Hybrid Precoding-Based Millimeter-Wave Massive …oa.ee.tsinghua.edu.cn/dailinglong/publications/paper...IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 37, NO. 1, JANUARY 2019

IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 37, NO. 1, JANUARY 2019 131

Hybrid Precoding-Based Millimeter-Wave MassiveMIMO-NOMA With Simultaneous Wireless

Information and Power TransferLinglong Dai , Senior Member, IEEE, Bichai Wang , Student Member, IEEE,

Mugen Peng , Senior Member, IEEE, and Shanzhi Chen , Senior Member, IEEE

Abstract— Non-orthogonal multiple access (NOMA) has beenrecently considered in millimeter-wave (mmWave) massiveMIMO systems to further enhance the spectrum efficiency.In addition, simultaneous wireless information and power trans-fer (SWIPT) is a promising solution to maximize the energyefficiency. In this paper, for the first time, we investigatethe integration of SWIPT in mmWave massive MIMO-NOMAsystems. As mmWave massive MIMO will likely use hybridprecoding (HP) to significantly reduce the number of requiredradio-frequency (RF) chains without an obvious performanceloss, where the fully digital precoder is decomposed into a high-dimensional analog precoder and a low-dimensional digital pre-coder, we propose to apply SWIPT in HP-based MIMO-NOMAsystems, where each user can extract both information and energyfrom the received RF signals by using a power splitting receiver.Specifically, the cluster-head selection algorithm is proposed toselect one user for each beam at first, and then the analogprecoding is designed according to the selected cluster headsfor all beams. After that, user grouping is performed based onthe correlation of users’ equivalent channels. Then, the digitalprecoding is designed by selecting users with the strongestequivalent channel gain in each beam. Finally, the achievablesum rate is maximized by jointly optimizing power allocationfor mmWave massive MIMO-NOMA and power splitting factorsfor SWIPT, and an iterative optimization algorithm is developedto solve the non-convex problem. Simulation results show thatthe proposed HP-based MIMO-NOMA with SWIPT can achievehigher spectrum and energy efficiency compared with HP-basedMIMO-OMA with SWIPT.

Index Terms— SWIPT, mmWave, massive MIMO, NOMA,hybrid precoding, power allocation, power splitting.

Manuscript received March 12, 2018; revised July 4, 2018; accepted Sep-tember 6, 2018. Date of publication October 8, 2018; date of current versionDecember 14, 2018. This work was supported in part by the State MajorScience and Technology Special Project under Grant 2017ZX03001025-006,in part by the National Natural Science Foundation of China for OutstandingYoung Scholars under Grant 61722109, in part by the National Natural ScienceFoundation of China under Grant 61571270, and in part by the Royal Acad-emy of Engineering through the U.K.-China Industry Academia PartnershipProgramme Scheme under Grant U.K.-CIAPP\49. (Corresponding author:Shanzhi Chen.)

L. Dai and B. Wang are with the Tsinghua National Laboratory for Informa-tion Science and Technology and the Department of Electronic Engineering,Tsinghua University, Beijing 100084, China (e-mail: [email protected];[email protected]).

M. Peng is with the Key Laboratory of Universal Wireless Communications,Ministry of Education, Beijing University of Posts and Telecommunications,Beijing 100876, China (e-mail: [email protected]).

S. Chen is with the State Key Laboratory of Wireless Mobile Communi-cation, China Academy of Telecommunication Technology, Beijing 100191,China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSAC.2018.2872364

I. INTRODUCTION

M ILLIMETER-WAVE (mmWave) massive MIMO hasbeen considered as one of the promising techniques

