Flexible Functional Split Design for DownlinkC-RAN with Capacity-Constrained Fronthaul

Yong Zhou, Member, IEEE, Jie Li, Yuanming Shi, Member, IEEE, and Vincent W.S. Wong, Fellow, IEEE

Abstract—In cloud radio access networks, functional splitrefers to a division of signal processing functionalities between thebaseband unit (BBU) pool and the remote radio heads (RRHs).The functionality of baseband signal precoding can either beperformed by BBU pool or RRHs, which corresponds to differentfunctional splits. The compression-after-precoding (CAP) anddata-sharing (DS) strategies are the realizations of these twofunctional splits. In this paper, we propose a flexible functionalsplit design to enable dynamic functional configuration of eachactive RRH to use either CAP or DS strategy. Our goal is tominimize the aggregate power consumption, while taking intoaccount limited fronthaul capacity, fronthaul power consumption,and quality of service requirement. We formulate a joint RRHmode (i.e., CAP, DS, sleep) selection, precoding design, andfronthaul compression problem. The formulated problem is anon-convex quadratically constrained combinatorial optimizationproblem. Through sequential convex programming and `1-normconvex relaxation, the problem is transformed into a sequence ofsemidefinite programming problems. An efficient algorithm basedon the majorize minimization scheme is developed to solve theproblem. Simulations demonstrate the importance of consideringthe limited fronthaul capacity and the performance improvementof the proposed algorithm compared with the pure CAP and DSstrategies.

Index Terms—Cloud radio access network, flexible functionalsplit, capacity-constrained fronthaul, energy efficiency, semidefi-nite relaxation.

I. INTRODUCTION

By improving the spatial frequency reuse and reducing thedistance between the user equipments (UEs) and the accesspoints, the ultra dense deployment of small cells is recognizedas an efficient and effective method to boost the networkcapacity of the fifth generation (5G) wireless networks [1].However, with the densification of small cells, every new celladds to co-channel interference, which is a key performance-limiting factor in radio access networks (RANs).

Copyright (c) 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.

Manuscript received October 25, 2018; revised January 22, 2019 and March12, 2019; accepted April 10, 2019. This work was supported in part bythe ShanghaiTech University Start-Up Funds, in part by the National NatureScience Foundation of China under Grant 61601290, in part by the ShanghaiSailing Program under Grant 16YF1407700, and in part by the NaturalSciences and Engineering Research Council (NSERC) of Canada. The editorcoordinating the review of this paper and approving it for publication was S.Misra.

Y. Zhou, J. Li, and Y. Shi are with the School of Information Scienceand Technology, ShanghaiTech University, Shanghai 201210, China. (e-mail:zhouyong, lijie3, shiym@shanghaitech.edu.cn).

V. W.S. Wong is with the Department of Electrical and Computer Engineer-ing, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada(e-mail: vincentw@ece.ubc.ca).

With the virtualization of baseband signal processing func-tionalities, cloud RAN (C-RAN) has been proposed as apromising network architecture for 5G wireless networks [2].In C-RAN, the baseband unit (BBU) pool, composed of mul-tiple BBUs, performs centralized baseband signal processingand coordinates the transmissions of low-cost remote radioheads (RRHs). The digitized baseband inphase and quadraturesamples of radio signals between the BBU pool and the RRHsare transmitted through low-latency optical fronthaul links.C-RAN can enhance the spectrum and energy efficiency bysuppressing co-channel interference via cooperative transmis-sion/reception [3], [4]. It can also reduce the network capitalexpenditure and operating expenditure by adapting to spatialand temporal traffic variations via statistical multiplexing.

The aforementioned benefits of C-RAN are achieved atthe cost of imposing a significant burden on fronthaul links.However, the fronthaul links are usually capacity-constrainedin practice [5]–[7], which may become the bottleneck ofthe centralized signal processing and affect the resourceallocation processes across RRHs. The compression-after-precoding (CAP) and data-sharing (DS) strategies are twofundamental cooperative strategies in C-RAN. In the CAPstrategy, the BBU pool performs centralized precoding andcompresses the precoded baseband signals before deliveringthem to the corresponding RRHs through fronthaul links. Onthe other hand, in the DS strategy, the BBU pool transmitsthe precoding coefficients along with the original signals tothe RRHs, which perform local precoding. Based on thesetwo strategies, resource allocation [8], fronthaul compression[9], RRH clustering [10]–[12], and device-to-device (D2D)communications [13] are studied to alleviate the fronthaulcapacity constraint. Specifically, Zhao et al. in [8] proposea joint transmit beamforming design and user data allocationscheme to minimize the requirement on fronthaul capacity.Given the finite capacity of fronthaul links, the weightedsum-rate of the CAP strategy can be enhanced by jointlycompressing the precoded signals for different RRHs [9].By balancing the tradeoff between the cooperation gain andfronthaul capacity constraint, a dynamic user-centric clusteringscheme is investigated in [10] to maximize the weighted sum-rate. Under the fronthaul capacity constraint, we propose amulti-timescale resource allocation mechanism to guaranteeefficient resource sharing among multiple service providersas well as to address the user mobility issue [11]. Moreover,the authors in [12] propose an approximate stochastic cuttingplane algorithm to address the short-term precoding and long-term user-centric clustering problems for sum-rate maximiza-tion. Taking into account dynamic traffic arrival, the authors in

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[13] formulate a stochastic optimization problem to maximizethe overall throughput of C-RAN with D2D communications,which allow direct communication between two adjacent UEswithout going through fronthaul links. However, the aforemen-tioned studies focus on maximizing the spectrum efficiencywithout considering the power consumption issue in C-RAN.

With an increasing number of RRHs, minimizing the powerconsumption becomes an important design objective of C-RAN due to the economic concern of network operators [14]–[16]. By exploiting spatial and temporal traffic fluctuations,power consumption can be significantly reduced by switch-ing off idle RRHs to provide on-demand services for UEs[17]. The authors in [18] and [19] propose dynamic RRHsand virtual base stations clustering and resource provisioningschemes to adapt to the fluctuations of UEs’ capacity demand,which can enhance the energy efficiency and data rate. In C-RAN, the power consumption introduced by fronthaul links iscomparable to that of RRHs and thus cannot be neglected. Bytaking into account the fronthaul power consumption, a jointRRH selection and precoding design problem is formulated in[20] to minimize the aggregate power consumption. To effi-ciently solve this problem, a low complexity algorithm basedon group sparse precoding is proposed. Such an optimizationframework is extended to account for both downlink anduplink transmissions in [21], and to address the generalizedsparse and low-rank optimization in [22]. By modeling thefronthaul power consumption as a function of the fronthauldata rate, the energy efficiency of C-RAN is investigated in[23]. The authors in [24] exploit the benefit of non-orthogonalmultiple access (NOMA) in C-RAN to enhance the energyefficiency. Moreover, to address the channel uncertainty, arobust beamforming problem is formulated in [25], where analternating direction method of multipliers (ADMM)-based al-gorithm is proposed to solve the problem. However, the impactof the fronthaul capacity constraint on power consumption isnot studied in the aforementioned studies.

To minimize the aggregate power consumption, it is neces-sary to take into account the limited fronthaul capacity as itaffects the number of RRHs required to be active, which inturn determines the circuit and fronthaul power consumption.Hence, the effect of the limited fronthaul capacity on the ag-gregate power consumption of C-RAN should be investigated.The concept and benefit of flexible functional splits betweenthe BBU pool and RRHs in the physical (PHY) and mediumaccess control (MAC) layers are discussed in [26] and [27].The authors in [28] formulate an integer linear programmingproblem to minimize the inter-cell interference by dynami-cally adjusting the functional split in PHY and MAC layers.However, the radio transmission of data streams between theRRHs and the UEs, as an indispensable component of C-RAN, is not taken into account. Differently, the CAP and DSstrategies correspond to different divisions of signal processingfunctionalities between the BBU pool and RRHs. Specifically,the baseband signal precoding functionality in the CAP and DSstrategies is performed centrally by the BBU pool and locallyby the RRHs, respectively. The fronthaul capacity required bythe CAP and DS strategies depends on different parameters. Inparticular, the fronthaul data rate of the CAP strategy depends

on the precoding gain, quantization noise, and the numberof antennas on the RRH, while the fronthaul data rate ofthe DS strategy is determined by the number of UEs servedby the RRH. The maximizations of energy efficiency fordownlink C-RAN using DS and CAP strategies are separatelystudied in [29]. Flexible functional split enables each RRH tosupport either the CAP or DS strategy, so as to fully utilizethe fronthaul capacity based on the quality of service (QoS)requirement of UEs and channel conditions. However, utilizingflexible functional split design to reduce power consumptionhas not been studied. Moreover, as most existing works (e.g.,[30], [31]) use the CAP strategy to maximize the spectrumefficiency, the impact of fronthaul compression on the tradeoffbetween the aggregate power consumption and the fronthaulcapacity requirement has not been investigated.

Different from the aforementioned studies, in this paperwe propose a flexible functional split design to minimizethe aggregate power consumption of downlink C-RAN, whiletaking into account the fronthaul capacity constraint and thequality of service requirement. The power consumption underconsideration includes the RRH transmit power, RRH circuitpower, and frontaul power consumption. Each RRH can beswitched off to save power, which corresponds to the sleepmode. Each active RRH can flexibly be configured to supporteither the CAP or DS strategy to further reduce the powerconsumption, leading to a mixture of RRHs using the CAP andDS strategies in the network. Such a flexible functional splitdesign takes the advantages of both the CAP and DS strategies,and enables the full utilization of the fronthaul capacity forgiven quality of service requirement. The main contributionsof this paper are summarized as follows:

1) We formulate a joint RRH mode (i.e., CAP, DS, sleep) se-lection, precoding design, and fronthaul compression problemto minimize the aggregate power consumption, while takinginto account the limited fronthaul capacity, per-RRH powerconstraint, and QoS requirement.

