Green Full-duplex Self-backhaul and Energy Harvesting ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSAC.2016.2611846, IEEE Journal on Selected Areas in Communications 1

Green Full-duplex Self-backhaul and Energy Harvesting Small Cell Networks with Massive MIMO Lei Chen, F. Richard Yu, Senior Member, IEEE, Hong Ji, Senior Member, IEEE, Bo Rong, Xi Li, and Victor C.M. Leung, Fellow, IEEE

Abstract—With the dense deployment of small cell networks, the powering and backhaul problem of small cell base stations (SBSs) has attracted great attentions, and energy harvesting technology as well as self-backhaul technology have been proposed as promising solutions. Although some excellent works have been done on energy harvesting and self-backhaul in small cell networks, most existing works do not consider them jointly. In this paper, we aim at green small cell networks by jointly achieving self-backhaul and energy harvesting. In addition, fullduplex (FD) and massive multiple-input and multiple-output (MIMO) technologies are also exploited to enhance the system performance. In order to improve the energy efficiency (EE) further, a novel precoding scheme is designed to eliminate both the inter-tier and multi-user interference. Based on the proposed precoding scheme, we formulate the cell association and power allocation problem as an optimization problem to optimize the system EE performance, with the energy arrival rate and remaining battery energy in SBSs involved. The formulated optimization problem implies a sleep mechanism to control the on/off of SBSs, which will further reduce the energy consumption of small cell networks. In addition, to reduce the computation complexity to solve this non-convex problem, we propose to transform the original problem into a difference of convex program, which can be efficiently solved via a constrained concave convex procedurebased algorithm. Extensive simulation results are presented to justify the effectiveness of the proposed scheme that with different system configurations. Index Terms—Small cell networks, self-backhaul, energy harvesting, massive MIMO, full-duplex

I. I NTRODUCTION AND MOTIVATION With the explosive demand for improving mobile data rate as well as reducing the capital expenses (CapEx) and operation expenses (OpEx), small cell networks have been considered as a promising technology of next generation cellular networks [1] [2]. In particular, dense small cell networks have attracted This work is jointly supported by Project 61271182, 61302080, and 61501047 of the National Natural Science Foundation of China and the Natural Sciences and Engineering Research Council of Canada. L. Chen, H. Ji and X. Li are with the Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, P.R. China (e-mail:[email protected], [email protected] and [email protected]). F. R. Yu is with the Dept. of Systems and Computer Eng., Carleton University, Ottawa, ON, Canada (e-mail: [email protected]). B. Rong is with the Communications Research Centre Canada, Ottawa, ON, Canada (e-mail:[email protected]) V. C. M. Leung is with the Dept. of Electrical and Computer Eng., the University of British Columbia, Vancouver, BC, Canada (e-mail: [email protected]).

great attentions, where a mass of small cell base stations (SBSs) are deployed to improve user experience further [3]. However, with the dense deployment of massive SBSs, the powering and backhaul problem becomes increasingly severe. On one hand, the energy consumption and the cost of optical backhaul will increase sharply with the increase of the number of SBSs. On the other hand, since SBSs are densely and irregularly located, some of them may be inaccessible to the traditional power grid [4]. Therefore, solving the powering and backhaul problem is critical to satisfy the quality of service (QoS) of users and reduce the CapEx and OpEx. Energy harvesting technology, which can harvest ambient renewable energy (e.g., solar and wind energy), has been proposed as a promising alternative solution to green wireless networks [5]–[10]. It is estimated that applying energy harvesting technology to small cell networks can achieve a 20 percent CO2 reduction in the information and communication technology industry [11]. Furthermore, due to the high CapEx and OpEx of traditional fibre backhaul, researchers pay more attention on wireless backhaul, which further facilitates the deployment of SBSs. The authors of [12]–[14] proposed the microwave backhaul scheme and the mmwave backhaul scheme is researched in [15], [16]. The microwave and mmwave, with a significantly wide bandwidth, can provide high-capacity backhaul link. However, both of them can only perform well in line-of sight (LoS) environments, which leads to more demands for the deployment of SBSs (e.g., the location of SBSs and the height of antennas). Those demands can hardly be satisfied in urban or mountain environments because of massive obstructions. Moreover, the equipment of microwave and mmwave is typically heavy and expensive, which prevents the fast deployment of SBSs [17] [18]. Another wireless backhaul candidate is the cellular communication technology (e.g., LTE), which uses the cellular spectrum to access and backhaul, and is suitable for the non-LoS environment [19]–[21]. With the cellular communication technologybased backhaul (called self-backhaul in the literature [18]), the SBSs do not necessarily require extra backhaul hardware or spectrum, and consequently, self-backhaul is regarded as promising technology in future small cell networks [18]. Despite the previous work on energy harvesting and selfbackaul, there is still a lack of study that jointly considers these two issues in small cell networks. Moreover, most existing works do not consider the recent advances of full-duplex (FD) technologies enabled by self-interference cancellation

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and massive multiple-input and multiple-output (MIMO). FD enables the radios to transmit and receive simultaneously in the same frequency band, which nearly doubles the spectrum efficiency [22]–[24]. Nevertheless, the FD technology originates from the time division duplex (TDD) system, which makes it unsuitable for access links in the frequency division duplex (FDD) system [18]. In this paper, we use the FD technology for backhauls, in which FD communication hardware is equipped in SBSs. Consequently, SBSs can receive data from the macro base station (MBS) and transmit data to SBSs in downlink (DL), transmit data to MBS and receive data from their users in uplink (UL) in the same frequency simultaneously, which is termed as FD self-backhaul. As another promising technology, massive MIMO can achieve simultaneous multi-user transmission in the same frequency band by utilizing the large degree of spatial freedom, and also can improve the spectrum efficiency as well as energy efficiency (EE) [25]. Due to the fact that the MBS is also responsible for the transmission to SBSs in our proposed FD self-backhaul scheme, the MBS with massive MIMO can transmit data to or receive data from SBSs as well as its users together simultaneously in the same frequency band. This is different from our previous works in [26], where the spectrum is segmented to avoid the co-channel interference among SBSs and the users of MBS. In this way, the spectrum efficiency and EE of backhaul and access link will be improved significantly. In [27], [28], the authors analyzed the gain of incorporation of massive MIMO into small cell networks, but did not take into account the backhaul challenge and simplified the power allocation of MBS and SBSs by equal power allocation. Although jointly considering self-backhaul and energy harvesting technologies can bring many benefits to small cell networks, it is challenging to study them jointly, as the energy arrival and the battery capacity are limited in energy harvesting systems. Moreover, since the self-backhaul typically consumes extra energy of MBS to support backhaul links, the cell association and power allocation in energy harvesting small cell networks with self-backhaul will be more challenging than that in the traditional energy harvesting small cell networks, especially in our proposed FD self-backhaul scheme with massive MIMO, because it involves power allocation in multiuser MIMO systems. Furthermore, the inter-tier interference in small cell networks and the multi-user interference caused by multi-user MIMO channel in massive MIMO system make the cell association and power allocation in our proposed FD self-backhaul and energy harvesting small cell networks more complex. The distinct features of this paper are summarized as follows. •

We propose an architecture of FD self-backhaul and energy harvesting small cell networks with massive MIMO. In our proposed scheme, the MBS is equipped with massive MIMO antennas, while the SBSs with multiantenna array are powered by renewable energy and have the FD capability. By treating the SBSs as special macro users, we can achieve the concurrent transmissions of the access link of users and the backhaul link of SBSs at the same time-frequency resource block.