for 5G wireless communications, since it can provide widerbandwidth and achieve higher spectrum efficiency [1], [2].It is well known that in conventional MIMO systems, eachantenna usually requires one dedicated radio-frequency (RF)chain to realize the fully digital signal processing [3], [4].In this way, the use of a very large number of antennasin mmWave massive MIMO systems leads to an equallylarge number of RF chains, which will result in unaffordablehardware cost and energy consumption [5]. To address thisissue, hybrid precoding (HP) has been proposed to signifi-cantly reduce the number of required RF chains in mmWavemassive MIMO systems without an obvious performanceloss [6]. The key idea of HP is to decompose the fully digitalprecoder into a high-dimensional analog precoder (realized bythe analog circuit) to increase the antenna array gain and alow-dimensional digital precoder (realized by a small numberof RF chains) to cancel interference [7]–[10]. Usually, twotypical HP architectures are adopted [5]: 1) Fully-connectedarchitecture, where each RF chain is connected to all antennas;2) Sub-connected architecture, where each RF chain is con-nected to only a subset of antennas. For general comparison,the fully-connected architecture can achieve higher spectrumefficiency, while the sub-connected architecture is expected toachieve higher energy efficiency [5].

To further increase the spectrum efficiency, non-orthogonalmultiple access (NOMA) has been recently considered inmmWave massive MIMO systems [11]–[14]. It has beenshown that NOMA can significantly improve the spectrumefficiency compared to the conventional orthogonal multipleaccess (OMA) schemes [15]–[18]. By using NOMA, morethan one user can be supported in each beam with the aid ofintra-beam superposition coding and successive interferencecancellation (SIC) [15], [16], which is essentially differentfrom conventional mmWave massive MIMO using one beamto serve only one user at the same time-frequency resources.Particularly, NOMA was applied to beamspace MIMO for thefirst time in [11], which can be regarded as a low-complexityrealization of HP, and power allocation was optimized to max-imize the achievable sum rate. In addition, NOMA was alsoutilized in fully-connected HP architecture in [12], and digitalprecoding was designed by modifying the conventional block

0733-8716 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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132 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 37, NO. 1, JANUARY 2019

diagonalization (BD) precoding scheme. Furthermore, a moresophisticated digital precoding design, i.e., minorization-maximization (MM) based precoding, was proposed in [13]to maximize the achievable sum rate. Besides, power allo-cation was optimized in [14] to maximize the energy effi-ciency of mmWave massive MIMO-NOMA systems, and aniterative algorithm was proposed to obtain the optimal powerallocation.

In addition to improving the spectrum efficiency, energyefficiency is also one of the key performance indicators (KPIs)for 5G, which is expected to be 100 times compared withthat of current 4G wireless communications [19]. To thisend, simultaneous wireless information and power trans-fer (SWIPT), which was initially proposed in [20], hasattracted great interests in recent years [21]–[25]. The keyidea of SWIPT is that both information and energy couldbe extracted from the same received RF signals, which canbe realized by power splitting receivers in practice [26]. Withthe help of SWIPT, the battery-powered wireless communi-cation devices can harvest energy from the RF signals toprolong their lifetime, which provides the potential to exploremore energy-efficient networks, especially for Internet ofThings (IoT) with millions of wireless devices [27]. However,the trade-off between information rate and harvested energylevel should be carefully considered to facilitate efficientSWIPT in multi-user systems, since inter-user interferencesare usually harmful for the information decoding (ID), whilethey can be useful for energy harvesting (EH) [21].

In fact, some efforts have been endeavored to addressthis problem. Particularly, a joint transmit beamformingand power splitting optimization was investigated in [28],where the transmit power was minimized under the signal-to-interference-and-noise ratio (SINR) and EH quality ofservice (QoS) constraints for multi-user MIMO systems.In addition, the joint transceiver and power splitting designfor downlink multi-user MIMO SWIPT networks was alsoinvestigated based on the mean square error (MSE) criterionin [29]. For multi-cell multi-user downlink SWIPT systems,the joint transceiver and power splitting design was studied tooptimize the energy efficiency in [30]. Although SWIPT hasthe potential to realize energy efficient wireless communica-tions, and has been investigated in some multi-user systems,the application of SWIPT in mmWave massive MIMO-NOMAsystems has not been considered in the literature to the best ofour knowledge, where new challenges will arise for the jointtransceiver and power splitting optimization.