2) To tackle the non-convex quadratical constraints, wetransform the formulated problem into a sequence ofrank-constrained semidefinite programming (SDP) problemsthrough sequential convex programming (SCP) and `1-normconvex relaxation. We handle the combinatorial RRH modeselection by using the group sparse precoding approach anddevelop an efficient algorithm based on the majorize mini-mization (MM) scheme to solve the problem.

3) Simulations demonstrate the convergence of the proposedalgorithm and show that the fronthaul capacity constraint hasa significant impact on the aggregate power consumption. Inaddition, the CAP strategy performs better than the DS strategyin the high target data rate and/or low fronthaul capacityregimes. By taking advantages of both the CAP and DSstrategies, the proposed algorithm outperforms both baselinestrategies in terms of the energy efficiency.

The remainder of this paper is organized as follows. Sec-tion II presents the network topology, the CAP and DSstrategies, the signal reception model, and the power con-sumption model. In Section III, we formulate a non-convexquadratically constrained optimization problem to minimizethe aggregate power consumption and transform it into a

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BBU pool

RRH 2

DS

RRH 3

Sleep

RRH 1

CAP

UE 1

M

1C M

2C M

3C

RRH R

DS

UE 2 UE 3 UE U

Fronthaul link

Radio channel

· · ·

· · ·

· · ·

M

RC

Fig. 1: An illustration of the architecture of a C-RAN, which consists of theBBU pool, the optical fronthaul links of finite capacity, the multi-antennaRRHs, the radio channels, and the single-antenna UEs. An RRH can eitherbe in the active or sleep mode. Each active RRH can flexibly be configuredto support either the CAP or DS strategy.

sequence of rank-constrained SDP problems. The proposedalgorithm is presented in Section IV. The performance of theproposed algorithm is evaluated in Section V. Finally, SectionVI concludes this paper.

Notation: R and C denote the real and complex domains,respectively. The absolute value of a scalar is denoted as| · |. The conjugate transpose and `p-norm of a vector aredenoted as (·)H and ‖ · ‖p, respectively. The inverse, trace,determinant, and rank of a matrix are denoted as (·)−1, Tr(·),det(·), and rank(·), respectively. Denote 1x and Ix as theunit vector of length x and the identity matrix of order x,respectively. Indicator function 1x equals to 0 if x = 0, and1 otherwise. X 0 and X 0 indicate that matrix X ispositive semidefinite and definite, respectively.

II. SYSTEM MODEL

Consider the downlink transmission of a C-RAN, whichconsists of one BBU pool, R RRHs, and U UEs, as shown inFig. 1. We denote R = 1, 2, . . . , R and U = 1, 2, . . . , Uas the sets of the RRHs and UEs, respectively. The r-thRRH is equipped with Nr omni-directional antennas. EachUE has a single omni-directional antenna and it receives asingle independent data stream from the BBU pool, whichperforms centralized baseband signal processing, cooperativestrategy selection, and coordinated resource allocation. Thedata streams for all UEs are assumed to be available at theBBU pool. The BBU pool connects to each RRH via anoptical fronthaul link of finite capacity. In addition to theradio frequency (RF) functionality (e.g., power amplification),each RRH has baseband signal processing capabilities suchas precoding. After receiving the data streams from the BBUpool, the RRHs forward the data streams to the correspondingUEs over quasi-static radio channels. The global channel stateinformation (CSI) is assumed to be available at the BBU pool,as in [8]–[10].

To fully utilize the available resources (e.g., radio spectrum,transmit power, and fronthaul capacity) to meet the UEs’QoS requirement, we propose a flexible functional split design

for C-RAN. In particular, each active RRH can flexibly beconfigured to support either the CAP or DS strategy, as shownin Fig. 2(a). The block diagrams of the CAP and DS strategiesare illustrated in Figs. 2(b) and 2(c), respectively. In the CAPstrategy, based on the CSI and UEs’ QoS requirement, theBBU pool performs centralized precoding and delivers thecompressed signals to the RRHs, as shown in Fig. 2(b). Onthe other hand, in the DS strategy, the BBU pool deliversboth the signals and precoding vectors to the correspondingRRHs, which perform local precoding, as shown in Fig. 2(c).The CAP strategy and DS strategy correspond to the PHY-RF split and MAC-PHY split proposed for 5G RAN in [32],[33], respectively. The fronthaul interfaces supporting the CAPand DS strategies follow the common public radio interface(CPRI) and Fx interface [32], respectively. Hence, the fron-thaul interface should change accordingly with the cooperativestrategy (i.e., CAP or DS) selected by its connected RRH. Weassume that the RRHs can switch among the sleep, CAP, andDS modes with negligible delay. Due to the differences inbaseband signal processing and data sharing, the CAP and DSstrategies are different in terms of the fronthaul data rate andthe RRH transmit power, as discussed in detail as follows.

A. CAP Strategy

We denote su as the signal intended for UE u ∈ U . Withoutloss of generality, the signals are assumed to be independentand identically distributed (i.i.d.) Gaussian random variableswith zero mean and unit variance. In the BBU pool, theprecoded baseband signal for the r-th RRH supporting theCAP strategy, denoted as xr ∈ CNr×1, is given by

xr =∑u∈U

wrusu, ∀ r ∈ RC, (1)

where wru ∈ CNr×1 denotes the precoding vector at RRH rfor UE u, and RC ⊆ R denotes the set of active RRHs usingthe CAP strategy. Note that the coefficients of the precodingvector wru should be set to 0 if RRH r is not serving UE u.

In order to reduce the amount of information delivered overthe fronthaul links, the BBU pool compresses and quantizesthe precoded baseband signals before transmitting them to theRRHs. Each xr is independently compressed and quantizedacross the RRHs. Note that it is possible to leverage jointsignal compression to further alleviate the fronthaul capacityconstraint as in [9], which is out of the scope of this paper. Thecompressed signal for the r-th RRH using the CAP strategycan be expressed as

xr = xr + qr, ∀ r ∈ RC, (2)

where qr ∈ CNr×1 denotes the quantization noise vector,which is independent of xr and is assumed to be Gaussiandistributed with zero mean and variance σ2

q,r1Nr . Accordingto the rate-distortion theory [34], the achievable compressionrate equals to the mutual information between the compressedsignal xr and the precoded baseband signal xr. As a result, forthe CAP strategy, the data rate of the r-th fronthaul, ∀ r ∈ RC,

4

Precoding

Design

Centralized

PrecodingMUX

COMPR

BBU pool

· · ·· · ·

RRH rRRH 1 RRH R

Fronthaul· · · · · ·

CAP CAP DS

··· ···

(a) Flexible functional split design

BBU pool

CPRI

Centralized

Precoding

Precoding

Design

r

COMPR

xr

su

wru

RRH r

Fronthaul

CSI

QoS

(b) CAP strategy

Fx

Precoding

Design

wru

CSI

QoS

MUX

Fronthaul

BBU pool

su

DEMUX

wrusu

Precoding

RF

xr

RRH r

(c) DS strategy

Fig. 2: An illustration of the block diagram of the flexible functional split between the BBU pool and RRHs, where COMPR, MUX, and DEMUX representthe compression, multiplexer, and demultiplexer, respectively.

can be calculated by

B log2 det

(∑u∈U

wruwHru+σ2

q,rINr

)−NrB log2

(σ2q,r

), (3)

where B denotes the channel bandwidth. According to (3),the fronthaul data rate of the CAP strategy depends on thevalues of the precoding coefficients wru and the quantizationnoise σ2

q,r as well as on the number of the antennas ofRRH r. In particular, a higher precoding gain and smallerquantization noise lead to smaller signal distortion, but alsoa higher fronthaul data rate. In this paper, such a tradeoff isbalanced by jointly optimizing the precoding coefficients andquantization noise.

B. DS Strategy

In the DS strategy, the BBU pool delivers both signal suand its corresponding precoding vectors wru to a clusterof RRHs serving UE u through fronthaul links. Similar tothe CAP strategy, all coefficients of the precoding vector wru

should be set to 0 if RRH r is not within the serving clusterof UE u. After receiving the signals and the correspondingprecoding vectors, each RRH performs local precoding. As aresult, the signal transmitted by the r-th RRH can be writtenas

xr =∑u∈U

wrusu, ∀ r ∈ RD, (4)

where RD ⊆ R denotes the set of active RRHs using the DSstrategy. As each active RRH can be configured to supporteither the CAP or DS strategy, we have RC ∩RD = ∅.

According to (4), as the signals and corresponding precod-ing vectors are required to perform local precoding at eachRRH, the fronthaul data rate is the summation of the datarates required by its serving UEs. For simplicity, the overheadintroduced by CSI estimation and precoding vector delivery

is ignored due to its negligible size compared with the datastream. As a result, for the DS strategy, the data rate of ther-th fronthaul can be expressed as∑

u∈U1‖wru‖22B log2(1 + γu), ∀ r ∈ RD, (5)

where γu denotes the target signal-to-interference-plus-noiseratio (SINR) of UE u. According to (5), the fronthaul datarate of the DS strategy is determined by the number of UEsserved by the RRH and the target SINR of all serving UEs.In particular, having more serving UEs at each RRH leadsto a higher cooperation gain, but also a higher fronthaul datarate. Comparing with (3), different parameters influence thefronthaul data rates of the CAP and DS strategies.