MBS SBS User Interference Area

Battery

Fig. 1: The network model. Furthermore, to avoid the multi-user and inter-tier interference, we propose a precoding scheme of MBS and SBSs, where an advanced Block Digitalization (BD) precoding method is proposed to project the transmission signal into the null space of interference channel matrix. • Then we formulate the cell association and power allocation as an optimization problem from the EE perspective, which implies a SBS sleep problem, while taking into account the lowest QoS requirement of users, the energy arrival rate, and the remaining energy of SBSs. In addition, the residual self-interference of FD communications is involved in the formulated problem. • Since the formulated problem is non-convex, its computational complexity is prohibitively high. To solve it efficiently, we transfer the original problem into a difference of convex program (DCP) [29] by appropriate variable substitution, and then solve it via a constrained concave convex procedure (CCCP)-based [30] iterative algorithm. Furthermore, the convergence of the proposed iteration algorithm is proved. • Extensive simulations are conducted with different system configurations to verify the effectiveness of the proposed FD self-backhaul and energy harvesting scheme for small cell networks with massive MIMO. It can be shown that our proposed scheme achieves good performance in terms of EE, energy consumption and cost. The rest of this paper is organized as follows. Section II introduces the framework of our proposed FD self-backhaul and energy harvesting small cell networks with massive MIMO. Section III presents the precoding scheme design and problem formulation. After that, we solve the optimization problem in Section IV and demonstrate the simulation results in Section V. Finally, Section VI concludes this study. Notation: We use boldface upper and lower case symbols to denote matrices and column vectors, respectively. The conjugate operator is denoted by (·) H . IL denotes the L × L dimension identity matrix. The determinant and trace operators are denoted by det(·) and Tr(·), respectively. The norm of a vector is denoted by · . •

II. S YSTEM MODEL In this paper, we consider a two-tier small cell network consisting of one MBS with MIMO antennas array and N SBSs with multi-antenna array, where the MBS uses the conventional grid power while the SBS is capable of harvesting energy from renewable energy (e.g., solar and wind), as shown



in Fig. 1. The energy arrival rate in SBSs is defined by λ EH . Let Am and As denote the number of antennas in MBS and SBS, respectively. K users with single antenna can access to MBS or any SBS. The user accessed to either MBS and SBS is named by MU and SU, respectively. It should be noted here that MU located in the interference area 1 of SBSs (as shown in Fig. 1) will suffer the inter-tier interference from SBSs. Let U m and Uns be the set of usersassociated to MBS and SBS n, respectively, and U = U m Uns be the set of all users. Considering that some SBSs may be shut off because of the lack of remaining energy, we define B s as the set of SBSs in which Uns is non-null, U nv as the set of MUs (i.e. victim MUs) located in the interference area of SBS n, and B us as the set of the SBSs interfering MU u. If B us is null, it indicates that MU u is not a victim MU and does not suffer any intertier interference from SBSs. For ease of analysis, full buffer traffic model is assumed in both MBS and SBSs. Note that we focus on the DL transmission of the considered networks in this paper. The proposed FD self-backhauling scheme of small cell networks with massive MIMO is introduced in Subsection II-A and the MIMO DL signal is described in Subsection II-B. A. FD Self-backhauling Scheme of Small Cell Networks with Massive MIMO As shown in Fig. 2, SBSs are equipped with FD hardware in our proposed scheme, enabling in-band backhaul capacity for themselves. In the DL, a SBS can receive data from the MBS while simultaneously transmitting to its users in the same frequency band. In this mechanism, the small cell can effectively backhaul itself, eliminating the need for a separate backhaul solution or frequency band. Therefore, selfbackhauling can significantly reduce the cost and complexity of rolling out small cell networks. Due to the limitation of self-interference cancellation technologies, nevertheless, the backhaul DL of SBSs will suffer self-interference from access DL of SUs. Moreover, with the massive number of antennas in MBS and and multi-antennas in SBSs, both MBS and SBSs can transmit data to multiple users simultaneously in the same frequency band via the multi-user MIMO technology. In this paper, we study the FD self-backhaul in massive MIMO-equipped small cell networks with the SBSs acting as special MUs. In our proposed scheme, not only the MBS transmits data to MUs and SBSs, but also SBSs could transfer data to their users simultaneously in the same frequency band. In other words, by jointly considering FD and massive MIMO technologies, we achieve not only the concurrent transmission of MUs and SUs in a same frequency band, but also the simultaneous access and backhaul of SBSs in the same frequency band. Therefore, this scheme will improve the spectrum efficiency and EE, and meanwhile decrease the cost of backhaul infrastructure. To reap the benefits of massive MIMO antennas, perfect channel state information (CSI) is assumed to be available 1 The interference area is the marginal coverage area of a SBS, which depends on the received signal power threshold ζ. If the received signal power of one MU from a SBS exceeds ζ, we think the MU locates the interference area of the SBS.

Massive MIMO antennas

Self-interference Antennas array MU

MU

SU

SU

Fig. 2: The FD self-backhaul scheme with massive MIMO.

at transmitters, and the TDD protocol is adopted for the exploitation of the channel reciprocity, which allows the MBS to estimate its DL channel from UL pilots sent by the users.

B. MIMO DL Signaling In this subsection, we take a typical user u as an example to analyze the access DL signal of MUs and SUs, and a typical SBS n to analyze the backhaul DL signal of SBSs, with the assumption that all channels follow independent and identically distributed (i.i.d.) CN (0,1). 1) Access DL of MUs and SUs: As described in Subsection II-A, the MBS with massive MIMO serves MUs for accessing and the SBSs for backhauling at the same time-frequency resource block. The received signal at MU u can be given as H m m m H yum = (hm u ) wu xu + (hu )

+

H (hm u )

n∈Bs

Wnb xbn

+

K u ∈U

m

wum xm u

,u =u

H s s (hs,n u ) Wn xn

+ nm u ,

(1)

s n∈Bu

where the first term is the desired signal, in which h m u ∈ CAm ×1 , wum ∈ CAm ×1 and xm u are defined as the channel vector, precoding vector and transmitting signal of user u at MBS, respectively; the second term is the multi-user interference from other MUs; the third term is the multi-user interference from backhaul signals of all SBSs, in which W nb ∈ CAm ×As and xbn are the precoding matrix and the transmitting signal of SBS n at MBS, respectively; the forth term is the inter-tier is the channel interference from some SBSs, in which h s,n u s vector from SBS n to user u, and W ns ∈ CAs ×Un and xsn are the precoding matrix and transmitting signal symbol vector of all SUs associated to SBS n, respectively; the last term is the additive white Gaussian noise (AWGN) with m H 2 E{nm u (nk ) } = σ . With respect to SBS n, it utilizes its antennas to support multi-user MIMO transmission. For SUs, they suffer not only the inter-tier interference from the MBS but also the multiuser interference from other SUs in the same SBS, then the



received signal of user k associated to SBS n is given as s,n H s,n s,n s,n H yus,n = (hs,n wus,n u ) wu xu + (hu ) ˆ xu ˆ H + (hm u )

u ∈U

u ˆ∈Usn ,ˆ u=u

m H wum xm u + (hu )

Wnb xbn + ns,n u , (2)

n∈Bs

m

where the first term is the desired signal, in which w us,n ∈ ∈ C1×1 are the elements of W ns and CAs ×1 and xs,n u xsn , representing the precoding vector and transmitting signal intended for user u in SBS n, respectively; the second term represents the multi-user interference from other SUs in SBS n; the third and forth term are the inter-tier interference from 2 2 MBS; and the last term is the AWGN with E{(ns,n u ) }= σ . 2) Backhaul DL of SBSs: In our proposed FD self-backhaul scheme of small cell networks with massive MIMO, the MBS is responsible for achieving the access DL of MUs as well as backhaul DL of SBSs at the same time-frequency resource block. For the SBS n, the received signal from the MBS can be expressed as wkm xm ynb =(Hbn )H Wnb xbn + (Hbn )H k k∈Um

+ (Hbn )H

N

Wnb xbn + χbn + nbn ,

(3)

n ∈Bs ,n =n

where the first term is the desired signal and H bn ∈ CAm ×As is the channel matrix from MBS to SBS n; the second and third term are the multi-user interference from MUs and other SBSs, H respectively. The last term is the AWGN with E{n bn nbn } = σ 2 IAs . Different from the access DL, the backhaul DL of SBSs suffers the self-interference besides the multi-user interference. According to [31], the self-interference can be expressed as √ H s s (4) χbn = γ(Hs,n SI ) Wn xn , As ×As is the self-interference channel matrix where Hs,n SI ∈ C among antennas in SBS n, γ is the self-interference cancellation factor, which is determined by specific self-interference cancellation technologies. Any self-interference cancellation technology (e.g., [18]) can be applied at SBSs, and the analysis in this paper is a general case. For the simplification of our model, the intra-tier interference in small cell tier is neglected in (1)−(3) due to the low transmission power of SBSs. In addition, even though the intra-tier interference is considered, it also can be cancelled completely by the proposed precoding scheme design in next section, but will increase the complexity of our model drastically.

