sacrificing the functionalities and benefits of such networks. In this trend, energy-efficient D2D communication through different approaches has been investigated in some recent papers [2]–[5]. Wu et al. [2] have investigated the problem of energy-efficient uplink resource sharing over mobile D2D multimedia communications underlaying cellular networks with multiple potential D2D pairs and cellular users. In [3], joint channel and power allocation was studied to improve the energy efficiency of user equipments

I

Manuscript received August 25, 2016; accepted September 21, 2016. Date of publication September 29, 2016; date of current version December 15, 2016. The associate editor coordinating the review of this paper and approving it for publication was K. W. Choi. M. R. Mili and P. Tehrani are with the Information Engineering Department, University of Padova, 35121 Padova, Italy (e-mail: [email protected]; [email protected]). M. Bennis is with the Department of Electrical Engineering, Centre for Wireless Communications, University of Oulu, 90570 Oulu, Finland (e-mail: [email protected]). Digital Object Identifier 10.1109/LWC.2016.2614507

in which an iterative combinatorial auction algorithm is introduced to solve the problem efficiently. In order to improve the energy efficiency of wireless users, Chen et al. [4] formulated joint mode selection and spectrum sharing as a coalition formation game and proposed a coalition formation algorithm to jointly design mode selection and spectrum sharing in a D2D system. In contrast to existing works, we (i) consider a multi-channel scenario such as OFDMA system and (ii) formulate a multiobjective optimization problem (MOOP) to maximize the energy efficiency. In resource allocation based on OFDMA, D2D communications share the same spectrum with the macrocell network and aim at an efficient utilization of spectrum resources. The MOOP simultaneously maximizes the rate and minimizes the total transmission power from D2D transmitters when D2D users transmit data by reusing the resources of cellular users. We then solve this MOOP based on the weighting coefficients method that linearly combine the competing objective functions into a single objective function. In our numerical results, we will show that this technique enables us to study a tradeoff between energy efficiency and data rate. In this letter, we consider OFDMA D2D communication in underlay mode. A framework for optimal power allocation in D2D communication is provided, that relies on OFDMA at the physical layer under full and average CSI of the intercell interferers. Providing all interfering CSI from other D2D links and from the macrocell at the desired D2D transmitter is very difficult, so we investigate the effect of providing these CSIs by comparing two different scenarios. In the first scenario full CSI of the intercell interferers is available at the D2D transmitters, whereas in the second scenario only average CSI of the intercell interferers is available at the transmitters. The rest of this letter is organized as follows. We will introduce the system model of an OFDMA D2D communication system in Section II. In Section III, we investigate the multiobjective optimization problem in D2D communication. Section IV presents the numerical results, and conclusions are given in Section V. II. S YSTEM M ODEL In this letter, we consider macrocells of a cellular network serving a region with K users index by 1, . . . , K and an underlay popoulation of D2D transmitters and receivers. Each D2D transmitter adjusts its power level considering the interference caused by other D2D pairs and the macrocell base station.

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MILI et al.: ENERGY-EFFICIENT POWER ALLOCATION IN OFDMA D2D COMMUNICATION

The D2D communications are considered where M pairs numbered 1, . . . , M employ N subchannels. The D2D pairs can reuse the channel resources occupied by the cellular users, and multiple D2D pairs can share the same channel simultaneously, thus creating interference to each other. We use the following parameters to describe the system model: (n) • Pm : Transmit power of the m−th D2D transmitter over subchannel n. ˜ (n) : Transmit power from the macrocell base station to • P k the k−th macrocell user over subchannel n. (n) • |Hmm |2 : The channel gain between the m−th D2D transmitter and its receiver. ˜ (n) |2 : The channel gain between the macrocell base • |H k station and the k−th macrocell user. (n) • |Hm |2 : Channel gain between macrocell base station and m−th D2D receiver. • Pm : Maximum transmit power of the m−th D2D transmitter. • N0 : The power spectral density (PSD) of the background Gaussian noise. • pcm : A constant value of the circuit power consumption of the m−th D2D transmitter. (n) • SINRm,d : The signal to interference and noise ratio received of the mth D2D receiver over subchannel n. (n) • SINRk,c : The signal to interference and noise ratio received of the kth macrocell user over subchannel n. In the following section, we formulate a MOOP to find the energy efficient power allocation in OFDMA D2D communication. III. M ULTIOBJECTIVE O PTIMIZATION F ORMULATION Energy efficiency (EE), as a measure for the performance of wireless communication systems, is defined as [4]   M N (n) ln 1 + SINR m=1 n=1 m,d EE = M N (1) M (n) m=1 n=1 Pm + m=1 pcm In this section, we formulate an optimization problem that maximizes the energy efficiency of the D2D communications, while guaranteeing the constraints on the minimum data rate for D2D and cellular users and the maximum transmit power of D2D transmitters to get the optimum transmit power as max (n) Pm