C. Signal Reception ModelWith full spatial frequency reuse, each UE can simultane-

ously receive its own signal transmitted from both the RRHsin RC and the RRHs in RD over radio channels. The signalreceived at UE u is given by

yu =∑

r∈RC∪RD

hHruxr + nu, ∀ u ∈ U , (6)

where hru ∈ CNr×1 denotes the channel fading vectorbetween RRH r and UE u and incorporates the effects of bothpath loss and small-scale fading, and nu denotes the additivewhite Gaussian noise (AWGN) at UE u with zero mean andvariance σ2

n,u.By substituting (2) and (4) into (6), we have

yu =∑

r∈RC∪RD

hHruwrusu +

∑k∈U\u

∑r∈RC∪RD

hHruwrksk

+∑r∈RC

hHruqr + nu, ∀ u ∈ U , (7)

where the second term of the right hand side is the co-channelinterference.

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By using single user detection (i.e., treating the co-channelinterference as noise), according to (7), the received SINR atUE u ∈ U can be written as

SINRu =

∣∣∣∑r∈RC∪RD hHruwru

∣∣∣2Iu+σ2

n,u

, (8)

where Iu denotes the summation of the co-channel interferenceand quantization noise power, given by

Iu =∑

k∈U\u

∣∣∣∣∣ ∑r∈RC∪RD

hHruwrk

∣∣∣∣∣2

+

∣∣∣∣∣ ∑r∈RC

hHruσq,r1Nr

∣∣∣∣∣2

. (9)

D. Power Consumption Model

The aggregate power consumption consists of RRH transmitpower, RRH circuit power, and fronthaul power consumption.According to (2), the transmit power of the r-th RRH usingthe CAP strategy is given by

P txr =

∑u∈U‖wru‖22 +Nrσ

2q,r, ∀ r ∈ RC. (10)

Similarly, according to (4), the transmit power of the r-thRRH using the DS strategy can be expressed as

P txr =

∑u∈U‖wru‖22, ∀ r ∈ RD. (11)

Based on (10) and (11), the RRH transmit power of theCAP strategy involves the quantization noise power, whichis different from that of the DS strategy.

The RRH circuit power consists of the RF circuit and basicbaseband processing power consumption. They depend on thetransmission mode of the RRH (i.e., being in either activeor sleep mode). In particular, the circuit power of RRH r ∈Rν , ν ∈ C,D is modeled by a piecewise function,

P cc,νr =

P cc,νa,r , if P tx

r > 0,P ccs,r, if P tx

r = 0,(12)

where P cc,νa,r and P cc

s,r denote the circuit power of the r-thRRH in Rν in the active and sleep modes, respectively, andP cc,νa,r > P cc

s,r.Similarly, the power consumption of the r-th fronthaul in

the active and sleep modes are denoted as P fha,r and P fh

s,r,respectively, and P fh

a,r > P fhs,r. By denoting RS ⊆ R as the set

of the RRHs in the sleep mode, the total power consumptionof RRH circuits and fronthaul links is given by

P cf =∑r∈RC

(P cc,Ca,r + P fh

a,r

)+∑r∈RD

(P cc,Da,r + P fh

a,r

)+∑r∈RS

(P ccs,r + P fh

s,r

)=∑r∈RC

(P cc,Ca,r + P fh

a,r − P ccs,r − P fh

s,r

)+∑r∈RD

(P cc,Da,r + P fh

a,r − P ccs,r − P fh

s,r

)+∑r∈R

(P ccs,r + P fh

s,r

).

By denoting P difr,C = P cc,C

a,r + P fha,r − P cc

s,r − P fhs,r > 0,

P difr,D = P cc,D

a,r + P fha,r − P cc

s,r − P fhs,r > 0, and omitting the

constant term∑r∈R

(P ccs,r + P fh

s,r

), minimizing the aggregate

power consumption is equivalent to minimizing Pagg, whichis given by

Pagg =∑

r∈RC∪RD

∑u∈U

1

ηr‖wru‖22 +

∑r∈RC

(1

ηrNrσ

2q,r + P dif

r,C

)+∑r∈RD

P difr,D, (13)

where ηr > 0 denotes the drain efficiency [35] of the RFpower amplifier of the r-th RRH.Discussions: There exist performance tradeoff between theDS and CAP strategies in terms of the cooperation gain, thefronthaul data rate, and the power consumption. The mainadvantage of the DS strategy is that each RRH receives theoriginal signals of its serving UEs without distortion. However,the cooperation gain that can be achieved by the DS strategy isdetermined by the RRH cluster size (i.e., the number of RRHscooperatively transmitting the same signal). In particular, alarger cluster size contributes to a higher cooperation gain, butalso leads to a larger fronthaul data rate, as each cooperatingRRH is required to receive a copy of the original signal. Notethat a larger cluster size for each UE corresponds to moreUEs served by each RRH. Therefore, the fronthaul capacityconstraint limits the cluster size and the cooperation gain. Inthe high traffic load regime (e.g., high target data rate and largenumber of UEs), the DS strategy may require more RRHs to beactive than the CAP strategy, so as to achieve a large enoughcooperation gain to meet the target data rate requirement ofUEs, leading to higher circuit power consumption. For theCAP strategy, the RRHs can receive the precoded basebandsignal by utilizing all UEs’ signals, and hence, achieving fullcooperation. The fronthaul data rate of the CAP strategy can beadjusted by changing the quantization noise, which determinesthe compression resolution. Compared to the DS strategy, themain disadvantage of the CAP strategy is the signal distortiondue to quantization noise, which leads to larger transmit powerconsumption. In the low traffic load regime (e.g., low targetdata rate and small number of UEs), the DS strategy is able toachieve full cooperation, and hence can consume less powerthan the CAP strategy, which suffers from quantization noise.

III. PROBLEM FORMULATION AND TRANSFORMATION

To minimize the aggregate power consumption, we need toreduce both the RRH transmit power and the number of activeRRHs and corresponding fronthaul links. However, there existsa tradeoff between these two aspects. Specifically, to reducethe RRH transmit power, more RRHs are required to be activeto meet UEs’ QoS requirement. On the other hand, having lessactive RRHs leads to lower RRH circuit and fronthaul powerconsumption, but also higher RRH transmit power. Such atradeoff is further affected by other factors, including the ca-pacity constraints of fronthaul links, maximum transmit powerconstraints of the RRHs, and UEs’ QoS constraints. Hence,the RRH mode (i.e., CAP, DS, sleep) selection, precodingdesign, and fronthaul compression should jointly be optimized

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to minimize the aggregate power consumption. Note that theprecoding coefficients and the quantization noise not onlyaffect the RRH modes for the reduction of RRH circuit powerand fronthaul power consumption, but also play an importantrole in further reducing the transmit power consumption whenthe RRH modes are fixed. Based on the above discussions,the aggregate power consumption minimization problem isformulated as

minimizeRC,RD,RS

wru,σ2q,r

Pagg (14a)

subject to∑u∈U‖wru‖22 +Nrσ

2q,r ≤ PM

r , ∀ r ∈ RC, (14b)∑u∈U‖wru‖22 ≤ P

Mr , ∀ r ∈ RD, (14c)∑

u∈U‖wru‖22 = 0, ∀ r ∈ RS, (14d)

B log2 det

(∑u∈U

wruwHru + σ2

q,rINr

)−NrB log2

(σ2q,r

)≤ CM

r ,∀ r ∈ RC, (14e)∑u∈U

1‖wru‖22Blog2(1 + γu) ≤ CMr ,

∀ r ∈ RD, (14f)∣∣∑r∈RC∪RD hH

ruwru

∣∣2Iu + σ2

n,u

≥ γu, ∀u ∈ U , (14g)

RC ∩RD = ∅, (14h)(RC ∪RD

)∩RS = ∅, (14i)

RC ∪RD ∪RS = R, (14j)

where PMr and CM

r denote the maximum transmit power ofthe r-th RRH and the capacity of the r-th fronthaul link,respectively. Constraints (14b), (14c), and (14d) represent themaximum transmit power constraints of the RRHs in RC,RD, and RS, respectively. Constraints (14h), (14i), and (14j)ensure that each RRH can be configured to support one of theCAP, DS, and sleep modes. The aggregate power consumptionminimization problem in (14) is a non-convex quadraticallyconstrained combinatorial optimization problem, which is gen-erally difficult to solve and imposes the following challenges:First, the objective function (14a) is a combinatorial functiondue to both the RRH selection (i.e., either being in theactive or sleep mode) and the cooperative strategy selection(i.e., supporting either the CAP or DS strategy). Second, thecapacity constraints of fronthaul links supporting the CAP andDS strategies (i.e., (14e) and (14f)), and the QoS constraintsof the UEs in terms of the SINR (i.e., (14g)) are non-convexquadratically constrained.

To address the aforementioned challenges, we transformproblem (14) into a sequence of rank-constrained SDP prob-lems. We define precoding matrix Wu = wuw

Hu ∈ CNT×NT

as a new optimization variable for UE u ∈ U , where NT =∑Rr=1Nr and wu = [wH

1u,wH2u, . . . ,w

HRu]H ∈ CNT×1. We

have constraints Wu 0 and rank(Wu) = 1 for UE u ∈ U .Precoding vector wu is given by the eigenvector of Wu. The

maximum transmit power constraints of the RRHs using theCAP strategy (i.e., (14b)) can equivalently be expressed as∑

u∈UTr (BrWu) +Nrσ

2q,r ≤ PM

r , ∀ r ∈ RC, (15)

where Br ∈ RNT×NT denotes a block diagonal matrix withidentity matrix INr as the r-th main diagonal block matrixand zeros elsewhere.