In this paper, we propose to integrate SWIPT in HP-basedmmWave massive MIMO-NOMA systems to realize thespectrum- and energy-efficient wireless communications.1 Par-ticularly, a power splitting receiver is used for each user toachieve SWIPT by dividing the received signal into two partsfor simultaneous information retrieval and energy storage.In such an system, we investigate the joint optimization oftransceiver for ID and power splitting for EH, includinguser grouping, hybrid precoding design, power allocation,

1Simulation codes are provided to reproduce the results presented in thispaper: http://oa.ee.tsinghua.edu.cn/dailinglong/publications/publications.html.

and power splitting factors design. Specifically, the contribu-tions of this paper can be summarized as follows.

1) We propose to integrate SWIPT in HP-based mmWavemassive MIMO-NOMA systems, including both thefully-connected architecture and sub-connected archi-tecture. To the best of our knowledge, it is the firsttime to consider SWIPT in massive MIMO-NOMAsystems. On the one hand, HP architecture at the basestation (BS) can significantly reduce the number ofrequired RF chains without an obvious performanceloss, which can largely save the energy consumptionat the BS, while guarantee the spectrum efficiency ofmmWave massive MIMO systems. On the other hand,by using SWIPT, users can harvest energy from thereceived RF signals to prolong their life, which makes itmore energy-efficient at the users. Note that although theapplication of SWIPT in conventional MIMO systemshave been studied [21]–[23], [28], [29], the introductionof NOMA will result in additional challenges for thejoint transceiver and power splitting optimization.

2) To enable the HP-based mmWave massive MIMO-NOMA systems with SWIPT, we investigate the jointtransceiver and power splitting optimization. Specif-ically, the cluster-head selection (CHS) algorithm isproposed to select one user for each beam, and thenthe analog precoding is designed to obtain the antennaarray gain according to the selected cluster heads forall beams. After that, user grouping is performed basedon the equivalent channel correlation of the remainingusers and the cluster-heads. Then, the digital precodingis designed to cancel the inter-user interference byselecting users with the strongest equivalent channelgain in each beam. Finally, the achievable sum rateis maximized by jointly optimizing power allocationas well as power splitting factors, which is very dif-ficult to obtain the optimal solutions due to the cou-pling of different users’ power allocation factors aswell as the power splitting factors. To address thisissue, an iterative optimization algorithm is developedto solve the non-convex problem, and the convergenceand computational complexity are also analyzed.

3) The performance in terms of both spectrum effi-ciency and energy efficiency of the proposed HP-basedmmWave massive MIMO-NOMA systems with SWIPTis evaluated by simulations. The convergence of thedeveloped iterative optimization algorithm for jointpower allocation and power splitting is validated, and itis shown that only 10 times of iteration are required tomake it converged. Furthermore, we show that the pro-posed mmWave massive MIMO-NOMA systems withSWIPT can achieve higher spectrum and energy effi-ciency than those of mmWave massive MIMO-OMAsystems with SWIPT.

The rest of this paper is organized as follows. The systemmodel of HP-based mmWave massive MIMO-NOMA sys-tem with SWIPT is introduced in Section II. User groupingand hybrid precoding design are discussed in Section III.In Section IV, the joint power allocation and power splitting

DAI et al.: HYBRID PRECODING-BASED mmWAVE MASSIVE MIMO-NOMA WITH SWIPT 133

optimization problem is formulated to maximize the achiev-able sum rate, under the achievable rate QoS and EH QoS con-straints for each user. Furthermore, an iterative optimizationalgorithm is proposed to solve the non-convex problem. Sim-ulation results are provided in Section V. Finally, conclusionsare drawn in Section VI.

Notation: We use upper-case and lower-case boldface lettersto denote matrices and vectors, respectively; (·)T , (·)H , (·)−1,and ‖ · ‖p denote the transpose, conjugate transpose, matrixinversion, and lp norm operation, respectively. E {·} denotesthe expectation. |Γ| denotes the number of elements in set Γ.A(i, :)i∈Γ denotes the submatrix of A that consists of theith row of A for all i ∈ Γ, while A(:, j)j∈Γ denotes thesubmatrix of A that consists of the jth column of A forall j ∈ Γ. We use the notation CN (m,R) to denote thecomplex Gaussian distribution with mean m and covari-ance R, and U (a, b) to denote the uniform distribution in therange (a, b). ⊗ denotes the kronecker product. Finally, IN isthe N × N identity matrix, and Φ denotes the empty set.