s.t.

EE

(2a)

N    (n) ln 1 + SINRm,d ≥ Rm,d ∀m ∈ {1, ..M} (2b) n=1 N    (n) ln 1 + SINRk,c ≥ Rk,c ∀k ∈ {1, ..K}

(2c)

n=1 N 

P(n) m ≤ Pm

∀m ∈ {1, ..M}

(2d)

n=1

Note that (2b) and (2c), guarantees the quality of services (QoS) of D2D and cellular users,respectively. We replace the original problem (2) with the following MOOP that jointly maximizes the data rate of the D2D connections

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(the numerator of (1)) and minimizes the total transmission power of D2D transmitters (the denominator of (1)) as [9] M  N    (n) ln 1 + SINRm,d

max (n)

Pm

m=1 n=1 M  N 

min (n)

Pm

(3a)

P(n) m

(3b)

m=1 n=1

s.t.

(2b)-(2d)

In order to solve a MOOP, several methods can be offered. In this letter, a well known technique to solve MOOPs is to linearly combine the competing objective functions into a single objective function, through weighting coefficients that reflect the required preferences [6]. Hence, the objective functions in the MOOP (3) can be changed into 

max (n)

Pm

M  N    (n) α ln 1 + SINRm,d



m=1 n=1

− (1 − α)

M  N 

P(n) m

(4a)

m=1 n=1

s.t.

(2b)-(2d)

In the following, we solve this optimization problem under two different assumptions: full and average CSI of the intercell interferers which can be made available at the D2D transmitters. A. Full CSI of the Intercell Interferers Available at the D2D Transmitters The SINRs of D2D receiver and macrocell users under full CSI of the intercell interferers can be respectively expressed using the following equations: (n),Full

SINRm,d

=

M j=1 j=m

SINR(n),Full k,c (n)



(n) (n) 2 Pm Hmm





(n) (n) 2 (n) (n) 2 Pj Hjm + P˜ Hm + N0 k



(n) ˜ (n) 2 P˜ k H k

=

M (n) (n)

2 j=1 Pj Hjk + N0 (n)

(5)

(n)

(n)

(6)

where Pj |Hjm |2 and Pj |Hjk |2 are the interference power generated from j−th D2D pair on the m−th D2D receiver and k−th macrocell user in subchannel n, respectively. By considering (5) and (6) as SINR in (4), the obtained optimization problem due to the interference terms becomes a nonconvex. In this letter, we use a technique based on “difference of two convex functions/sets” (DC) programming to convexify the nonconvex function [7]. This approach converts the nonconvex function into the difference of two convex functions and the discounted term is approximated by its first order Taylor series. Therefore, the obtained function and the optimization problem will be convex. This technique, which is based on an

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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 5, NO. 6, DECEMBER 2016

iteration procedure, expresses the nonconvex function (4a) in DC form as follows: f (p) − h(p)

max p

g(p) =

M  N 

P(n) m

(7)

m=1 n=1

where ⎡ M  M N





 ⎢ (n) (n) 2 (n) (n) 2 ⎢ f (p) = ln⎣ Pj Hjm + P˜ k Hm

m=1 n=1

j=1 j=m

⎤ + N0



(n) 2 ⎥ ⎥ + P(n) m Hmm ⎦

h(p) =

M  M N





2  ⎥ ⎢ (n) (n) 2 (n)

˜ (n)

Hm ln⎢ P + P

H

+ N0 ⎥ j jm k ⎦ ⎣

m=1 n=1

≥ f (p(t) ) − h(p(t) ) − ∇h(p(t) ), (p(t) − p(t) )