Similarly, the maximum transmit power constraints of theRRHs using the DS strategy and being in the sleep mode (i.e.,(14c) and (14d)) are, respectively, given by∑

u∈UTr (BrWu) ≤ PM

r , ∀ r ∈ RD, (16)∑u∈U

Tr (BrWu) = 0, ∀ r ∈ RS. (17)

By defining Bc,r ∈ RNT×Nr as the matrix composed ofthe columns from

∑r−1k=1Nk + 1 to

∑rk=1Nk of matrix Br,

we have wruwHru=BH

c,rWuBc,r. The capacity constraints ofthe fronthaul links with the CAP strategy (i.e., (14e)) can beexpressed as

B log2 det(∑

u∈U BHc,rWuBc,r +

(σ2q,r + ε

)INr)

−NrB log2

(σ2q,r + ε

)≤ CM

r , ∀ r ∈ RC, (18)

where ε > 0 is a small fixed regularization parameter.By defining Ωr =

∑u∈U BH

c,rWuBc,r+(σ2q,r + ε

)INr , the

non-convex term in constraint (18) can be linearized by usingSCP [36]. Hence, the non-convex fronthaul capacity constraintcan be tackled in an iterative manner. In the (m+1)-th iteration(m = 0, 1, 2, . . .), constraint (18) can be rewritten as

log2 det(Ω(m+1)r

)+

1

ln 2Tr

((Ω(m+1)r

)−1(Ωr−Ω(m+1)

r

))−Nr log2

(σ2q,r + ε

)≤ CM

r

B, ∀ r ∈ RC, (19)

where

Ω(m+1)r =

∑u∈U

BHc,rW

(m)u Bc,r +

(σ2(m)q,r + ε

)INr , (20)

and W(m)u and σ2(m)

q,r are obtained from the m-th iteration.Since ‖wru‖22 = Tr (BrWu), the capacity constraints of

the fronthaul links supporting the DS strategy (i.e., (14f)) canbe written as∑

u∈U1Tr(BrWu) log2(1 + γu) ≤ CM

r

B, ∀ r ∈ RD. (21)

The indicator function in constraint (21) can equivalently beexpressed as an `0-norm of a scalar, which indicates whetheror not this scalar is equal to zero. Thereby, constraint (21) canbe written as∑u∈U‖Tr (BrWu)‖0 log2(1 + γu) ≤ CM

r

B, ∀ r ∈ RD. (22)

Such a non-convex `0-norm can be approximated by aconvex reweighted `1-norm, which is widely used in compres-sive sensing [37]. Similar to (19), in the (m+1)-th iteration,

7

constraint (22) can be rewritten as∑u∈U

β(m+1)ru Tr (BrWu) log(1 + γu) ≤ CM

r

B, ∀ r ∈ RD,

(23)

where β(m+1)ru can be iteratively updated according to

β(m+1)ru =

1

Tr(BrW

(m)u

)+ c1

(24)

and c1 > 0 is a constant regularization factor.To achieve the target SINR, the QoS constraint of UE u can

be rewritten ashHuWuhu

hHu

(∑k∈U\u Wk

)hu+hH

uΛqhu+σ2n,u

≥ γu,

∀ u ∈ U , (25)

where hu = [hH1u, . . . ,h

HRu]H ∈ CNT×1, and Λq ∈ RNT×NT

is a block diagonal matrix with identity matrix σ2q,rINr as the

r-th main diagonal block square matrix. Note that σ2q,r = 0

for RRH r /∈ RC.Based on the above transformation, problem (14) can be

tackled by iteratively solving the following problem,

P(m+1) : minimizeRC,RD,RS

Wu,σ2q,r

∑r∈RC∪RD

∑u∈U

1

ηrTr (BrWu)

+∑r∈RC

(1

ηrNrσ

2q,r + P dif

r,C

)+∑r∈RD

P difr,D (26a)

subject to constraints (14h), (14i), (14j), (15),(16), (17), (19), (23), (25),rank (Wu) = 1, ∀ u ∈ U , (26b)Wu 0, ∀ u ∈ U . (26c)

Problem P(m+1) still cannot directly be solved due to thecombinatorial objective function (26a) and the non-convexrank-one constraint (26b). Given RRH sets RC, RD, andRS, problem P(m+1) is a rank-constrained SDP problem. Bydropping the rank-one constraint [38], the convex relaxationproblem can be efficiently solved by using the interior-pointmethod [39]. Finally, the aggregate power minimization prob-lem in (14) can be solved by developing an MM algorithm toiteratively update parameters Ω(m)

r and β(m)ru according

to (20) and (24) by solving (26).

IV. GROUP SPARSE PRECODING ALGORITHM

In this section, we develop an efficient algorithm to tacklethe combinatorial challenge based on the group sparse pre-coding approach and mitigate the non-convex rank-one con-straint. The proposed algorithm is composed of two stages, asdiscussed in the following two sub-sections.

A. Stage One: Identify Active RRHs

In the first stage, we identify the RRHs that are required tobe active to meet UEs’ QoS requirement. Suppose all active

RRHs are initially configured to support the CAP strategy (i.e.,RD = ∅), problem P(m+1) can be simplified as

minimizeRC,RS

σ2q,r,Wu

∑r∈RC

1

ηr

(∑u∈U

Tr (BrWu) +Nrσ2q,r

)

+∑r∈RC

P difr,C

subject to constraints (15), (17), (19), (25),(26b), (26c),

RC ∩RS = ∅,RC ∪RS = R.

(27)

When RRH r is switched off, all coefficients of precodingvector wr = [wH

r1, . . . ,wHrU ]H should be set to 0, yielding

‖wr‖22 =∑u∈U Tr (BrWu) = 0 and a group-sparsity

structure of precoding vector w = [wH1 , . . . , w

HR]H. As a

result, problem (27) can be expressed as

minimizeWu,σ2

q,r

∑r∈R

1

ηr

(∑u∈U

Tr (BrWu)+Nrσ2q,r

)+∑r∈R

1∑u∈U Tr(BrWu)+Nrσ2q,rP

difr,C

subject to constraints (15), (19), (25), (26b), (26c),

(28)

where ∀ r ∈ RC in constraints (15) and (19) is replaced by∀ r ∈ R. Problem (28) is non-convex due to the indicatorfunction in the objective function. An indicator function isequivalent to the `0-norm of a scalar, which can further beapproximated by a convex reweighted `1-norm. Thus, we have

1 ∑u∈U

Tr(BrWu)+Nrσ2q,r

≈ µ(m+1)r

(∑u∈U

Tr (BrWu) +Nrσ2q,r

),

where µ(m+1)r can be iteratively updated according to

µ(m+1)r =

1∑u∈U Tr

(BrW

(m)u

)+Nrσ

2(m)q,r + c2

, (29)

and c2 > 0 is a constant regularization factor.Through convexifying the indicator function in the objective

function, we need to solve the following optimization problem,

minimizeWu,σ2

q,r

∑r∈R

(1

ηr+ µ(m+1)

r P difr,C

)×(∑

u∈UTr (BrWu) +Nrσ

2q,r

),

subject to constraints (15), (19), (25), (26b), (26c),

(30)

where ∀ r ∈ RC in constraints (15) and (19) is replaced by∀ r ∈ R. After dropping rank-one constraint (26b), problem(30) is an SDP problem, which can be efficiently solved byconvex programming solver (e.g., CVX [40]). We show thetightness of the rank-one constraint relaxation as follows.

Theorem 1. Let W?u denote the precoding matrix of UE u ∈

U as the solution of problem (30) without rank-one constraint

8

Algorithm 1: An algorithm for identifying activeRRHs.

1 Initialize variables W(0)u and σ2(0)

q,r satisfyingconstraints (15) for all r∈R and (25), and calculateP

(0)Alg1.

2 m := 0 and ∆(m)1 := 1010.

3 while ∆(m)1 > δ1 and m < φ1 do

4 Update parameters Ω(m+1)r and µ(m+1)

r according to (20) and (29), respectively.

5 Solve problem (30) with parameters Ω(m+1)r and

µ(m+1)r , and obtain W(m+1)

u , σ2(m+1)q,r ,

and P (m+1)Alg1 .

6 ∆(m+1)1 :=

∣∣P (m+1)Alg1 − P (m)

Alg1

∣∣.7 m := m+ 1.

8 RS :=r |(∑

u∈U Tr(BrW

(m)u

)+Nrσ

2(m)q,r

)<ϕ

.9 RC :=R \ RS.

(26b), then rank (W?u) = 1 always holds.

Proof. Please refer to Appendix A.

The MM algorithm [41] can be used to solve a sequenceof convex optimization problems (i.e., problem (30) withoutthe rank-one constraint) in an iterative manner. We denoteP

(m+1)Alg1 as the value of the objective function of problem (30)

in the (m+1)-th iteration. The convergence threshold and themaximum number of iterations are denoted as δ1 and φ1, re-spectively. The proposed algorithm based on the MM schemeto identify the active RRHs is summarized in Algorithm 1. Itis shown in [41] that the MM algorithm always converges to astationary point of the original problem. After solving problem(27) by using Algorithm 1, we can obtain the set of RRHs insleep mode as RS =r |

(∑u∈U Tr (BrWu) +Nrσ

2q,r

)<ϕ,

and set of RRHs using the CAP strategy as RC =R\RS, whereϕ is a predefined small constant. Besides, we obtain the con-verged objective value of problem (27) denoted by PC

agg andquantization noises for active RRHs given by σ2

q,r, r∈RC.