II. SYSTEM MODEL

In this paper, we consider a single-cell downlink mmWavemassive MIMO-NOMA system, where the BS is equippedwith N antennas and NRF RF chains to simultaneously serveK single-antenna users [12]–[14], and each user is equippedwith a power splitting receiver for SWIPT.

Fig. 1 shows three architectures of mmWave massive MIMOsystems, i.e., the fully digital MIMO as shown in Fig. 1 (a),the fully-connected HP architecture as shown in Fig. 1 (b), andthe sub-connected HP architecture as shown in Fig. 1 (c). FromFig. 1, we can see that for the fully digital MIMO, eachantenna requires one dedicated RF chain, and thus the numberof RF chains is equal to the number of antennas, which resultsin unaffordable energy consumption and hardware cost. On thecontrary, the number of RF chains in HP architectures isless than the number of antennas, which can be realized bya high-dimensional analog precoder and a low-dimensionaldigital precoder. Specifically, for the fully-connected HP archi-tecture in Fig. 1 (b), each of the NRF RF chain is connectedto all N antennas by finite-resolution phase shifters, whereNNRF phase shifters are required, and thus the full array gaincan be exploited by every RF chain. For the sub-connectedHP architecture in Fig. 1 (c), each RF chain is connected toonly a subset of N BS antennas, so only N phase shiftersare required. In general, the sub-connected architecture iseasier to be implemented and will likely be more energyefficient, while it may suffer some performance loss comparedto the fully-connected architecture. In this paper, both ofthe fully-connected and sub-connected architectures will beconsidered.

In HP-based mmWave massive MIMO systems, the numberof beams cannot exceed the number of RF chains, and eachbeam can only support one user at most [7]. Therefore, to fullyachieve the multiplexing gain, we assume that the numberof beams G is equal to the number of RF chains NRF,i.e., G = NRF. On the contrary, each beam can support morethan one user by using NOMA. Let Sg for g = 1, 2, · · · , Gdenote the set of users served by the gth beam with |Sg| ≥ 1,

Fig. 1. System models of mmWave MIMO architectures: (a) Fullydigital MIMO; (b) Fully-connected HP architecture; (c) Sub-connectedHP architecture.

and we have Si ∩ Sj = Φ for i �= j as well asG∑

g=1|Sg| = K .

Then, the received signal at the mth user in the gth beam canbe modeled as

yg,m = hHg,mA

G∑

i=1

|Si|∑

j=1

di√

pi,jsi,j + vg,m

= hHg,mAdg

√pg,msg,m

︸︷︷︸desired signal

+hHg,mAdg

⎛

⎝m−1∑

j=1

√pg,jsg,j +

|Sg|∑

j=m+1

√pg,jsg,j

⎞

⎠

︸︷︷︸intra−beam interferences

+hHg,mA

∑

i�=g

|Si|∑

j=1

di√

pi,jsi,j

︸︷︷︸inter−beam interferences

+ vg,m︸︷︷︸noise

, (1)

where sg,m is the transmitted signal with E{|sg,m|2} = 1,pg,m is the transmitted power for the mth user in the gth beam,


vg,m is the noise following the distribution CN (0, σ2

v

),

dg is the NRF × 1 digital precoding vector for the gth beam,A of size N × NRF is the analog precoding matrix, andwe have ‖Adg‖2 = 1 for g = 1, 2, · · · , G. Particularly,for the fully-connected architecture, the analog precodingmatrix A(full) can be expressed as

A(full) =[a(full)

1 , a(full)2 , · · · , a(full)

NRF

], (2)

where the elements of a(full)n ∈ N×1 for n = 1, 2, · · · , NRF

have the same amplitude 1/√

N but different phases [6].For the sub-connected architecture, the analog precodingmatrix A(sub) is

A(sub) =

⎡

⎢⎢⎢⎢⎣

a(sub)1 0 · · · 00 a(sub)

2 0...

. . ....