III. P RECODING S CHEME D ESIGNS AND P ROBLEM F ORMULATION From the perspective of EE, the multi-user and inter-tier interference in (1), (2), (3) lead to more power consumption in access DL and backhaul DL, and then decreasing the EE performance. Specially, inter-tier interference cancellation is always a non-trivial challenge for wireless networks [32]– [35]. In this paper, we cancel the multi-user interference and inter-tier interference by designing precoding schemes of

both MBS and SBSs. In this way, the inter-tier interference problem, regarded as the traditional challenge of small cell networks, can be solved perfectly, which is another benefit of the combination of massive MIMO with small cell networks. In this section, we first introduce the precoding scheme of MBS and SBSs in detail, and then formulate an optimization problem maximizing the EE of the consider system with some constraints. Note that we make an assumption that the cell association scheme of all users has been decided in the precoding scheme design section III-A. A. Precoding Scheme Designs We propose an advanced Block Digitalization (BD) [36] [37] precoding scheme to cancel both the multi-user and inter-tier interference. The traditional BD precoding scheme is utilized to cancel multi-user interference for the MIMO multiuser DL channel by constraining the precoding scheme of each user to lie in the null space of the aggregated channel matrix of other users. In our proposed advanced BD precoding scheme, the precoding scheme of each user is constructed to lie in the null space of the aggregated channel matrix of all interfered links (including not only multi-user interference links but also inter-tier interference). In this way, not only the inter-tier interference but also the multi-user interference can be eliminated completely simultaneously. In the following, the joint precoding scheme will be introduced in detail. 1) Precoding Scheme in the MBS: As described in Subsection II-A, the MBS is responsible to transmit data to MUs and SBSs, so we need to provide the individual precoding schemes of MUs and SBSs. We define Uu,b = U B s as the set of all users and SBSs. According to the traditional BD precoding m scheme, we further define by H u the aggregated DL channel matrix of all elements of U u,b except for user u from MBS b and by Hn the aggregated DL channel matrix of all elements of Uu,b except for SBS n from MBS. As stated in [38], the m b singular value decomposition (SVD) of H u and Hn can be presented as m m m m (1) m (0) H Λu 0 Hu = Uu V u Vu , (5) 0 0 and b

b

Hn = Un m

Λbn 0

0 0

H b (1) b (0) Vn Vn ,

(6)

b

respectively. Uu and Un are the left singular matrix of m b b Hu and Hn separately. Λm u and Λn are diagonal matrixes m b whose diagonal elements are singular values of H u and Hn m (1) m (0) respectively. Sub-matrixes V u and V u are the right singular matrixes corresponding to nonzero and zero singular b (1)

m

values of Hu , respectively. Similarly, sub-matrixes V n

b (0) Vn

and

are the right singular matrixes corresponding to nonzero b and zero singular values of H n , respectively. Theorem 1. If the condition U + A s × N − 1 < Am is satisfied, the precoding matrix of SBS n and MU u can be b (0)

constructed by W nb = Vn

(0) m 1/2 Wnb and wum = vm Pu u



respectively, where Wnb is the candidate precoding matrix to m (0) (0) is one column vector of V u be decided for SBS n, v m u m and Pu is the allocated transmission power to MU u, and then the multi-user interference among all SBSs and MUs and inter-tier interference from MBS to SUs will be eliminated completely. Proof: Since the precoding schemes of MUs and SBSs are similar, we take the proof of SBSs as an example. According to the theory of SVD in [38], the column vectors b (0)

belonging to V n b

b (0)

b

locate in the null space of H n , which b

= 0. From the definition of H n , it can be means Hn Vn b m m H m observed that Hn = [Hm SU , HSBS , HMU ] , where HSU is the aggregated DL channel matrix of all SUs from MBS, m HSBS is the aggregated DL channel matrix of all SBSs except for SBS n from MBS, and H m MU is the aggregated DL channel matrix of all MUs from MBS. Then, it is (0) m b (0) H b = 0, (HSBS )H Vn = 0, obvious that (H m SU ) Vn (0) b H = 0 hold. If the precoding matrix of and (Hm MU ) Vn SBS n is constructed by W nb = Vsm (0) Wnb , it can be m H b H b observed that (H m SU ) Wn = 0, (HSBS ) Wn = 0, and m H b 2 (HMU ) Wn = 0 . In this way, the transmission signal from

MBS to SBSs will not interfere with SUs, MUs and other SBSs, implying the inter-tier interference to SUs and multib (0)

user interference are cancelled. However, V n will not exist when Am < rnb (rnb is the rank of H bn ). Due to the assumption that all channels follow i.i.d. CN (0,1), r nb can be expressed b (0)

will make as rnb = min(Am , U + As × (N − 1). Vn sense only when U + As × (N − 1) < Am . Similarly, only when the condition that U + A s × N − 1 < Am is (0) m 1/2 Pu satisfied, the precoding scheme of MU u w um = vm u can cancel the inter-tier interference from MU u to SUs and multi-user interference among MUs and SBSs. As a result, U + As × N − 1 < Am is a necessary condition of Theorem 1. 2) Precoding Scheme in the SBSs: H vn = [..., (hs,n u ), ...] ∈ n CUv ×As , u ∈ Unv is defined as the DL interference channel s,n matrix of all victim users interfered by SBS n 3 . Hu is the aggregated DL channel matrix of all SUs in SBS n except for SU u. To avoid the inter-tier interference to the victim MUs and the multi-user interference among SUs in the same SBS, the precoding matrix w us,n of SUs in SBS n should satisfy s,n the condition (H vn )H wus,n = 0, (Hu )H wus,n = 0, ∀u ∈ Uns . s,n s,n is the null space of s,n = [H , Hv ]H and V We define H u u n u s,n H . As in Theorem 1, if the condition A s > Unv +Uns − u us,n Pun,s 1/2 , 1 is satisfied, wun,s can be constructed by w un,s = v s,n and P n,s 1/2 is the us,n is one column vector of V where v u u allocated power to SU u. In this way, the inter-tier interference from SBSs to victim MUs and multi-user interference among SUs in the same SBS can be eliminated completely.

After the precoding in MBS and SBSs, the received signal of MU u can be rewritten as H m (0) m 1/2 m yum = (hm Pu xu + nm u ) vu u,

(7)

and the available link rate of MU u can be given as

H m 2 m (hm u ) vu Pu Rum = log 1 + . σ2

(8)

The received signal of SU u can be rewritten as H s,n s,n 1/2 s,n u Pu yus,n = (hs,n xu + ns,n u ) v u ,

(9)

and the available link rate of SU u becomes

H s,n 2 s,n u Pu (hs,n u ) v s,n Ru = log 1 + . σ2

(10)

The received signal of SBS n from MBS can be rewritten as b (0)

ynb = (Hbn )H Vn

Wnb xbn + χbn + nbn .

(11)

The self-interference signal of SBS n can be rewritten as √ H s s 1/2 s χbn = γ(Hs,n xn , (12) SI ) Vn Pn where Vns = [..., vus,n , ...], u ∈ Uns and Psn = diag(..., Pus,n , ...), u ∈ Uns are the aggregated precoding matrix and transmission power matrix, respectively.

b (0)

with dimensions We further define H bn = (Hbn )H Vn As × Am − rnb as the effective channel matrix of SBS n after the iter-tier and multi-user interference cancellation, b Wnb ∈ CAm −rn ×As is the precoding matrix of SBS n to be determined. According to [37], the effective channel of SBS n can be decomposed into multiple parallel independent point to-point channel by letting the precoding scheme W nb be the right singular vectors of H bn . Define the SVD decomposition (1) (0) H Λbn 0 , (13) Hbn = Ubn Vnb Vnb 0 0

where Ubn and Vnb are unitary matrices, Λ bn is a rnb × rnb diagonal matrix, r nb = min(As , Am − rnb ) is the rank of the effective channel H bn . Then, by constructing W nb = b b 1/2 (1) Pbn Vnb , where Pbn ∈ Crn ×rn is a diagonal matrix b (j = 1, ..., rnb ) scale the power transwhose elements Pn,j mitted into each column of W nb , and multiplying the received H signal ynb with Ubn , the MIMO channel between MBS and SBS n is transformed into rnb parallel single-input singleoutput channels. The received signal of SBS n can be rewritten as Irnb 0 1/2 b H ˜ n + Ubn χbn ˜ nb =Λbn Pbn x y 0 0 H Irnb 0 + Ubn nbn , (14) 0 0

2 Wb n

is defined for the channel decomposition of the channel between MBS and SBS n 3 If the intra-tier interference is considered, some SUs severed by other SBSs but suffered intra-tier interference from SBS n will be considered in Hvn

˜ bn is the effective transmitting where the rnb × 1 vector x signal from MBS to SBS n. If the multi-user and inter-tier interference precoding is not performed in MBS, the number of effective channels between MBS and SBSs should be min(Am , As ). However, it will be rnb = min(As , Am − rnb )



now, indicating that the spatial degree of freedom of channel between the MBS and SBSs decreases because of the interference cancellation. After substituting (12) into (14), the available link rate of SBS n from MBS is