B. Stage Two: Identify Cooperative Strategies and OptimizePrecoding Matrices and Quantization Noise

In the second stage, we determine the set of active RRHsswitching to support the DS strategy, and optimize the pre-coding matrices and quantization noise, to further reduce thepower consumption. We utilize the following ordering criterionto determine the priorities of RRHs using the CAP strategy tobe switched to support the DS strategy,

θr =1

ηrNrσ

2q,r, ∀ r ∈ RC. (31)

The RRH with a larger θr has a higher priority to supportthe DS strategy. In particular, the RRHs with more transmitantennas, smaller drain efficiency, and larger quantizationnoise are likely to consume more power and generate higherinterference according to (8) and (10). We denote the numberof active RRHs (i.e., cardinality of RC) as α. Based on the

ordering criterion (31), we order the RRHs in a descendingorder, i.e., θπ1 ≥ θπ2 ≥ · · · ≥ θπα , to determine the setof active RRHs using the DS strategy. For simplicity, weiteratively select the active RRHs to support the DS strategy.Thus, we introduce another iteration which is outside theiterations used to update Ω

(m+1)r and β(m+1)

ru . The RRH setssupporting the DS and CAP strategies in the τ -th outer iter-ation are denoted as RD(τ) = π1, π2, . . . , πτ and RC(τ) =πτ+1, πτ+2, . . . , πα, respectively. Based on the above def-initions, we have RD(τ) ∪ RC(τ) = RC. Given RRH setsRC(τ), RD(τ), and RS, the RRH circuit and fronthaul powerconsumption is fixed. Hence,

∑r∈RC(τ) P

difr,C+

∑r∈RD(τ) P

difr,D

is a constant and can be omitted in the objective function. Asa result, we can solve the following problem in the (m+1)-thinner iteration to reduce the aggregate power consumption,

minimizeWu,σ2

q,r

∑r∈RC(τ)

1

ηr

(∑u∈U

Tr (BrWu) +Nrσ2q,r

)

+∑

r∈RD(τ)

1

ηr

∑u∈U

Tr (BrWu)

subject to constraints (15), (16), (17), (19), (23),(25), (26b), (26c),

(32)

where ∀ r ∈ RC and ∀ r ∈ RD in all constraints arereplaced by ∀ r ∈ RC(τ) and ∀ r ∈ RD(τ), respectively.Similarly, problem (32) without rank-one constraint (26b) isan SDP problem and can efficiently be solved. The tightnessof the rank-one constraint relaxation is shown in the followingtheorem.

Theorem 2. Let W?u denote the precoding matrix of UE u ∈

U as the solution of problem (32) without rank-one constraint(26b), then rank (W?

u) = 1 always holds.

Proof. Please refer to Appendix B

We denote P (m+1)Alg2 as the value of the objective function of

problem (32) in the (m+1)-th inner iteration. The convergencethreshold and the maximum number of iterations are denotedas δ2 and φ2, respectively. The proposed algorithm to solveproblem (32) is summarized in Algorithm 2. We denote P (τ)

agg

as the converged objective value of problem (32) for the τ -th outer iteration. Finally, combining the above two stages,the algorithm for solving the aggregate power consumptionminimization problem (14) is given in Algorithm 3. The setof RRHs using the DS strategy, RD(0), and the iteration index,τ , are initialized in Step 1. By using Algorithm 1, we solveproblem (27) to check the feasibility and identify the setof RRHs required to be active (Step 2). If problem (27) isfeasible, then we determine the set of RRHs using the CAPstrategy, RC, the set of RRHs in the sleep mode, RS, thequantization noise, σ2

q,r, as well as the aggregate powerconsumption, PC

agg, and then sort the ordering criterion (31)in a descending order (Steps 3 – 5). Otherwise, the algorithmterminates (Steps 6 and 7). We initialize RC(0) in Step 8. Inthe τ -th iteration, we move one active RRH from set RC(τ)

to set RD(τ) based on the ordering of active RRHs (Steps 10and 11), and solve problem (32) using Algorithm 2 to obtain

9

Algorithm 2: An algorithm for optimizing precodingmatrices and quantization noise.

1 Initialize variables W(0)u and σ2(0)

q,r satisfyingconstraints (15) for all r∈RC(τ), (16) for allr∈RD(τ), and (25), and calculate P (0)

Alg2. m := 0,∆

(m)2 := 1010.

2 while ∆(m)2 > δ2 and m < φ2 do

3 Update parameters Ω(m+1)r and β(m+1)

ru according to (20) and (24), respectively.

4 Solve problem (32) with parameters Ω(m+1)r and

β(m+1)ru , and obtain W(m+1)

u , σ2(m+1)q,r ,

and P (m+1)Alg2 .

5 ∆(m+1)2 :=

∣∣P (m+1)Alg2 − P (m)

Alg2

∣∣.6 m := m+ 1.

P(τ)agg (Step 12). If the aggregate power consumption in the τ -

th iteration is smaller than PCagg, then we update the values

of PCagg and τ (Steps 13 – 15). Otherwise, we break the loop

(Steps 16 and 17). The loop stops when either τ > α orP

(τ)agg +

∑r∈RC(τ) P

difr,C +

∑r∈RD(τ) P

difr,D ≥ PC

agg. In Step 18,we determine sets RC(τ) and RD(τ), and recover precodingvectors wu and quantization noise σ2

q,r to serve all UEs.Note that the final precoding vector wu is the eigenvectorof Wu,∀u ∈ U . By using the iteratively reweighted methodand the MM-based algorithm, the solution of the proposedalgorithm is always a stationary point of the original problem[42].

The overall algorithm (i.e., Algorithm 3) runs Algorithm 1once and Algorithm 2 at most R times. Algorithms 1 and 2solve a sequence of SDP problems, i.e., problems (30) and(32) without rank-one constraint, respectively. To solve theSDP problem with U matrix optimization variables of sizeNT×NT, the interior-point method takes O(

√UNT log(1/ε))

iterations and O(UN6T) floating point operations to achieve

an optimal solution with accuracy ε > 0. Note that themaximum number of SDP problems required to be solved forAlgorithms 1 and 2 are φ1 and φ2, respectively. Hence, theoverall computational complexity of the proposed algorithm isgiven by O

((φ1 +Rφ2)U1.5N6.5

T log(1/ε)).

V. PERFORMANCE EVALUATION

In this section, we evaluate the energy efficiency of theproposed flexible functional split design for downlink C-RANand compare the aggregate power consumption with that ofthe pure CAP and DS strategies. Specifically, in the CAPand DS strategies, all active RRHs work in the CAP and DSmodes, respectively. In the simulations, the RRHs and UEsare randomly distributed in a circular network coverage areawith radius 500 m. We consider quasi-static Rayleigh fadingchannels and set the path loss exponent to be 4. The channelbandwidth B and noise power σ2

n,u are set to be 10 MHz and−100 dBm, respectively. The number of RRHs (i.e., R) in thenetwork coverage area is 10. The maximum transmit powerof the r-th RRH (i.e., PM

r ,∀ r ∈ R) is 80 mW. Each RRH

Algorithm 3: Aggregate power minimization algo-rithm.

1 Initialize RRH set RD(0) := ∅ and τ := 1.2 Solve problem (27) using Algorithm 1.3 if problem (27) is feasible then4 Obtain RC, RS, σ2

q,r, α, and PCagg.

5 Calculate the ordering criterion (31) and sort themin a descending order: θπ1

≥ θπ2≥ · · · ≥ θπα .

6 else7 Go to End.

8 RC(0) := RC.9 while α− τ ≥ 0 do

10 RC(τ) := RC(τ−1) \ πτ.11 RD(τ) := RD(τ−1) ∪ πτ.12 Solve problem (32) using Algorithm 2 and obtain

P(τ)agg.

13 if P (τ)agg +

∑r∈RC(τ) P

difr,C +

∑r∈RD(τ) P

difr,D < PC

agg

then14 PC

agg :=

P(τ)agg +

∑r∈RC(τ) P

difr,C +

∑r∈RD(τ) P

difr,D.

15 τ := τ + 1.16 else17 Break.

18 Use RRHs given in sets RC(τ) and RD(τ), precodingvectors wu, and quantization noise σ2

q,r to serveall UEs.

19 End

using the DS strategy only needs to superimpose the receivedsignals weighted by the corresponding precoding coefficients,which is a simple operation and consumes less power than thequantization codebook based signal decompression operationperformed by each RRH using the CAP strategy. Hence, thepower differences between the active and sleep modes for theCAP and DS strategies (i.e., P dif

r,C and P difr,D, ∀ r ∈ R) are set

to be 500 mW and 400 mW, respectively. The drain efficiencyof the RF power amplifier of the r-th RRH (i.e., ηr, ∀ r ∈ R)is 0.25. The constant regularization factors (i.e., ε, c1, and c2)are all set to be 10−5. The convergence thresholds (i.e., δ1and δ2) are set to 1, and the predefined small constant (i.e.,ϕ) is set to 10−3. The maximum number of iterations (i.e., φ1and φ2) used in Algorithms 1 and 2 are set to be 30 and 15,respectively. Each RRH is equipped with two antennas andeach UE is equipped with a single antenna. We denote thetarget data rate as κu = B log2(1 + γu),∀u ∈ U .