0 0 · · · a(sub)NRF

⎤

⎥⎥⎥⎥⎦. (3)

Without loss of generality, we assume that M = N/NRF

is an integer, and each RF chain is connected to M anten-nas in the sub-connected architecture. Then, the elements ofa(sub)

n ∈ M×1 for n = 1, 2, · · · , NRF have the same amplitude1/

√M [7], [8].

For the N × 1 channel vector hg,m of the mth user inthe gth beam, we consider the widely used mmWave MIMOchannel model as shown below [6]–[8]:

hg,m =

√N

Lg,m

Lg,m∑

l=1

α(l)g,ma

(ϕ(l)

g,m, θ(l)g,m

), (4)

where Lg,m denotes the number of paths for the mth userin the gth beam. α

(l)g,m is the complex gain of the lth path.

ϕ(l)g,m and θ

(l)g,m are the azimuth angle of departure (AoD) and

elevation AoD of the lth path, and a(ϕ(l)g,m, θ

(l)g,m) presents

the N × 1 array steering vector. Particularly, for the typicaluniform linear array (ULA) with N1 elements in horizon andN2 elements in vertical, where N = N1N2 [7], we have

a (ϕ, θ) = aaz (ϕ) ⊗ ael (θ) , (5)

where aaz (ϕ) = 1√N1

[ej2πi(d1/λ) sin(ϕ)

]i∈J(N1)

, ael (θ) =1√N2

[ej2πj(d2/λ) sin(θ)

]j∈J(N2)

, J (n) = {0, 1, · · · , n − 1},λ is the signal wavelength, d1 is the horizontal antennaspacing, and d2 is the vertical antenna spacing. In mmWavecommunications, we usually have d1 = d2 = λ/2 [7].

With the aid of power splitting receiver, the received signalat each user will be divided into two parts. One part isforwarded to the information decoder for ID, and the otheris processed for EH [29]. Let βg,m, where 0 < βg,m < 1,denote the power splitting factor for the mth user in the gthbeam, then the signal for EH can be represented as

yEHg,m =

√1 − βg,myg,m, (6)

and the harvested energy is [29]

PEHg,m = η (1−βg,m)

⎛

⎝G∑

i=1

|Si|∑

j=1

∥∥hH

g,mdi

∥∥2

2pi,j + σ2

v

⎞

⎠, (7)

where hHg,m = hH

g,mA is the equivalent channel vector, and0 ≤ η ≤ 1 is the energy conversion efficiency. In themeanwhile, the signal for ID at the mth user in the gth beamcan be expressed as

yIDg,m =

√βg,myg,m + ug,m, (8)

where ug,m is the noise caused by the power splitter followingthe distribution CN (0, σ2

u).By using NOMA in each beam, intra-beam superposition

coding at the transmitter and SIC at the receiver are performed.Without loss of generality, we assume that ‖hH

g,1dg‖2 ≥‖hH

g,2dg‖2 ≥ · · · ≥ ‖hHg,|Sg|dg‖2 for g = 1, 2, · · · , G. Then,

the mth user in the gth beam can remove the interference fromthe jth user (for all j > m) in the gth beam by performingSIC [15], and the remaining received signal for ID at the mthuser in the gth beam can be rewritten as

yIDg,m =

√βg,m

⎛

⎝hHg,mdg

√pg,msg,m + hH

g,mdg

m−1∑

j=1

√pg,jsg,j

+ hHg,m

∑

i�=g

|Si|∑

j=1

di√

pi,jsi,j + vg,m

⎞

⎠+ ug,m.

(9)

Then, according to (9), the SINR at the mth user in thegth beam can be written as

γg,m =

∥∥hH

g,mdg

∥∥2

2pg,m

ξg,m, (10)

where

ξg,m =∥∥hH

g,mdg

∥∥2

2

m−1∑

j=1

pg,j +∑

i�=g

∥∥hH

g,mdi

∥∥2

2

|Si|∑

j=1

pi,j

+ σ2v +

σ2u

βg,m. (11)

As a result, the achievable rate at the mth user in thegth beam is

Rg,m = log2 (1 + γg,m) . (12)

Finally, the achievable sum rate is

Rsum =G∑

g=1

|Sg|∑

m=1

Rg,m, (13)

which can be improved by carefully designing user group-ing, analog precoding matrix A, digital precoding {dg}G

g=1,

power allocation {pg,m}G,|Sg|g=1,m=1, and power splitting factors

{βg,m}G,|Sg|g=1,m=1. Since it is very difficult to simultaneously

obtain the optimal solutions for all these design parameters,we consider to design user grouping and hybrid precoding atfirst as described in the next section. Then, joint optimizationof power allocation and power splitting will be introduced inSection IV.