Rnb = log

⎧ ⎪ ⎨ ⎪ ⎩

⎛ ⎜ det ⎝Irnb

⎞⎫ ⎪ ⎬ Λbn 2 Pbn ⎟ + ⎠ . 2 γ Hs,n Pus,n + σ 2 ⎪ ⎭ SI s u∈Un

(15) As mentioned in the beginning of this section, we study the precoding scheme based on the assumption that the cell association scheme of all users is determinate. Interestingly, it can be observed that the precoding scheme w um , Wnb , and wus,n of MU u, SBS n and SU u respectively can be obtained before cell association scheme is decided. For w um , the vector (0) vm is not related to the cell association scheme since the u m aggregated DL channel matrix H u includes the DL channel of all users and SBSs except for MU u, so we can obtain (0) of all users by regarding them as MUs. For the vector v m u s,n us,n is up to the aggregated channel matrix wu , the vector v s,n which only depends on the coverage area of SBS n. H u In the coverage area of SBS n, the users will be served by either SBS n or MBS and the users associated to MBS will us,n of all users in the coverage be victim users, so the vector v area of SBS n can be obtained by treating those users as SUs. Similarly, for W nb , it is calculated by two steps but the matrix b (0) Vn

(1) Vnb

in the first step and in the second step are also not related to the cell association scheme, so the matrix Λ bn of all SBSs can be acquired independently. Although the precoding is executed after the cell association progress, we can peer into the result of precoding in advance and exploit it to simplify the process of cell association. So far, the multi-user and inter-tier interference in (1), (2) and (3) have been eliminated perfectly by our proposed precoding scheme, based on this result, then we will search the optimal cell association and power allocation scheme by formulating an optimization problem in next subsection.

Then, we model the power dissipation U T P of the system as m ρm a m ρm Tr Pbn UT P (A, P) = u Pu + u∈U m

n∈Bs

+

s,n ρs as,n u Pu

+ P0m + B s P0s ,

n∈Bs u∈U s

(17) where the first three terms are the consumed transmit power of MUs, backhaul DL of SBSs and SUs, respectively, P 0m and P0s are the constant circuit power consumption of MBS and each SBS separately, which involves the power dissipations in the transmit filter, mixer, frequency synthesizer, and digital-toanalog converter. ρ m ≥ 1 and ρs ≥ 1 are constants accounting for the inefficiency of the power amplifier of MBS and SBS respectively. Hence, the EE of the considered system is defined as the total average number of bit/W successfully delivered to the users UT R (A, P) . (18) UEE (A, P) = UT P (A, P) The optimal user association scheme A, and power allocation policy P can be obtained by solving max UEE (A, P) A,P s,n s as,n s.t. C1 : Rnb ≥ u Ru , ∀n ∈ B , C2 :

s u∈Un

m am u Pu +

u∈U m

C3 :

⎧ ⎨ ⎩

m Tr Pbn ≤ Pmax ,

n∈Bs s,n ρs as,n + P0s u Pu

s u∈Un

(19)

⎫ ⎬ ⎭

T ≤ λEH T + Ens ,

∀n ∈ B s , C4 : Rum ≥ Rmin , ∀u ∈ U m , C5 : Rus,n ≥ Rmin ∀u ∈ Uns , ∀n ∈ B s ,

m s,n s C6 : am u ∈ {0, 1}, ∀u ∈ U ; au ∈ {0, 1}, ∀u ∈ Un , ∀n ∈ B s , as,n C7 : am u + u ≤ 1, ∀u s n∈Bu

B. Problem Formulation In this paper, we jointly optimize the cell association and power allocation scheme from the EE perspective in one time period taking into account the QoS requirement of users, energy arrival rate as well as remaining battery energy of s,n the user’s association SBSs. We denote by am u and au indicator. When user u is associated with MBS, a m u = 1; = 0. Similarly, when user u is associated with otherwise, am u s,n SBS n, as,n = 1; otherwise, a = 0. Moreover, let A and u u let P denote the cell association and power allocation scheme, respectively. The system throughout U T R can be expressed as UT R (A, P) =

u∈U m

m am u Ru +

s n∈Bs u∈Un

s,n as,n u Ru .

(16)

where C1 specifies that the backhaul DL rate of any SBS must be no less than the sum rate of SUs associated to it. C2 is the maximum transmission power constraint of MBS, m is the maximum transmission power of MBS. in which Pmax C3 is the energy causality constraint of SBSs in which E ns is the remaining energy in battery of SBS n and λ EH T is the energy that the SBS can harvest from the environment in the following time peroid. C4 and C5 specify the lowest QoS requirements for MUs and SUs. C6 and C7 indicate that all users only can access to one BS. From the section III-A, in order to eliminate the multi-user and the inter-tier interference, the constraints that A m > U + As × N − 1 and As > Unv + Uns − 1 should be satisfied, which will affect the feasibility of problem (19). To guarantee the feasibility of (19), the admission control mechanism is introduced in to limit the number of users. Actually, this paper just consider the cell association and power allocation in one spectrum resource



block and the redundant users can be scheduled on other spectrum resource blocks. Nevertheless, this will complicate our model and will be covered in the future works. Due to the energy limitation, one SBS will be shut off when it can not bring any gain. Therefore, (19) implies a SBS sleep optimization problem and its solution can be obtained by the optimal cell association scheme A ∗ . IV. S OLUTION TO THE O PTIMIZATION P ROBLEM The considered problem (19) is a combinatorial and nonconvex problem. The combinatorial nature comes from the integer constraint of A. And the non-convexity arises from the objective function and constraints C1, C4 and C5. In general, a brute force approach can be utilized to obtain the global optimal solution. However, such a method has exponential complexity with respect to (w.r.t.) the number of SBSs and users, which is computationally infeasible even for small size systems. In order to acquire an efficient cell association and power allocation algorithm, we introduce the following transformation.

Algorithm 1 Iterative solution algorithm Initialization a) Initialize the maximum number of iterations L max and the maximum tolerance 1 ; b) Set EE q = 0 and iteration index l = 0; 2: repeat a) Solve the optimization problem in (1) for the given q and obtain cell association and power allocation scheme {A , P }; b) if UT R (A , P ) − qUT P (A , P ) ≤ 1 then Convergence=true T R (A ,P ) return {A∗ , P∗ } = {A , P } and q ∗ = U UT P (A ,P ) ; else T R (A ,P ) Set q = U UT P (A ,P ) and l = l + 1 Convergence=false end if 3: until Convergence=true or l = L max 4: Output the optimal cell association and power allocation scheme A∗ , P∗ . 1:

A. Problem Transformation The fractional objective function in (19) can be classified as a nonlinear fractional program [39]. For ease of notation, F is defined as the set of all feasible solutions of problem (19). Without loss of generality, we further define the maximum EE q ∗ as q∗ =

∗

∗

UT R (A, P) UT R (A , P ) = max , ∀{A, P} ∈ F . (20) A,P UT P (A, P) UT P (A∗ , P∗ )

B. Some Approximations

The first step is to deal with the combinatorial constraint C6. Following the approach in [40], [42], [43], we relax a m u and as,n in C6 to be real-valued variables and then C6 can u be transformed as

Now, we can have the following Theorem. Theorem 2. If and only if max A,P

UT R (A, P) − q ∗ UT P (A, P) m s,n s s C6 : 0≤am u ≤ 1, ∀u ∈ U ; 0≤au ≤ 1, ∀u ∈ Un , n ∈ U . (23)

= UT R (A∗ , P∗ ) − q ∗ UT P (A∗ , P∗ ) = 0, the maximum EE q ∗ is achieved. Proof: Theorem 2 can be proved by following a similar approach as in [39]. We propose an iterative algorithm (known as the Dieback method [39]) for solving (19) with an equivalent objective function. The similar algorithm is also adopted in [40]. In each iteration, we need to solve the following optimization problem for a given q. UT R (A, P) − qUT P (A, P)

(21)

s.t. C1, C2, C3, C4, C5, C6, C7.