In Fig. 3, we first evaluate the convergence of the proposedalgorithm for the flexible functional split design in downlinkC-RAN with different number of UEs (i.e., U ) when CM

r = 80Mbps and κu = 20 Mbps, ∀ r ∈ R, u ∈ U . Accordingto Algorithm 3, the convergence of the proposed algorithmis guaranteed as long as Algorithms 1 and 2 converge. Themaximum number of iterations for the loops in Algorithms1 and 2 are set as 30 and 15, respectively. The objectivevalues obtained by Algorithms 1 and 2 after each iteration

10

5 10 15 20 25 300

500

1000

1500

2000

2500

3000

3500

(a) Convergence of Algorithm 1

2 4 6 8 10 12 14800

1000

1200

1400

1600

1800

2000

2200

2400

2600

(b) Convergence of Algorithm 2

Fig. 3: Convergence of Algorithms 1 and 2 for different number of UEs inthe network when CM

r = 80 Mbps and κu = 20 Mbps, ∀ r ∈ R, u ∈ U .

are plotted in Figs. 3(a) and 3(b), respectively. As can beseen, Algorithm 1 converges after about 12 to 18 iterations,while Algorithm 2 converges after about 2 to 5 iterations. Inparticular, the larger the number of UEs in the network, thelarger the number of iterations is required for the algorithm toconverge. Overall, Algorithm 3 always converges after a smallnumber of iterations.

In Fig. 4, we then investigate the impact of the limitedfronthaul capacity on the aggregate power consumption whenU = 8 and κu = 20 Mbps, ∀ u ∈ U . With the variationof the fronthaul capacity, the aggregate power consumptionchanges significantly, which demonstrates the importance oftaking into account the limited fronthaul capacity. For the DSstrategy, the fronthaul capacity constraint limits the numberof cooperating RRHs for each UE, which in turn limitsthe achievable cooperation gain. Hence, in the low fronthaulcapacity regime, the DS strategy is less likely to meet theQoS requirement of all UEs due to the limited cooperationgain. In particular, when CM

r = 40 Mbps or 60 Mbps, theDS strategy is infeasible (i.e., the QoS requirement of all UEscannot be simultaneously satisfied). Hence, the correspondingpoints are marked with stars, as shown in Fig. 4. On the otherhand, the CAP strategy is feasible in the low fronthaul capacity

40 50 60 70 80 90 100 110 120 130 1401500

2000

2500

3000

3500

4000

CAP strategyDS strategyFlexible functional splitInfeasible

Fig. 4: Aggregate power consumption versus fronthaul capacity when U = 8and κu = 20 Mbps, ∀ u ∈ U .

10 15 20 25 30 35 40 451200

1400

1600

1800

2000

2200

2400

2600

2800

3000

CAP strategyDS strategyFlexible functional splitInfeasible

Fig. 5: Aggregate power consumption versus target data rate when U = 8and CM

r = 120 Mbps, ∀ r ∈ R.

regime. Hence, by transforming the advantage of generatinglow fronthaul data rates to the requirement of activating lessRRHs, the CAP strategy outperforms the DS strategy whenthe fronthaul capacity is small. With the increase of CM

r from60 Mbps to 120 Mbps, the aggregate power consumption ofall considered strategies decreases as less RRHs are requiredto be active to meet the QoS requirement of all UEs. WhenCMr > 120 Mbps, the aggregate power consumption cannot

be further reduced by increasing the fronthaul capacity. Whenthe fronthaul capacity is large enough to deliver multiple datastreams, the DS strategy not only requires a similar number ofactive RRHs as that of the CAP strategy, but also consumesless transmit power (e.g., no quantization noise in the DSstrategy) and processing power (e.g., no signal decompressionis needed in the DS strategy). As a result, the DS strategyoutperforms the CAP strategy when the fronthaul capacity islarge. The proposed flexible functional split design exploits theadvantages of both the CAP and DS strategies, i.e., activatingless RRHs and using a lower transmit power, respectively.Hence, the flexible functional split design always achieves abetter performance than both the CAP and DS strategies forall values of the fronthaul capacity.

Fig. 5 shows the impact of the target data rate of UEs on

11

10 15 20 25 30 35 40 45 0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

DS modeCAP mode

Fig. 6: Percentage of RRHs in the DS and CAP modes versus target data ratefor the flexible functional split design when U = 8 and CM

r = 120 Mbps,∀ r ∈ R.

the aggregate power consumption when U = 8 and CMr = 120

Mbps, ∀ r ∈ R. For a given number of UEs, the target datarates of UEs reflect the traffic load in the network. As wecan see, the aggregate power consumption of all strategiesunder consideration increases with the target data rates of UEs.This is because supporting higher data rates requires higherfronthaul data rates, which in turn requires more active RRHsas each RRH is connected to a fronthaul link with limitedcapacity. Hence, in the low traffic load regime, maximizing thenumber of RRHs in the sleep mode is crucial in minimizingthe aggregate power consumption. As can be seen, neither theDS nor CAP strategy dominates the other across the entiretarget data rate regime. For example, when the target datarate is less than 25 Mbps, the DS strategy achieves a betterperformance than the CAP strategy. On the other hand, whenthe target data rate is larger than 30 Mbps, the CAP strategyachieves a better performance than the DS strategy. This isbecause the fronthaul data rate of the DS strategy directlydepends on the target data rate and the number of servingUEs, while the fronthaul data rate of the CAP strategy dependson the logarithm of the SINR and increases slowly with thetarget data rate. In the high traffic load regime (e.g., the targetdata rate is 40 Mbps or above), the sets of RRHs using theCAP and DS strategies are critical optimization variables. Asshown in Fig. 5, the DS strategy becomes infeasible in thisregime and the corresponding points are plotted with stars. Byappropriately setting the transmission mode for each RRH, theflexible functional split design outperforms both the CAP andDS strategies in terms of the energy efficiency.

In Fig. 6, we compare the percentage of RRHs in the DSand CAP modes for the flexible functional split design withdifferent target data rates of UEs when U = 8 and CM

r =120 Mbps, ∀ r ∈ R. As we can see, when the target datarate is low (i.e., less than 15 Mbps), almost all active RRHsare switched to the DS mode, as the fronthaul capacity isnot the dominant performance-limiting factor in the low datarate regime. With the increase of the target data rate from 15Mbps to 35 Mbps, the percentage of RRHs in the DS modedecreases, while the percentage of RRHs in the CAP mode

4 6 8 10 12 14 161000

1500

2000

2500

3000

3500

4000

4500

CAP strategyDS strategyFlexible functional splitInfeasible

Fig. 7: Aggregate power consumption versus number of UEs when CMr = 120

Mbps and κu = 20 Mbps, ∀ r ∈ R, u ∈ U .

increases, i.e., less active RRHs are switched to the DS mode.This is because the fronthaul link is not able to support thetransmission of multiple data streams without compression. Byfurther increasing the target data rate, the percentage of RRHsin the DS mode almost remains at about 34%. As we can see,in the moderate and high target data rate regimes, the proposedflexible functional split design adjusts the transmission modesof all RRHs according to their channel conditions so as tofully exploit the advantages of both DS and CAP modes.

Fig. 7 illustrates the impact of the number of UEs onthe aggregate power consumption of all strategies under con-sideration when CM

r = 120 Mbps and κu = 20 Mbps,∀ r ∈ R, u ∈ U . With the increase of the number of UEs, thetraffic load in the network increases, which imposes a higherrequirement on the fronthaul capacity. As a result, more RRHsare required to be active to support the QoS requirement ofall UEs in the network, leading to higher power consumption.When the number of UEs is small, the required fronthaul datarate of the DS strategy is smaller than the fronthaul capacity,and hence, the DS strategy outperforms the CAP strategy interms of the energy efficiency. When the number of UEs islarge, the DS strategy becomes infeasible, while the CAPstrategy becomes more favourable by activating less RRHs.Overall, the proposed flexible functional split design adapts tothe network traffic load and outperforms both the CAP andDS strategies for all values of the number of UEs.

Fig. 8 shows the impact of the number of UEs on thefraction of active RRHs in downlink C-RAN when CM

r = 120Mbps and κu = 20 Mbps, ∀ r ∈ R, u ∈ U . Similar to thetrends observed in Fig. 7, the fraction of the active RRHsincreases with the number of UEs. As we can see, the fractionof the active RRHs of the proposed flexible functional splitdesign is always smaller than that of the DS strategy dueto its better utilization of the fronthaul capacity. When thenumber of UEs reaches 14 or more, the DS strategy becomesinfeasible, while the proposed flexible functional split designcan still guarantee the QoS requirement of all UEs. Moreover,the gap in terms of the active RRHs between the DS strategyand the flexible functional split design also increases with thenumber of UEs.

12

4 6 8 10 12 14 160.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

DS strategyFlexible functional splitInfeasible

Fig. 8: Fraction of active RRHs versus number of UEs when CMr = 120

Mbps and κu = 20 Mbps, ∀ r ∈ R, u ∈ U .