III. USER GROUPING AND HYBRID PRECODING

We know that the number of users K is larger than thenumber of RF chains NRF in the considered system, whileonly NRF different analog precoding vectors are availableat the same time [8]. Therefore, to enable hybrid precoding,we propose the CHS algorithm to select one user for eachbeam (there are G = NRF beams), and then the analogprecoding is designed to obtain the antenna array gain accord-ing to the selected cluster heads for all beams. After that,user grouping is performed based on the equivalent channelcorrelation between the remaining users and the cluster-heads.Then, the digital precoding is designed to cancel inter-userinterference by selecting users with the strongest equivalentchannel gain in each beam.

A. The Proposed CHS Algorithm

To improve the system performance, we propose to selectthe cluster head for each beam by minimizing the channelcorrelation of the selected cluster heads. In this way, users indifferent beams will enjoy low channel correlation, which isbeneficial for inter-beam interference cancellation.

In the proposed CHS algorithm, an adaptive threshold δ isintroduced to measure the channel correlation of the clusterheads. Specifically, the user with the highest channel gainis selected as the cluster head for the first beam, and thenusers whose channel correlation with the first selected useris less than the threshold δ will be considered as the clusterhead candidates for other beams. Particularly, the user withthe highest channel gain out of the cluster head candidates isselected as the cluster head for the second beam. After that,the cluster head candidates will be updated by selecting userswhose channel correlation with the second selected user is lessthan the threshold. This procedure is repeated until there is nocandidate. Next, the threshold is updated by adding a smallincrement, and then the cluster head candidates are obtained byselecting users whose channel correlations with the previouslyselected cluster heads are less than the threshold. The thresholdwill be adaptively updated until the cluster heads are selectedfor all G beams. The details of the proposed CHS algorithmare described in Algorithm 1, and the set of the selectedcluster heads is denoted as Γ.

The proposed CHS algorithm enjoys the polynomial com-plexity. Specifically, in each iteration, the maximum complex-ity is (2+2(K−1))(K −1) from step 9 to step 14, while themaximum complexity is 2(K − 1) from step 15 to step 18.Therefore, the complexity of Algorithm 1 is O(GK2).

B. Analog Precoding

In this paper, we consider the typical two-stage HP pro-posed in [9].2 The key idea of this scheme is to divide theHP design into two step, i.e., analog precoding and digitalprecoding. Particularly, for analog precoding, only quantizedphase changes can be applied due to the practical constraintsof phase shifters [10]. Considering B bits quantized phaseshifters, the non-zero elements of the fully-connected analog

2Note that more sophisticated HP schemes can be considered to furtherenhance the performance of mmWave massive MIMO-NOMA systems.

Algorithm 1 Proposed CHS AlgorithmInput:

The number of users K , and the number of beams G;Channel vectors: hk for k = 1, 2, · · · , K;The initial threshold: δ.

Output:The cluster head set Γ.

1: Λ = [a1, a2, · · · , aK ], where ak = ‖hk‖2;2: hk = hk/ak for k = 1, 2, · · · , K;3: [∼,O] = sort (Λ,′ descend′);4: Γ = O (1);5: Γc = O/Γ;6: Ω = Γc;7: g = 2.8: while g ≤ G do9: if Ω == Φ then

10: while Ω == Φ do11: δ = δ + (1 − δ)/10;

12: Ω ={i ∈ Γc

∣∣∣∣∣∣hH

i hj

∣∣∣ < δ, ∀j ∈ Γ

}.