(22)

max A,P

The proposed algorithm is summarized in Algorithm 1. It should be noted that the convergence of Algorithm 1 is guaranteed (the good convergence performance of Algorithm 1 has been proven in [41] and [40]). In the following subsection, a series of approximations is adopted to transform problem (21) into a DCP.

s,n The relaxed a m can be interpreted as the time u and au sharing factor that represents the ratio of time when user n is associated to the MBS or SBS n. It is more difficult to implement multi-BS association than single-BS association in a practical system, and thus we adopt the method in [44] to revert the multi-BS association results to single BS association. However, even after relaxing the variables, problem (21) is still nonconvex due to the nonconvex objective function. Thus, to make problem (21) tractable and solvable, a second step is necessary. Next, we give a proposition with respect to the equivalent problem of (21). m m and Proposition: If we define P˜um = am u Pu , ∀u ∈ U s,n s,n s,n s s ˜ Pu = au Pu , ∀u ∈ Un , n ∈ U , there exists an equivalent



formulation of problem (21) as follows. ˜m ˜ s,n am as,n max u Ru + u Ru ˜ A,P

u∈U m

−q

n∈Bs

+

ρm Tr(Pbn )

n∈Bs

s u∈Un

s u∈Un

ρm P˜um +

u∈U m

improve the system performance. Furthermore, by substituting s,n 2 Hs,n Pu in (15) by Q, the self-interference can SI

ρ P˜us,n + P0m + B s P0s s

(24)

n∈Bs u∈U s

s.t.C1 : Rnb ≥ C2 :

P˜um +

u∈U m

C3 :

⎧ ⎨ ⎩

s ˜ s,n as,n u Ru , ∀n ∈ B ,

s u∈Un

ρs P˜us,n + P0s

s u∈Un

˜m C4 &C5 : am u Ru +

m Tr(Pbn ) ≤ Pmax ,

n∈Bs

⎫ ⎬ ⎭

T ≤ λEH T + Ens , ∀n ∈ B s ,

˜ s,n as,n u Ru ≥ Rmin , ∀u,

s n∈Bu

C6 , C7, The equivalent problem (24) can be recovered by substituP˜ m P˜ s,n tion of variable P um = aum and Pus,n = aus,n into problem u u s,n = 0 and a = 0. Due to the loss of (21), except for a m u u s,n definition when a m = 0 and a = 0, it is not a one-to-one u u s,n = 0 and a = 0 certainly hold owing mapping. However, a m u u to the optimality. Obviously, BS will not allocate any power to one user if it is not associated with the BS. Thus, it becomes a one-to-one mapping when the complete mapping between m m ˜m (am u , Pu ) and (au , Pu ) is defined as ˜m Pu if am m u > 0 , am (25) Pu = u 0 otherwise s,n Similarly, the complete mapping between (a s,n u , Pu ) and s,n ˜ s,n (au , Pu ) is s,n P˜u if as,n u >0 . as,n u Pus,n = (26) 0 otherwise

Thus, the solution to problem (21) can be obtained by solving problem (24). However, due to the self-interference in R nb , it still is difficult to handle problem (24). To this end, we introduce an additional constraint to problem (24), which is given by 2 Pus,n ≤ Q. (27) C8 : Hs,n SI s u∈Un

C8 can be interpreted as the maximum self-interference temperature [40], [45] (tolerable interference level) in each SBS. In general, adding an additional constraint to the optimization problem, typically results in a performance lower bound of the original problem due to the smaller feasible set. By varying 4 the value of Q, the resource allocator is able to control the amount of self-interference in each SBS to 4 The maximum self-interference temperature variable Q is not an optimization variable in the proposed framework. However, a suitable value of Q can be found via simulation in an off-line manner.

be decoupled from the constraint C1, which facilitates the design of an efficient cell association and power allocation algorithm. Then, the available link rate of SBS n’ backhaul DL is lower bounded by

b 2 b ¯ nb = log det Irb + Λn Pn R ≤ n γQ + σ 2 ⎧ ⎛ ⎞⎫ ⎪ ⎪ ⎬ ⎨ Λbn 2 Pbn ⎜ ⎟ log det ⎝Irnb + ⎠ . 2 ⎪ γ (Hs,n Pus,n + σ 2 ⎪ ⎭ ⎩ SI ) s u∈Un

(28) ¯ nb in (28) into the constraint By substituting the lower bound R C1 of problem (24), a modified optimization problem is available. Note that problem (24) mentioned in the rest of this paper means the modified optimization problem with constraint C8. In order to solve this problem, we have the following Theorem. Theorem 3. Given q, problem (24) is a DCP, where the objective function is concave, the feasible set formed by all constraints in (24) except C1 is a convex set, C1 is a concave˜ concave constraint w.r.t. the optimization variable A and P. s,n s,n ˜ s,n ˜m Proof: Define Cum = am u Ru and Cu = au Ru . According to [46] (Sec. 2.3.3), the function f (t, x) = x log{1 + xt } is the well known perspective operation of the function g(t) = log{1 + t}, and the perspective function has same convexity with the original function. Since g(t) = log{1 + t} is concave w.r.t. t, the function f (t, x) is jointly concave w.r.t. ˜m t and x. As a result, we have the conclusion that C um = am u Ru s,n ˜ s,n ˜ and Cu Ru are joint concave w.r.t A and P. In addition to ˜ is linear w.r.t. P, ˜ the objective function the fact that UT P (A, P) ˜ Since the of problem (24) is jointly concave w.r.t. A and P. constraints C2 , C3 , C6 , C7, and C8 are linear constraints and the constraint C4 &C5 are concave, the feasible set ¯b formed by these constraints is a convex set. Meanwhile, R n b is concave w.r.t. Pn , so problem (24) becomes a difference of convex problem since the constraint C1 is a concave-concave constraint [29], [47]. For ease of presentation, we rewrite problem (24) as

˜ = UT R (A, P) ˜ − qUT P (A, P) ˜ U(A, P) s ˜ s,n ¯ nb − as,n s.t. C1 : R u Ru ≥ 0, ∀n ∈ B ,

max ˜ A,P

(29)

s u∈Un

˜ ∈ F. {A, P}

C. The Proposed CCCP Based Solution Algorithm In this subsection, the CCCP, which is widely adopted for solving DCP [30] [48], is used to solve problem (29). The main idea of the CCCP-based algorithm is to iteratively approximate the original nonconvex feasible set (decided by C1 ) by a convex subset and then solve the resulting convex approximation in each iteration. As the nonconvex part in C1 of problem (29) ˜ s,n stems from the fact that function C us,n = as,n u Ru is concave



Algorithm 2 The Proposed Low-Complexity Solution 1:

2: 3: 4: 5: 6:

Initialization: Initialize maximum number of iterations L2max and the maximum tolerance 2 ; Initialize the algo˜ 0 ) and set the iteration rithm with a feasible point ([A] 0 , [P] number l=0. Repeat: t s,n Compute the affine approximation Cûs,n ([αs,n u ] , αu ) according to (30). ˜ t+1 ). Solve problem (31), and update ([A] t+1 , [P] Set t = t + 1. ˜ t+1 ) − U([A]t , [P] ˜ t ) ≤ 2 or t ≥ Until: U([A]t+1 , [P] 2 Lmax .

but not convex, we approximate this function in the t-th t s,n iteration by its first-order Taylor expansion Cûs,n ([αs,n u ] , αu ) t s,n around the current point [α s,n ] , where α is defined as u u s,n ˜ s,n αs,n = (a , P ) for the sake of brief notations. According u u u to [49], the first-order Taylor expansion Cûs,n is t s,n s,n s,n t Cûs,n ([αs,n u ] , αu ) = Cu ([αu ] )

t s,n s,n t s s + ΔCus,n ([αs,n u ] )(αu − [αu ] ), ∀u ∈ Un , n ∈ B , (30)

s,n s,n t which is an affine function w.r.t. α s,n u . Here, ΔCu ([αu ] ) s,n s,n t is the first-order derivative of the function C u ([αu ] ) w.r.t. αs,n u . Thus, in the t-th iteration of the proposed CCCP based iterative algorithm, the following convex optimization problem,

max ˜ A,P

˜ U(A, P)

(31)

¯ nb − s.t. C1 : R

t s,n s Cûs,n ([αs,n u ] , αu ) ≥ 0, ∀n ∈ B ,

s u∈Un

˜ ∈ F, {A, P}

max ˜ A,P

¯ nb − s.t. R

g

(34) t s,n s Cûs,n ([αs,n u ] , αu ) ≥ g, ∀n ∈ B ,

s u∈Un

˜ t+1 ) which implies is solved, and the solution is ([A] t+1 , [P] s,n n+1 [αu ] . This procedure is carried out iteratively until convergence or the maximum number of allowable iterations is reached. We summarize the proposed low-complexity solution as Algorithm 2, where we assume that an initial feasible ˜ 0 ) of the DCP (29) is available (how to obtain point ([A]0 , [P] an initial feasible point will be introduced in the following subsection). Since Cus,n (αs,n u ) is concave and is approximated t s,n by its first-order Taylor expansion Cûs,n ([αs,n u ] , αu ) in (30), it is obvious that s s ˆ s,n s,n t s,n Cus,n (αs,n u ) ≤ Cu ([αu ] , αu )∀u ∈ Un , n ∈ B ,

(32)

which implies that t s,n ¯b ¯ nb − Cûs,n ([αs,n Cus,n (αs,n R u ) ≤ Rn − u ] , αu ). s u∈Un