= f (p(t) ) − h(p(t) )

(14)

Finally, for 0 ≤ α ≤ 1 we can have   α f (p(t+1) ) − h(p(t+1) ) − (1 − α)g(p)   ≥ α f (p(t) ) − h(p(t) ) − (1 − α)g(p)

(15)

(8)

(9)

B. Average CSI of the Intercell Interferers Available at the D2D Transmitters

j=1 j=m

in which p is the N ×M transmit power matrix and f (p)−h(p) is a DC function. To obtain the Taylor series of h(p) we need its derivative which can be easily derived as follows: ∇h(p)nm =

f (p(t+1) ) − h(p(t+1) ) ≥ f (p(t+1) ) − h(p(t) ) − ∇h(p(t) ), (p(t+1) − p(t) )

= max f (p) − h(p(t) ) − ∇h(p(t) ), (p − p(t) )

Therefore, the objective value after each iteration is either unchanged or increased and since the constraint set is compact it can be concluded that the above DC approach converges to a local minimum. Noting that the computational complexity of DC approach is O(M 3 ) which is shown in [7].





at the end of each iteration the solution of problem (4) will be improved as follows

∂h(p) (n)

∂P ⎡ m

The SINRs received in a D2D receiver m and macrocell user k over subchannel n under average CSI of the intercell interferers respectively becomes as



(n) 2 P(n) m Hmm

n,Avg (16) SINRm,d = M

(n)

2

(n)

2 + N0 j=1 Ijm + I j=m



2

(n)

M ⎢ ⎥

Hml

⎢ ⎥ =⎢ ⎥





2 M (n) (n) 2 ⎣ ⎦



(n) (n) ˜ l=1 j=1 Pj Hjl + Pk Hm + N0 l=m

j=l

(10) In this technique, h(p) is approximated with its first order approximation as h(p(t) ) + ∇h(p(t) ), (p − p(t) ) at point p(t) to convexify the function. (Here X,Y denote the standard inner product on RN×M ). A feasible p(0) as the first iteration is selected and then the next iterations will be generated to obtain the solution of the following problem:   max α f (p) − h(p(t) ) − ∇h(p(t) ), (p − p(t) )

(n)

Pm

− (1 − α)

M  N 

P(n) m

(11a)

m=1 n=1

(2b) and (2d) Since h(p) is a concave function, its gradient is also its super gradient so we have h(p) ≤ h(p(t) ) + ∇h(p(t) ), (p − p(t) )



j=m

∀m = 1, 2, ...M λnm

(13)

(17)

(n) (n) (n) (n) (n) where |Ijm |2 = E[Pj |Hjm |2 ] and |I (n) |2 = E[P˜ k |Hm |2 ] (E[x] denotes the statistical expectation) are the average intercell interference generated from j−th D2D transmitter and the macrocell base station all on subchannel n, respectively. Applying the expectation on the interference power from surrounding D2D pairs in the denominator of (16), representing the average intercell interference power, changes the optimization problem (4) into a convex problem. This is because the expectation in the denominator is a constant value and according to the definition of the convex function (the Hessian is positive definite), (4a) becomes convex. The minimum power allocation of D2D transmitter m over subchannel n can be obtained as λnm + α = P(n) m 1 − α + μnm 

 

 M

(n) 2 (n) (n) 2 (n) j=1 E Pj Hjm +E P Hm + N 0

(12)

and we can deduce h(p(t+1) ) ≤ h(p(t) ) + ∇h(p(t) ), (p(t+1) − p(t) )

(n),Avg

SINRk,c



(n) ˜ (n) 2 P˜ k H k

=

M (n)

2 j=1 Ijk + N0

μnm



(n) 2

Hmm

, (18)

and are the Lagrange multiplier. Equation (18) where is obtained by taking the derivative of the Lagrangian and setting it equal to zero, based on the Karush-Kuhn-Tucker (KKT)

MILI et al.: ENERGY-EFFICIENT POWER ALLOCATION IN OFDMA D2D COMMUNICATION

Fig. 1. Equation (4a) under full CSI of the intercell interferers versus the number of iterations for M = 6.

Fig. 2.

Energy efficiency versus Pm for M = 6.