13: end while14: end if15: Ω =

{i ∈ Ω

∣∣∣∣∣∣hH

i hj

∣∣∣ < δ, ∀j ∈ Γ

};

16: Γ = Γ ∪ Ω (1);17: Γc = O/Γ;18: g = g + 1.19: end while20: return Γ.

precoding matrix A(full) belong to

1√N

{ej 2πn

2B : n = 0, 1, · · · , 2B − 1}

, (14)

while the non-zero elements of the sub-connected analogprecoding matrix A(sub) belong to

1√M

{ej 2πn

2B : n = 0, 1, · · · , 2B − 1}

. (15)

Based on the cluster head set Γ obtained in the previoussubsection, the analog precoding can be designed according tothe channel vectors of users in Γ. More particularly, the analogprecoding vectors can be obtained by maximizing the arraygains |hH

Γ(g)a(full)g |2 for the fully-connected architecture and

|hHΓ(g)a

(sub)g |2 for the sub-connected architecture, separately,

where g = 1, 2, · · · , G. As a result, the ith element, where i =1, 2, · · · , N , of the fully-connected analog precoding vectora(full)

g can be expressed as

a(full)g (i) =

1√N

ej 2πn

2B , (16)

where

n = argminn∈{0,1,··· ,2B−1}

∣∣∣∣angle

(hΓ(g) (i)

)− 2πn

2B

∣∣∣∣ . (17)

Similarly, the ith element of the sub-connected analog pre-coding vector a(sub)

g , where i = (g − 1)M + 1, (g − 1)M +2, · · · , gM , is

a(sub)g (i) =

1√M

ej 2πn

2B , (18)

where n is the same as that in (17).


C. User GroupingAfter obtaining the analog precoding, the equivalent channel

vectors for all K users can be written as

hHk = hH

k A, (19)

where k = 1, 2, · · · , K . Then, user grouping can be realizedaccording to the correlation of equivalent channels. Specifi-cally, user m (m /∈ Γ) can be classed as the gth beam, where

g = argmaxg∈{1,2,··· ,G}

∣∣hH

mhΓ(g)

∣∣

∥∥hm

∥∥

2

∥∥hΓ(g)

∥∥

2

. (20)

In this way, users in the same beam will enjoy high correlationof equivalent channels, while the equivalent channels of usersin different beams have low correlation owing to the proposedCHS algorithm, which is conducive to the inter-beam interfer-ence cancellation and thus the improvement of multiplexinggains.

D. Digital PrecodingAfter analog precoding and user grouping, the equivalent

channel vector for the mth user in the gth beam can be denotedas hH

g,m as introduced in Section II. Then, the design of digitalprecoding actually becomes a conventional MIMO-NOMAprecoding problem to eliminate inter-beam interference. With-out loss of generality, the low-complexity zero-forcing (ZF)precoding is adopted for digital precoding, according tothe equivalent channel vectors of users having the highestequivalent channel gain in each beam [11], [12].

Specifically, assuming that the mgth user has the highestequivalent channel gain in the gth beam, we have

H =[hm1 , hm2 , · · · , hmG

]. (21)

Then, the digital precoding matrix of size NRF ×NRF can begenerated by

D =[d1, d2, · · · , dG

]= H

(HHH

)−1(22)

After normalizing, the digital precoding vector for thegth beam can be written as

dg =dg∥

∥Adg

∥∥

2

. (23)

Afterwards, the users in each beam will be reordered suchthat ‖hH

g,1dg‖2 ≥ ‖hHg,2dg‖2 ≥ · · · ≥ ‖hH

g,|Sg|dg‖2 for g =1, 2, · · · , G, which is assumed in Section II for SIC.

Up to now, user grouping and hybrid precoding have beencarefully designed to obtain antenna array gains and multi-plexing gains. In the next Section, the joint optimization ofpower allocation and power splitting will be investigated tomaximize the achievable sum rate in (13).