˜ t ) generated in each iteration t solving the convex ([A]t , [P] optimization problem (31) with the affine approximation in (30), always belong to the proper feasible set defined by C1 and F of (29). Inspired by [46] (Sec. 11.4), [50], [51], we propose a feasible initial point searching algorithm, instead of an arbitrary point as in the conventional CCCP, to obtain the ˜ 0 ) in Algorithm 2. The main advantage of the feasible ([A]0 , [P] proposed new initialization method stems from the fact that, once the proposed algorithm starts with a point in the feasible ˜ t ) generated set of the DCP (29), all the iterates ([A] t , [P] by the algorithm remain within the original feasible set of the DCP (29). In addition, if the CCCP is initialized with a random (infeasible) point, the CCCP may fail at the first iteration due to the infeasibility of problem. However, the task of computing a feasible point of a nonconvex optimization problem, e.g., problem (29), is NP-hard in general. This observation motivates the development of suboptimal, but lowcomplexity feasibility search procedures. The proposed feasible initial point searching algorithm is based on similar iterative affine approximations of the originally nonconvex constraints as used in Algorithm 2, but with the following two modifications: a) the proposed searching ˜ 0 ); b) in the algorithm starts with an arbitrary point ([A] 0 , [P] l-th iteration, instead of maximizing U as in problem (31), we maximizing the slack parameter g, which can be regarded as an abstract measure of the constraint violations. Then, the feasibility problem can be express as the following convex program

s u∈Un

(33) From (33), it is observed that that convex constraint C1 in problem (31) can be considered as a strengthening of the original nonconvex constraint C1 in problem (29). In other words, the feasible set in problem (31) is a proper subset of the feasible set in problem (29). As a result, provided that ˜ 0 ) is feasible for the DCP (29), then the initial point ([A]0 , [P]

˜ ∈F {A, P} If the current objective value g t+1 is zero, the algorithm stops; otherwise, the algorithm continues until convergence or until the maximum number of allowable iterations is reached. If no feasible point could be found with the proposed method, some admission control mechanisms can be adopted to reduce the number of users, which, however, is out of the scope of this paper. The proposed feasible initial point searching is summarized as Algorithm 3. Note that a solution of problem (34) with g = 0 obtained is always feasible for the DCP (29). Conversely, if the proposed Algorithm 3 fails to provide a feasible point of problem (29), then this does not imply that this problem is infeasible since Algorithm 3 operates only on a subset of the original feasible set of problem (29). The proposed Feasible Initial Point Searching Algorithm in Algorithm 3 together with the CCCP-based Algorithm 2 forms a two-step algorithm for solving the DCP in (29). In the first step, the algorithm 3 is applied to find a feasible point of the DCP in (29), instead of a random point. In the second step, the CCCP-based Algorithm 2 is applied, starting with the feasible point found in the first step. For convenience, the DCP solution algorithm in Algorithm 2 includes the feasible



Algorithm 3 The Proposed Feasible Initial Point Searching Algorithm 1:

2: 3: 4: 5: 6:

Initialization: Initialize maximum number of iterations 3 and the maximum tolerance 3 ; Initialize the algoTmax ˜ 0 ) ∈ F and set the rithm with a feasible point ([A] 0 , [P] iteration number t=0. Repeat: t s,n Compute the affine approximation Cûs,n ([αs,n u ] , αu ) according to (30). ˜ t+1 ) and Solve problem (34), and update ([A] t+1 , [P] t+1 [g] . Set t = t + 1. ˜ t+1 )−U([A]t , [P] ˜ t ) ≤ Until: [g]t+1 = 0 or U([A]t+1 , [P] 3 3 or t ≥ Tmax .

initial point searching algorithm in Algorithm 3 by default in the rest of this paper. D. Convergence And Computational Complexity Analysis 1) Convergence Analysis: Firstly, we analyze the conver˜ t) gence of Algorithm 2. We know that the point ([A] t , [P] is a feasible point of the convex optimization problem with concave objective function in problem (31), provided that the ˜ 0 ) is feasible for the DCP in feasible initial point ([A]0 , [P] ˜ t )} mono(29). As a consequence, the sequence {U([A] t , [P] tonically increases as the iteration number t grows. Since ˜ t )} is upper-bounded by transmisthe sequence {U([A]t , [P] sion power limit in C2 and the energy limit in C3 , the ˜ t )}, and thus the convergence of the sequence {U([A] t , [P] convergence of Algorithm 2 is guaranteed for any initial ˜ feasible point. Moreover, since the objective function U(A, P) is concave as we have proven in subsection IV-C, the point ˜ t ), i.e., the solution of problem (31), is unique ([A]t , [P] [46] (Sec. 4.2). Hence, for any given initial feasible point ˜ t ), the entries of the two sequences, {U([A] t , [P] ˜ t )} ([A]0 , [P] t ˜ t and {([A] , [P] )}, have a one-to-one correspondence. As a ˜ t )} implies result, the monotone convergence of {U([A] t , [P] t ˜ t the convergence of the sequence {([A] , [P] )} , for any initial ˜ 0 ). Let L([A]0 , [P] ˜ 0 ) denote the limit feasible point ([A]0 , [P] t ˜ t point of sequence {U([A] , [P] )} with the feasible initializa˜ 0 ) when the iteration number t goes to infinity, tion ([A]0 , [P] ˜ 0 ), we have i.e., given the initial feasible point ([A] 0 , [P] ˜ 0 ) lim ([A]t , [P] ˜ t ). L([A]0 , [P] t→∞

(35)

˜ 0 ) depends on the choice In general, the limit point L([A] 0 , [P] 0 ˜ 0 of the initial feasible point ([A] , [P] ). For natational simplicity, we write the limit points as L. Regarding the limit point L, we have the following lemma. ˜ t )} is the solution Lemma: The limit point L of {([A] t , [P] of the following convex optimization problem: ˜ max U(A, P) ˜ A,P

¯ nb − s.t. C1 : R ˜ ∈ F, {A, P}

(36)

∗ s,n s Cûs,n ([αs,n u ] , αu ) ≥ g, ∀n ∈ B ,

s u∈Un

(37)

∗ s,n where the affine function Cûs,n ([αs,n u ] , αu ) is obtained by s,n t s,n ∗ s,n ∗ replacing [αu ] with [αu ] and [αu ] is relevant elements of L in (35). Moreover, the limit point L satisfies the constraint C1 in (36) with equalities, i.e., ∗ s,n ∗ ¯b − R Cûs,n ([αs,n n u ] , [αu ] ) s u∈Un

=

¯ nb R

−

∗ Cûs,n ([αs,n u ] ) = 0.

(38)

s u∈Un

Proof: By definition (35), the point L is the limit point ˜ t )}, hence L is a feasible point of the sequence {([A] t , [P] for the convex optimization problem (36) and no strictly better solution exists. In addition, as we haven proven in ˜ in (36) is subsection IV-C, the objective function U(A, P) ˜ strictly concave in the variables (A, P), so the solution of problem (36) is unique [46](Sec. 4.2), which means that the limit point L is the solution of problem (36). We prove the second part of the Lemma by contradiction. Assuming that the constraint C1’’ of the n-th SBS is not active, i.e., ∗ s,n ¯ nb − Cûs,n ([αs,n R u ] , αu ) > 0, we can scale down the s u∈Un

variable Pñb to make the constraint active without violating the other constraints, which makes it possible that the MUs or other SBSs’ backhaul link can be allocated more power or lower interference level. Then the objective function will increase possibly, which contradicts the optimality of the point L. Hence, it can be concluded that all constraints C1 in (36) are active at the point L. According to the Lemma 2, no matter how to choose ˜ 0 ), only if it is feasible, the final the initial point ([A]0 , [P] convergence point can obtained by solving problem (36). In other words, the limit point L is a stationary point of the DCP (29) [52]. Therefore, we have the conclusion that our proposed Algorithm 2 not only converges but also converges to a stationary point. 2) Computational Complexity Analysis: We analyze the computational complexity and compare it with the brute force search algorithm. Since the considered original problem (19) is a combinational and non-convex problem and it still is non-convex even though the constant association variables are assumed, it is difficult to solve this problem effectively. If the brute force search approach is used to solve this problem, the complexitymwill be O((N + 1) K × (N × As )Qm × Θ), where P Qm = max is the quantity of the scale of transmission power after discretization and the value of Q m depends on the discretization interval . Θ ∈ [K Qm , K Qs ] is not certain due to the fact that different cell association scheme lead to all users different power allocation. Θ = K Qm means that λ +E s /T access to MBS and Θ = K Qs (Qs = EH n ) means that all users access to the SBS with lowest energy. For our proposed iteration solution algorithm, we assume that the iteration times of Algorithm 1, Algorithm 2 and Algorithm 3 are L 1 , L2 , and L3 , respectively. The main computational complexity of the proposed solution algorithm consists in solving L 1 × L2 × L3 times the convex optimization problem (31) and (34) in inner loop. CVX software is applied to solve the problem (31) and (34), and CVX employs GP with interior-point method. Therefore, the