VI. CONCLUSIONS

In this paper, we proposed a flexible functional split betweenthe BBU pool and the RRHs in downlink C-RAN with limitedfronthaul capacity. We formulated a joint RRH mode (i.e.,CAP, DS, sleep) selection, precoding design, and fronthaulcompression problem to minimize the aggregate power con-sumption. We took into account both the fronthaul capacityconstraint and fronthaul power consumption, and tackled thenon-convex fronthaul capacity constraints by using the SCPand `1-norm convex relaxation techniques. We transformedthe non-convex optimization problem into a sequence ofrank-constrained SDP problems. An iterative algorithm basedon group sparse precoding approach and MM scheme wasproposed to solve the problem. Simulation results showedthat the fronthaul capacity constraint has a significant impacton aggregate power consumption and the proposed flexiblefunctional split design outperforms both the pure CAP andDS strategies in terms of aggregate power consumption. Forfuture work, we will consider the uncertainty of radio channelsand the millimeter wave-based fronthaul, and investigate theirimpact on the energy efficiency of C-RAN.

APPENDIX

A. Proof of Theorem 1

For notational simplicity, we denote gr = µ(m+1)r P dir

r +1ηr,∀ r ∈ R. In addition, we denote ζr, λr, νu ≥ 0, and

Hermitian matrix Xu 0 as the Lagrangian multipliersof constraints (15), (19) for all r ∈ R, (25), and (26c),respectively. Hence, the Lagrangian of problem (30) is givenby

L1

(Wu, σ2

q,r, ζr, λr, νu, Xu)

=∑u∈U

Tr

(Wu

(∑r∈R

(grBr+ζrBr+ λrΞr

)

+∑

k∈U\u

νkγkhkhHk −νuhuhH

u−Xu

+ Γ1,

where Ξr = 1ln 2Bc,r

(Ω

(m+1)r

)−1BH

c,r, Γ1 depends onσ2

q,r, ζr, λr, νu, and other constant parameters inproblem (30). The dual problem of problem (30) is given by

maximizeζr,λr,νu,Xu

infWu,σ2

q,rL1. (33)

We denote Φ? =(W?

u, σ2?q,r

)and Ψ? =

(ζ?r , λ?r, ν?u, X?u) as the solutions of primal and

dual problems, respectively. Hence, the Karush-Kuhn-Tucker(KKT) conditions can be written as

∇WuL1

∣∣Φ?,Ψ? = 0, ∀u ∈ U , (34a)

X?uW

?u = 0, ∀u ∈ U , (34b)

ζ?r ≥ 0, λ?r ≥ 0, ν?r ≥ 0, ∀ r ∈ R, (34c)

where ∇WuL1

∣∣Φ?,Ψ? denotes the gradient of the Lagrangian

in (33) with respect to Wu at Φ? and Ψ?. According to (34a),for UE u ∈ U , we have∑

r∈R

(grBr + ζ?rBr + λ?rΞr

)+

∑k∈U\u

ν?kγkhkhHk − ν?uhuhH

u −X?u=0, ∀u ∈ U .

(35)

Based on (34b) and (35), for UE u ∈ U , we have

W?u

(∑r∈R

(grBr + ζ?rBr + λ?rΞr

)+

∑k∈U\u

ν?kγkhkhHk − ν?uhuhH

u

= W?uX

?u = 0. (36)

Hence, we have,

W?u(Y?

u−Z?u)=0⇔ rank (W?uY

?u)=rank (W?

uZ?u) , (37)

where Y?u=

∑r∈R

(grBr+ζ

?rBr+λ

?rΞr

)+

∑k∈U\u

(ν?kγkhkh

Hk

)and Z?u = ν?uhuh

Hu . By taking into account gr > 0, constraint

(34c), and the definition of Br, we have Y?u 0, and thus

rank (Y?u) = NT,∀u ∈ U . As a result, we have

rank (W?uY

?u) = rank (W?

u) = rank (W?uZ

?u)

≤ rank (Z?u) = 1, ∀u ∈ U .

As Wu = 0 cannot be the solution of problem (30) due toUEs’ QoS requirement, we conclude that solving problem (30)without the rank-one constraint always achieves rank (W?

u) =1,∀u ∈ U . Hence, the proof of Theorem 1 is complete.

B. Proof of Theorem 2

The Lagrangian of problem (32) without constraint (26b)can be written as

L2

(Wu,σ2

q,r,ζCr ,ζDr ,ζSr ,λCr ,λDr ,νu,Xu)

=∑u∈U

Tr

(Wu

( ∑r∈RC(τ)

(Br

ηk+ ζCr Br+λCr Ξr

)

13

+∑

r∈RD(τ)

(Br

ηk+ ζDr Br + λDr β

(m+1)ru log2 (1 + γu)

)

+∑r∈RS

ζSrBr +∑

k∈U\u

νkγkhkhHk − νuhuhH

u −Xu

))+ Γ2, (38)

where ζCr , λCr , ζ

Dr , λ

Dr , ζ

Sr , νu ≥ 0, and Xu 0 are the

Lagrangian multipliers for constraints (15), (19) for all r ∈RC(τ), (16), (23) for all r ∈ RD(τ), (17) for all r ∈ RS,(25), and (26c), respectively, and Γ2 includes all other termsunrelated to Wu and Xu. Following similar steps in the proofof Theorem 1, for UE u, we have

W?u (P?

u−Q?u)=0⇔ rank (W?

uP?u) = rank (W?

uQ?u) , (39)

where

P?u =

∑r∈RC(τ)

(Br

ηk+(ζCr )?Br+(λCr )?Ξr

)

+∑

r∈RD(τ)

(Br

ηk+(ζDr )?Br+(λDr )?β(m+1)

ru log2 (1+γu)

)+∑r∈RS

(ζSr )?Br +∑

k∈U\u

ν?kγkhkhHk , (40)

and Q?u=ν?uhuh

Hu , and (ζCr )?, (λCr )?, (ζDr )?, (λDr )?,

(ζSr )?, and ν?u denote the solution of the dual problem.Thus, we have P?

u 0 and rank (W?uP

?u) = rank (W?

u).As rank(W?

uQ?u)≤ rank(Q?

u) = 1, we obtain rank (W?u)≤

1. Due to QoS requirement of UEs, we have rank (W?u) =

1, ∀u∈U . Hence, the proof of Theorem 2 is complete.

REFERENCES

[1] J. G. Andrews, S. Buzzi, W. Choi, S. V. Hanly, A. Lozano, A. C. Soong,and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun.,vol. 32, no. 6, pp. 1065–1082, Jun. 2014.

[2] “C-RAN: The road towards green RAN,” China Mobile, Tech. Rep.,version 3.0, Dec. 2013.

[3] M. Peng, Y. Li, Z. Zhao, and C. Wang, “System architecture and keytechnologies for 5G heterogeneous cloud radio access networks,” IEEENetw., vol. 29, no. 2, pp. 6–14, Mar. 2015.

[4] Z. Li, S. Cui, J. Gu, and K. G. Shin, “Coordinated multi-point trans-missions based on interference alignment and neutralization,” in Proc.IEEE INFOCOM’16, San Francisco, CA, Mar. 2016.

[5] J. Liu, S. Xu, S. Zhou, and Z. Niu, “Redesigning fronthaul fornext-generation networks: Beyond baseband samples and point-to-pointlinks,” IEEE Wireless Commun., vol. 22, no. 5, pp. 90–97, Oct. 2015.

[6] A. Pizzinat, P. Chanclou, F. Saliou, and T. Diallo, “Things you shouldknow about fronthaul,” J. Lightw. Technol., vol. 33, no. 5, pp. 1077–1083, Mar. 2015.

[7] J. Bartelt, P. Rost, D. Wubben, J. Lessmann, B. Melis, and G. Fettweis,“Fronthaul and backhaul requirements of flexibly centralized radioaccess networks,” IEEE Wireless Commun., vol. 22, no. 5, pp. 105–111,Oct. 2015.

[8] J. Zhao, T. Q. Quek, and Z. Lei, “Coordinated multipoint transmissionwith limited backhaul data transfer,” IEEE Trans. Wireless Commun.,vol. 12, no. 6, pp. 2762–2775, Jun. 2013.

[9] S.-H. Park, O. Simeone, O. Sahin, and S. Shamai, “Joint precodingand multivariate backhaul compression for the downlink of cloud radioaccess networks,” IEEE Trans. Signal Process., vol. 61, no. 22, pp.5646–5658, Nov. 2013.

[10] B. Dai and W. Yu, “Sparse beamforming and user-centric clustering fordownlink cloud radio access network,” IEEE Access, vol. 2, pp. 1326–1339, Nov. 2014.

[11] B. Niu, Y. Zhou, H. Shah-Mansouri, and V. W.S. Wong, “A dynamicresource sharing mechanism for cloud radio access networks,” IEEETrans. Wireless Commun., vol. 15, no. 12, pp. 8325–8338, Dec. 2016.

[12] A. Liu and V. K. Lau, “Two-timescale user-centric RRH clusteringand precoding optimization for cloud RAN via local stochastic cuttingplane,” IEEE Trans. Signal Process., vol. 66, no. 1, pp. 64–76, Jan.2018.

[13] Y. Mo, M. Peng, H. Xiang, Y. Sun, and X. Ji, “Resource allocationin cloud radio access networks with device-to-device communications,”IEEE Access, vol. 5, pp. 1250–1262, Mar. 2017.

[14] R. L. Cavalcante, S. Stanczak, M. Schubert, A. Eisenblaetter, andU. Turke, “Toward energy-efficient 5G wireless communications tech-nologies: Tools for decoupling the scaling of networks from the growthof operating power,” IEEE Signal Process. Mag., vol. 31, no. 6, pp.24–34, Nov. 2014.

[15] W. Wu, J. Wang, M. Li, K. Liu, and J. Luo, “Energy-efficient trans-mission with data sharing,” in Proc. IEEE INFOCOM’15, Hong Kong,China, Apr. 2015.