Fig. 3.

671

Energy efficiency versus data rate of D2D users for M = 6.

the intercell interferers. Since having the channel side information between the macrocell base station and the D2D receiver at the desired D2D transmitter is very difficult, using average CSI of the intercell interferers increases the transmit power, which indicates a trade off between EE and complexity in such networks. The behavior of EE against the data rate of D2D links for different values of α is shown in Fig. 3. This figure, which reveals a trade off between energy efficiency and data rate, shows that the optimization problem under full CSI of the intercell interferers provides increased energy efficiency. V. C ONCLUSION

conditions [8]. It is worth noting that the power of the D2D transmitter in (18) is only a function of the direct channel gain (n) 2 between the transmitter and the receiver (|Hmm | ) and is inde(n) 2 pendent of all the intercell interfering channel gains (|Hjm | (n) and |Hm |2 ). In order to account for the optimum transmission power, the iteration search based on the sub-gradient method should be implemented.

IV. N UMERICAL R ESULTS In this section, we present and discuss some numerical results for energy efficient power allocation under full and average CSI of the intercell interferers made available at the D2D transmitters in order to discuss the significance of having CSI of the intercell interferers at the D2D transmitters. We assume that the number of subchannels is 10, K = 5, pcm = −5 dB and N0 = 1 to normalize all transmit powers with respect to the noise variance. It is assumed that each subchannel experiences independent and identically distributed Rayleigh fading. In Fig. 1, the behavior of the quation (4a) under full CSI of the intercell interferers versus the number of iterations based on DC programming is studied. This figure shows the convergence of the proposed algorithm. Fig. 2 plots EE versus the transmission power from the D2D transmitters under average and full CSI of the intercell interferers available at D2D transmitters for different values of α. Evidently, as can be seen in this figure, as the value of the transmission power increases, the value of EE decreases. This figure also shows that EE under full CSI of the intercell interferers is consistently higher than that under average CSI of

In this letter, we considered a coexistence scenario between macrocell and D2D communication. We first presented a joint optimization problem to obtain the energy efficient power allocation in OFDMA D2D communications under average and full CSI of the intercell interferers available at the D2D transmitters. By exploiting MOOP, we found a trade off between data rate and energy efficiency. Numerical results show that the performance obtained under full CSI of the intercell interferers is higher than under average CSI of the intercell interferers. R EFERENCES [1] R. Yin et al., “Joint spectrum and power allocation for D2D communications underlaying cellular networks,” IEEE Trans. Veh. Technol., vol. 65, no. 4, pp. 2182–2195, Apr. 2016. [2] D. Wu, J. Wang, R. Q. Hu, Y. Cai, and L. Zhou, “Energy-efficient resource sharing for mobile device-to-device multimedia communications,” IEEE Trans. Veh. Technol., vol. 63, no. 5, pp. 2093–2103, Jun. 2014. [3] F. Wang, C. Xu, L. Song, and Z. Han, “Energy-efficient resource allocation for device-to-device underlay communication,” IEEE Trans. Wireless Commun., vol. 14, no. 4, pp. 2082–2092, Apr. 2015. [4] H. Chen, D. Wu, and Y. Cai, “Coalition formation game for green resource management in D2D communications,” IEEE Commun. Lett., vol. 18, no. 8, pp. 1395–1398, Aug. 2014. [5] C. Gao et al., “Enabling green wireless networking with device-to-device links: A joint optimization approach,” IEEE Trans. Wireless Commun., vol. 15, no. 4, pp. 2770–2779, Apr. 2016. [6] Y. Collette and P. Siarry, Multiobjective Optimization: Principles and Case Studies. New York, NY, USA, Springer, 2003. [7] H. H. Kha, H. D. Tuan, and H. H. Nguyen, “Fast global optimal power allocation in wireless networks by local D.C. programming,” IEEE Trans. Wireless Commun., vol. 11, no. 2, pp. 510–515, Feb. 2012. [8] S. P. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004. [9] C. He, B. Sheng, P. Zhu, X. You, and G. Y. Li, “Energy- and spectralefficiency tradeoff for distributed antenna systems with proportional fairness,” IEEE J. Sel. Areas Commun., vol. 31, no. 5, pp. 894–902, May 2013.