TABLE I: Simulation parameters 0.01

Notation

Value 0.009

2.5GHz -174dBm/Hz 256 32 46dBm 20dBm 54dBm 20dBm 5 5

0.008 Eenergy efficiency [bps/Hz/w]

Carrier center frequency Power spectral density σ2 The number of antennas in MBS Am The number of antennas in SBS As m The maximum transmission power of MBS Pmax s The maximum transmission power of SBS Pmax The circuit power consumption in MBS P0m The circuit power consumption in SBS P0s Power amplifier inefficiency of MBS ρm Power amplifier inefficiency of SBS ρs

0.007 0.006 0.005 0.004 N=30, K=80, γ=0 N=30, K=40, γ=0 N=10, K=40, γ=0 N=30, K=80, γ=−30dB N=30, K=40, γ=−30dB N=10, K=40, γ=−30dB

0.003 0.002

computational complexity of solving either problem (31) or (34) is O(log(2(N + K) + N × K + 1)/t0 ς/ log(ξ)), where 2(N +K)+N ×K +1 is the the total number of constraints of problem (31) and (34), t 0 is the initial point for approximating the accuracy of the interior point method, 0 ≤ ς ≤ 1 is the stopping criterion for the interior point method, and ξ is used for updating the accuracy of the interior point method [53]. Considering the good convergence performance and low iteration times (we investigate it in simulation section) of our proposed algorithm, the computational complexity of original problem (19) is reduced largely by our proposed algorithm comparing to the brute force search algorithm. V. S IMULATION R ESULTS AND D ISCUSSIONS In this section, the effectiveness of our proposed FD selfbackhaul and energy harvesting small cell network architecture with massive MIMO and the proposed cell association and power allocation algorithm will be demonstrated by Monte Carlo simulations. In order to show the performance of our proposed network architecture clearly, two simulation scenarios are identified: multi-cell scenario and single-cell scenario. The multi-cell scenario focuses on the performance in terms of energy and cost saving while the single-cell scenario pays attention to evaluate the gains brought by FD and massive MIMO technologies. In the multi-cell scenario, we consider a classical model with seven cells and the distance of different MBS is 1000m. In the single-cell scenario, we consider a 500m × 500m square area covered by one MBS located in the center. Both in the two scenarios, users and SBSs are uniformly distributed. Other simulation parameters [40] [54] are summarized in Table I. A. The Influence of the Maximum Self-interference Temperature and Self-interference Cancellation Factor In this section, we focus on the impact of the value of Q on the system EE in single-cell scenario. As can be seen from (24) and (27), the self-interference temperature Q, which is the key for transforming problem (24) into a solvable optimization problem, plays an important role in the proposed cell association and power allocation algorithm. The value of Q imposes a limit on the spectrum efficiency of the backhaul link and access link of SBSs by controlling the amount of interference temperature. Fig. 3 shows the EE of the proposed algorithm versus the value of Q under different self-interference cancellation factor γ, different numbers of

0.001 0

0

5

10 15 20 25 30 35 40 45 50 The ratio of maximum self−interference temperature to noise [dB]

55

Fig. 3: EE versus the ratio of maximum self-interference temperature to noise (R min = 0.5bps/Hz, λEH = 60mW/s). SBSs N and different numbers of users K. The x-axis is the interference temperature-to-noise ratio, Q/σ 2 . It can be seen in Fig. 3 that the EE remains unchanged with the variation of Q if perfect self-interference cancellation technology is adopted, i.e., γ = 0. This is because problem (24) will be a convex optimization problem and the constraint (27) does not exist when γ = 0. When we set γ = −30dB, the EE will go up first and then go down with the increase of the value of Q. It can be explained as that the power allocated to SUs is limited by constraint (27) when Q is small but the rate of backhaul link will be limited when Q is large. In addition, it can be observed that the choice of Q is dependent on the number of users. This is because a higher value of Q can be tolerated for a larger number of users as the self-interference can be better coped with due to the multiple user diversity gain. On the other hand, as expected, the optimal value of Q is also sensitive to the number of SBSs since the multiple access gain is potential when there are more SBSs. In the following, we follow the assumption that the self-interference can be cancelled completely in [18] to simply the simulation progress. B. The Performance of Our Proposed Network Architecture 1) Multi-cell Simulation Scenario: In this scenario, we demonstrate the performance of our proposed network architecture in terms of grid power consumption, cost and outage probability by comparing it with the traditional fiber backhaul and grid power scheme. The fiber backhaul is based on the 10 GPON (gigabit capable PON) technology providing sustainable bandwidth per SBS. We evaluate the cost of networks via the sum of the CapEx and the OpEx during 20 years, where the CapEx includes equipments purchase, installation and backhaul infrastructure cost, the OpEx includes energy cost, spectrum and fiber leasing, maintenance cost, fault management and space rental fee [55]. For detailed parameters with respect to the cost, please refer to [55], [56]. And user density in this area is 1 × 10−3 /m2 .



0.3

30 Grid power with self−backhaul Grid power with fiber backhaul Energy harvesting with self−backhaul Energy harvesting with fiber backhaul

0.25

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Fig. 6: Outage probability versus SBS deployment density(Rmin = 0.5bps/Hz, λEH = 60mW/s, and γ = 0).

=

Form Fig. 4, we can find that the self-backhaul scheme will consume more power than fiber backhaul scheme. This is due to the fact that some energy must be consumed in the MBS to support the transmission of backhaul data to SBSs in our proposed self-backhaul scheme. This weakness can be remedied by its great advantage in reducing the network cost. As shown in Fig. 5, the cost of our proposed FD selfbackhaul and energy harvesting scheme is lowest compared to other schemes. On one hand, the energy harvesting strategy reduces the energy cost. On the other hand, the self-backhaul will reduce the backhaul infrastructure cost tremendously. At the same time, our proposed self-backhaul scheme will decrease the use of fiber and then the carbon dioxide emission will reduce in the progress of producing fiber. As a result, the proposed self-backhaul and energy harvesting small cell architecture is helpful to achieve green communication in small cell networks.

As shown in Fig. 4, the grid power consumption of all schemes will decrease significantly with the increase of SBS deployment density. The reason is that more users will be offloaded to SBSs when there are more SBSs and then the grid power consumption in MBS will reduce because of the low energy consumption of SBSs. Meanwhile, the increase of the number of SBSs offers a opportunities for users to access some closer SBSs and then the grid power consumption in SBSs will decrease accordingly. Unfortunately, with the further increase of SBS deployment density, the off-load and multiple access point gain will be weaken, which causes that the decrease rate of the grid power consumption of all schemes goes down. However, it can be observed that the schemes with energy harvesting strategy always outperform the schemes with grid power strategy. This is because that the schemes with energy harvesting strategy can harvest energy from the environment to power SBS and thus save vast grid energy.

2) Single-cell Simulation Scenario: Fig. 7, Fig. 8 and Fig. 9 show the effectiveness of introducing FD and massive MIMO technology into self-backhaul strategy. As shown in the three figures, our proposed FD self-backhaul scheme with massive MIMO is superior to other single-antenna scheme or half duplex (HD) scheme, which can be explained as follows. First, massive MIMO improves the spectrum efficiency and EE by utilizing the free degree of space. In this way, the access of users and the backhaul of SBSs can be operated at the same time frequency resource block, rather than at time division or frequency division pattern. Second, the multiantenna deployment in MBS and SBSs broadens the backhaul link by achieving multiple data streaming transmission. In single-antenna system, the single data stream transmission limits the backhaul link rate and then reduces the number of users associated to SBSs, resulting in the decrease of spectrum efficiency and EE. Third, the application of FD technology in the backhaul of SBS enables the simultaneous reception and transmission instead of the HD pattern (the first phase for transmission and the second phase for reception), which nearly

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doubles the spectrum efficiency. Based on these three reasons, our proposed FD self-backhaul scheme with massive MIMO always performs better in terms of EE and the capacity. Furthermore, after the inter-tier interference cancellation (ITIC) by exploiting our proposed precoding scheme, the performance of our proposed FD self-backhaul scheme with massive MIMO will be enhanced further. In this case, not only the signal to interference plus noise ratio (SINR) of users but also the SINR of the backhaul links will be enhanced once the intertier interference is eliminated completely. Then, the lowest rate requirement of users can be satisfied with less power consumption, which will improve the EE and capacity further. In Fig. 7, the EE keeps increasing with the number of SBSs rising, which is because the multiple SBSs gain is obtained and the sleep strategy is adopted. With the sleep strategy, the SBS with no users attached will be shut off, leading to less circuit power consumption. When the number of users is small, there will be sufficient power resources, then the EE will increase with the increase users as shown in Fig. 8. However, the power resource will be exhausted when there are too more users and then some users will be refused to access. Nevertheless, the EE will still increase since the multi-user diversity gain is obtained. In Fig. 10 and Fig. 11, we show the effectiveness of introducing sleep mechanism into energy harvesting strategy with different numbers of SBSs. In both figures, it can be observed that the performance of energy harvesting scheme with sleep mechanism outperforms the scheme without sleep mechanism; and the performance gap gets more broadened with more SBSs. The reason is that the sleep mechanism contributes to save energy and store those energy into battery of SBSs to serve for next time slot, which improves the probability that the SBSs have enough energy to support the operation of the SBSs and then rise the ratio of SUs to all users. It is obvious that the influence is more arresting when there are more SBSs since the probability that the SBSs