[16] M. Feng, S. Mao, and T. Jiang, “Boost: Base station on-off switchingstrategy for energy efficient massive MIMO HetNets,” in Proc. IEEEINFOCOM’16, San Francisco, CA, Mar. 2016.

[17] S. Han, C. Yang, and A. F. Molisch, “Spectrum and energy efficientcooperative base station doze,” IEEE J. Sel. Areas Commun., vol. 32,no. 2, pp. 285–296, Feb. 2014.

[18] D. Pompili, A. Hajisami, and H. Viswanathan, “Dynamic provisioningand allocation in cloud radio access networks (C-RANs),” Ad HocNetworks, vol. 30, pp. 128–143, Mar. 2015.

[19] D. Pompili, A. Hajisami, and T. X. Tran, “Elastic resource utilizationframework for high capacity and energy efficiency in cloud RAN,” IEEECommun. Mag., vol. 54, no. 1, pp. 26–32, Jan. 2016.

[20] Y. Shi, J. Zhang, and K. Letaief, “Group sparse beamforming for greencloud-RAN,” IEEE Trans. Wireless Commun., vol. 13, no. 5, pp. 2809–2823, May 2014.

[21] S. Luo, R. Zhang, and T. J. Lim, “Downlink and uplink energyminimization through user association and beamforming in C-RAN,”IEEE Trans. Wireless Commun., vol. 14, no. 1, pp. 494–508, Jan. 2015.

[22] Y. Shi, J. Zhang, W. Chen, and K. B. Letaief, “Generalized sparse andlow-rank optimization for ultra-dense networks,” IEEE Commun. Mag.,vol. 56, no. 6, pp. 42–48, Jun. 2018.

[23] B. Dai and W. Yu, “Energy efficiency of downlink transmission strategiesfor cloud radio access networks,” IEEE J. Sel. Areas Commun., vol. 34,no. 4, pp. 1037–1050, Apr. 2016.

[24] F. Zhou, Y. Wu, R. Q. Hu, Y. Wang, and K. K. Wong, “Energy-efficient NOMA enabled heterogeneous cloud radio access networks,”IEEE Netw., vol. 32, no. 2, pp. 152–160, Apr. 2018.

[25] D. Yan, R. Wang, E. Liu, and Q. Hou, “ADMM-based robust beamform-ing design for downlink cloud radio access networks,” IEEE Access,vol. 6, pp. 27 912–27 922, Jun. 2018.

[26] A. Maeder, M. Lalam, A. De Domenico, E. Pateromichelakis,D. Wubben, J. Bartelt, R. Fritzsche, and P. Rost, “Towards a flexiblefunctional split for cloud-RAN networks,” in Proc. EuCNC’14, Bologna,Italy, Jun. 2014.

[27] O. Simeone, A. Maeder, M. Peng, O. Sahin, and W. Yu, “Cloud radioaccess network: Virtualizing wireless access for dense heterogeneoussystems,” J. Commun. Netw., vol. 18, no. 2, pp. 135–149, Apr. 2016.

[28] D. Harutyunyan and R. Riggio, “Flexible functional split in 5G net-works,” in Proc. IEEE CNSM’17, Tokyo, Japan, Nov. 2017.

[29] T. T. Vu, D. T. Ngo, M. N. Dao, S. Durrani, D. H. Nguyen, and R. H.Middleton, “Energy efficiency maximization for downlink cloud radioaccess networks with data sharing and data compression,” IEEE Trans.Wireless Commun., vol. 17, no. 8, Aug. 2018.

[30] S.-H. Park, O. Simeone, O. Sahin, and S. Shamai Shitz, “Fronthaul com-pression for cloud radio access networks: Signal processing advancesinspired by network information theory,” IEEE Signal Process. Mag.,vol. 31, no. 6, pp. 69–79, Nov. 2014.

[31] P. Patil and W. Yu, “Hybrid compression and message-sharing strategyfor the downlink cloud radio-access network,” in Proc. IEEE ITA’14,San Diego, CA, Feb. 2014.

[32] ITU-T Standard Q11/15, “Transport network support of IMT-2020/5G,”Feb. 2018.

[33] 3GPP TR 38.801 V14.0.0, “Study on new radio access technology:Radio access architecture and interfaces (Release 14),” Mar. 2017.

[34] T. M. Cover and J. A. Thomas, Elements of Information Theory, 2ndEdition. John Wiley & Sons, 2006.

[35] G. Auer, V. Giannini, C. Desset, I. Godor, P. Skillermark, M. Olsson,M. A. Imran, D. Sabella, M. J. Gonzalez, O. Blume, and A. Fehske,

14

“How much energy is needed to run a wireless network?” IEEE WirelessCommun., vol. 18, no. 5, pp. 40–49, Oct. 2011.

[36] S. Boyd, “Sequential convex programming,” Lecture Notes, StanfordUniversity, 2008.

[37] E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity byreweighted `1 minimization,” J. Fourier Anal. Appl., vol. 14, no. 5, pp.877–905, Oct. 2008.

[38] Z.-Q. Luo, W.-K. Ma, A. M.-C. So, Y. Ye, and S. Zhang, “Semidefiniterelaxation of quadratic optimization problems,” IEEE Signal Process.Mag., vol. 27, no. 3, pp. 20–34, May 2010.

[39] S. Boyd and L. Vandenberghe, Convex Optimization. CambridgeUniversity Press, 2004.

[40] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convexprogramming, version 2.1,” http://cvxr.com/cvx, Jun. 2015.

[41] B. K. Sriperumbudur, D. A. Torres, and G. R. Lanckriet, “Amajorization-minimization approach to the sparse generalized eigenvalueproblem,” Machine Learning, vol. 85, no. 1, pp. 3–39, Dec. 2011.

[42] H. Wang, F. Zhang, Q. Wu, Y. Hu, and Y. Shi, “Nonconvex and nons-mooth sparse optimization via adaptively iterative reweighted methods,”[Online]. Available: https://arxiv.org/abs/1810.10167, 2018.

Yong Zhou (S’13, M’16) received the B.Sc. andM.Eng. degrees from Shandong University, Jinan,China, in 2008 and 2011, respectively, and the Ph.D.degree from the University of Waterloo, Waterloo,ON, Canada, in 2015. From 2015 to 2017, he workedas a postdoctoral research fellow in the Departmentof Electrical and Computer Engineering, The Uni-versity of British Columbia, Vancouver, Canada. Heis currently an Assistant Professor in the School ofInformation Science and Technology, ShanghaiTechUniversity, Shanghai, China. His research interests

include performance analysis and resource allocation of 5G and Internet ofThings (IoT) networks. He has served as a technical program committee (TPC)member for several conferences.

Jie Li received the B.S. degree in communicationengineering from Anhui University, Hefei, China, in2014. He is currently pursuing his M.S. degree inthe School of Information Science and Technology,ShanghaiTech University, Shanghai, China. His re-search interests include Age of Information (AoI)and Internet of Things (IoT) networks.

Yuanming Shi (S’13-M’15) received the B.S. de-gree in electronic engineering from Tsinghua Uni-versity, Beijing, China, in 2011. He received thePh.D. degree in electronic and computer engineeringfrom The Hong Kong University of Science andTechnology (HKUST), in 2015. Since September2015, he has been with the School of InformationScience and Technology in ShanghaiTech Univer-sity, where he is currently a tenured Associate Pro-fessor. He visited University of California, Berkeley,CA, USA, from October 2016 to February 2017. Dr.

Shi is a recipient of the 2016 IEEE Marconi Prize Paper Award in WirelessCommunications, and the 2016 Young Author Best Paper Award by the IEEESignal Processing Society. His research areas include optimization, statistics,machine learning, signal processing, and their applications to wireless com-munications and quantitative finance.

Vincent W.S. Wong (S’94, M’00, SM’07, F’16) re-ceived the B.Sc. degree from the University of Man-itoba, Winnipeg, MB, Canada, in 1994, the M.A.Sc.degree from the University of Waterloo, Waterloo,ON, Canada, in 1996, and the Ph.D. degree from theUniversity of British Columbia (UBC), Vancouver,BC, Canada, in 2000. From 2000 to 2001, he workedas a systems engineer at PMC-Sierra Inc. (now Mi-crochip Technology Inc.). He joined the Departmentof Electrical and Computer Engineering at UBCin 2002 and is currently a Professor. His research

areas include protocol design, optimization, and resource management ofcommunication networks, with applications to wireless networks, smart grid,mobile edge computing, and Internet of Things. Currently, Dr. Wong is anExecutive Editorial Committee Member of IEEE Transactions on WirelessCommunications, an Area Editor of IEEE Transactions on Communications,and an Associate Editor of IEEE Transactions on Mobile Computing. Hehas served as a Guest Editor of IEEE Journal on Selected Areas in Com-munications and IEEE Wireless Communications. He has also served on theeditorial boards of IEEE Transactions on Vehicular Technology and Journalof Communications and Networks. He was a Tutorial Co-Chair of IEEEGlobecom’18, a Technical Program Co-chair of IEEE SmartGridComm’14,as well as a Symposium Co-chair of IEEE ICC’18, IEEE SmartGridComm(’13, ’17) and IEEE Globecom’13. He is the Chair of the IEEE VancouverJoint Communications Chapter and has served as the Chair of the IEEECommunications Society Emerging Technical Sub-Committee on Smart GridCommunications. He received the 2014 UBC Killam Faculty Research Fellow-ship. He is an IEEE Communications Society Distinguished Lecturer (2019 -2020).