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feasible points. Meanwhile, the optimal solution obtained by the brute force searching (BFS) algorithm is presented as a benchmark, in a single-cell simulation scenario with 40 users and 5 SBSs. Both the good convergence and robustness can be observed from this figure. No matter where the initial point is, our algorithm will converge. In addition, the gap between Algorithm 2 and BFS algorithm gets more narrow after sufficient iterations, although our solution is not a global optimal solution. Furthermore, it can be observed from this figure that a significant decrease of gap between Algorithm 2 and BFS algorithm can be found from the first iteration to the 10-th iteration. After the 10-the iteration, the gain of more iterations is still increasing but with less rate. Thus, a tradeoff exits between the acceptable utility value and iteration steps. VI. C ONCLUSION AND F UTURE W ORK In this paper, we proposed a self-backhaul and energy harvesting small cell network architecture and introduced FD and

massive MIMO to enhance the performance of the considered network. In this way, the access of users and backhaul of SBSs can be achieved simultaneously in the same frequency band, improving the spectrum efficiency and EE. Furthermore, in order to decrease the power consumption further, we designed the precoding scheme of MBS and SBSs to mitigate the multiuser and inter-tier interference. Considering the energy limit of SBSs and the QoS requirement of users, we formulated the cell association and power allocation problem as an optimization problem, in which EE was taken as the optimization objective. Considering the high computation complexity for solving the non-convex optimization problem, we introduced some appropriate transformations to transform equivalently the original problem into a DCP, which can be efficiently solved with local optimality using a CCCP-based algorithm. Simulation results showed that the proposed self-backhaul and energy harvesting small cell networks are able to reduce the energy consumption and the cost of networks effectively and the FD and massive MIMO technologies promoted the increase of network performance in terms of EE and the number of acceptable users. In addition, simulation results also demonstrated the effectiveness and good convergence performance of our proposed CCCP-based cell association and power allocation algorithm. Future work is in progress to consider the spectrum resource allocation and non-perfect CSI in our proposed scheme. R EFERENCES [1] S. Fortes, A. Aguilar-Garcia, R. Barco, F. Barba, J. Fernandez-luque, and A. Fernandez-Duran, “Management architecture for location-aware self-organizing LTE/LTE-A small cell networks,” IEEE Comm. Mag., vol. 53, no. 1, pp. 294–302, Jan. 2015. [2] S. Bu and F. R. Yu, “Green cognitive mobile networks with small cells for multimedia communications in the smart grid environment,” IEEE Trans. Veh. Tech., vol. 63, no. 5, pp. 2115–2126, June 2014. [3] J. Xu, J. Wang, Y. Zhu, Y. Yang, X. Zheng, S. Wang, L. Liu, K. Horneman, and Y. Teng, “Cooperative distributed optimization for the hyperdense small cell deployment,” IEEE Comm. Mag., vol. 52, no. 5, pp. 61–67, May 2014.



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Lei Chen received the B.S. degree in Communication Engineering from Beijing University of Posts and Telecommunications (BUPT), Beijing, China, in 2011. He is currently working toward the Ph.D. degree with the School of Information and Communication Engineering, BUPT, Beijing, China. He is also with the University of British Columbia as a visiting scholar since Nov. 2014. His current research interests include 5G cellular network, fullduplex wireless, resource management, cross-layer design, and small cell networks.

F. Richard Yu (S’00-M’04-SM’08) received the PhD degree in electrical engineering from the University of British Columbia (UBC) in 2003. From 2002 to 2006, he was with Ericsson (in Lund, Sweden) and a start-up in California, USA. He joined Carleton University in 2007, where he is currently a Professor. He received the IEEE Outstanding Service Award in 2016, IEEE Outstanding Leadership Award in 2013, Carleton Research Achievement Award in 2012, the Ontario Early Researcher Award (formerly Premiers Research Excellence Award) in 2011, the Excellent Contribution Award at IEEE/IFIP TrustCom 2010, the Leadership Opportunity Fund Award from Canada Foundation of Innovation in 2009 and the Best Paper Awards at IEEE ICC 2014, Globecom 2012, IEEE/IFIP TrustCom 2009 and Int’l Conference on Networking 2005. His research interests include cross-layer/cross-system design, security, green ICT and QoS provisioning in wireless-based systems. He serves on the editorial boards of several journals, including Co-Editor-inChief for Ad Hoc & Sensor Wireless Networks, Lead Series Editor for IEEE Transactions on Vehicular Technology, and IEEE Communications Surveys & Tutorials. He has served as the Technical Program Committee (TPC) CoChair of numerous conferences.

Hong Ji received the B.S. degree in communications engineering and the M.S. and Ph. D degrees in information and communications engineering from the Beijing university of Posts and Telecommunications (BUPT), Beijing, China, in 1989, 1992, and 2002, respectively. From June to December 2006, she was a Visiting Scholar with the University of British Columbia, Vancouver, BC, Canada. She is currently a Professor with BUPT. She also works on national science research projects, including the HiTech Research and Development Program of China (863 program), The National Natural Science Foundation of China, etc. Her research interests include heterogeneous networks, peer-to-peer protocols, cognitive radio networks, relay networks, Long-Term Evolution/fifth generation, and cooperative communications.

Bo Rong (M07) is a Research Scientist at Communications Research Centre Canada, Ottawa. He is also an Adjunct Professor at Ecole de technologie superieure (ETS), Universite du Quebec, Canada. Dr. Rong has authored or coauthored over 100 technical papers in major journals and conferences, as well as one book and two book chapters in the areas of wireless networking & communications. Many of these publications have significance to the research community and industry. Dr. Rongs research interests include modeling, simulation, and performance analysis of next-generation wireless networks. He is a member of IEEE Communications Society and IEEE Broadcasting Society. He serves as an Associate Editor for IEEE COMMUNICATIONS LETTERS as well as the Guest Editor of special issues for IEEE COMMUNICATIONS MAGAZINE, IEEE WIRELESS COMMUNICATIONS MAGAZINE, and IEEE INTERNET OF THINGS JOURNAL.

Xi Li is an associate professor in the School of Information and Communication Engineering of Beijing University of Posts and Telecommunications (BUPT). She received her BE degree and PhD degree from Beijing University of Posts and Telecommunications in the major of communication and information system in 2005 and 2010 respectively. She has served as the chair of special track on cognitive testbed in Chinacom 2011, TPC member of IEEE WCNC 2012/2014/2015, PIMRC 2012, CloudCom2014, ICC 2015 and VTC-Fall 2016. She has published more than 60 papers in international journals and conferences. Her current research interests include wireless communication and networks and mobile Internet.

Victor C.M. Leung (S75-M89-SM97-F03) received the B.A.Sc. (Hons.) degree in electrical engineering from the University of British Columbia (U.B.C.) in 1977, and was awarded the APEBC Gold Medal as the head of the graduating class in the Faculty of Applied Science. He attended graduate school at U.B.C. on a Natural Sciences and Engineering Research Council Postgraduate Scholarship and completed the Ph.D. degree in electrical engineering in 1981. From 1981 to 1987, Dr. Leung was a Senior Member of Technical Staffin the satellite systems group at MPR Teltech Ltd. He started his academic career in the Department of Electronics at the Chinese University of Hong Kong in 1988. He returned to U.B.C. as a faculty member in 1989, where he currently holds the positions of Professor and TELUS Mobility Research Chair in Advanced Telecommunications Engineering in the Department of Electrical and Computer Engineering. He is a member of the Institute for Computing, Information and Cognitive Systems at U.B.C. He also holds adjunct/guest faculty appointments at Jilin University, Beijing Jiaotong University, South China University of Technology, the Hong Kong Polytechnic University and Beijing University of Posts and Telecommunications in China. Dr. Leung has co-authored more than 500 technical papers in international journals and conference proceedings, and several of these papers had been selected for best paper awards. His research interests cover broad areas of wireless networks and mobile systems.