IV. JOINT OPTIMIZATION OF POWER ALLOCATION

AND POWER SPLITTING

Although power allocation has been studied in existingMIMO-NOMA systems [17], [34]–[36], the joint optimizationof power allocation and power splitting has not been consid-ered. The introduction of power splitting factors will result inadditional challenges for the joint optimization in mmWave

massive MIMO-NOMA systems with SWIPT, since thereexists not only the coupling of power allocation factors fromdifferent users, but also the coupling of power allocation andpower splitting factors. On the other hand, the existing opti-mization methods for solving the joint optimization problemof power allocation and power splitting in MIMO systems withSWIPT cannot be directly used in MIMO-NOMA systemswith SWIPT, where there are multiple groups and multipleusers in each group, since both inter-group and intra-groupinterferences exist. Therefore, it is very difficult to obtain theoptimal solutions. To solve this intractable problem, an iter-ative optimization algorithm is developed in this Section toobtain the sub-optimal solutions. Specifically, the joint powerallocation and power splitting optimization problem can beformulated as

max{pg,m},{βg,m}

G∑

g=1

|Sg|∑

m=1

Rg,m

s.t. C1 : pg,m ≥ 0, ∀g, m,

C2 :G∑

g=1

|Sg|∑

m=1

pg,m ≤ Pt,

C3 : Rg,m ≥ Rming,m, ∀g, m,

C4 : PEHg,m ≥ Pmin

g,m , ∀g, m, (24)

where Rg,m is the achievable rate of the mthe user in thegth beam as defined in (12), the constraint C1 indicates thatthe power allocated to each user must be positive, C2 is thetransmitted power constraint with Pt being the maximum totaltransmitted power by the BS, C3 is the data rate constraint foreach user with Rmin

g,m being the minimum data rate for themth user in the gth beam, and C4 is the EH QoS constraintfor each user with Pmin

g,m being the minimum harvested energyfor the mthe user in the gth beam. Note that the optimizationproblem (24) is non-convex due to the non-convexity of theobjective function, and the constraints C3 as well as C4.

To solve the non-convex problem (24), an iterative opti-mization algorithm is developed. Particularly, according to theextension of the Sherman-Morrison-Woodbury formula [37],i.e.,

(A + BCD)−1 =A−1−A−1B(I+CDA−1B

)−1CDA−1,

(25)

we have

(1 + γg,m)−1

= 1 − pg,m

∥∥hH

g,mdg

∥∥2

2

(pg,m

∥∥hH

g,mdg

∥∥2

2+ ξg,m

)−1

, (26)

where g = 1, 2, · · · , G and m = 1, 2, · · · , |Sg|.On the other hand, let

yg,m = hHg,mdg

√pg,msg,m + hH

g,mdg

m−1∑

j=1

√pg,jsg,j

+ hHg,m

∑

i�=g

|Si|∑

j=1

di√

pi,jsi,j + vg,m +1

√βg,m

ug,m.

(27)


If the minimum mean square error (MMSE) detection is usedto solve sg,m from yg,m in (27), this detection problem canbe formulated as

cog,m = arg min

cg,m

eg,m, (28)

whereeg,m = E

{|sg,m − cg,myg,m|2

}(29)

is the mean square error (MSE), and cg,m is the channelequalization coefficient. Substituting (27) into (29), we have

eg,m = 1 − 2Re(cg,m

√pg,mhH

g,mdg

)

+ |cg,m|2(pg,m

∥∥hH

g,mdg

∥∥2

2+ ξg,m

). (30)

Then, by solving the partial derivatives of (28) based on (30),the optimal equalization coefficient co

g,m can be obtained by

cog,m =

(√pg,mhH

g,mdg

)∗(pg,m

∥∥hH

g,mdg

∥∥2

2+ ξg,m

)−1

. (31)

Substituting (31) into (30), the MMSE can be written as

eog,m = 1 − pg,m

∥∥hH

g,mdg

∥∥2

2

(pg,m

∥∥hH

g,mdg

∥∥2

2+ ξg,m

)−1

,

(32)

which is equal to (1 + γg,m)−1 in (26), i.e., we have

(1 + γg,m)−1 = mincg,m

eg,m. (33)

Then, the achievable rate of the mth user in the gth beam canbe rewritten as

Rg,m = log2 (1 + γg,m) = maxcg,m

(−log2eg,m) . (34)

Note that in (34), the polynomial division has been removedby using eg,m rather than γg,m, which significantly simplifiesthe objective function. Furthermore, to remove the log functionin (34), Proposition 1 is introduced [11], [34].

Proposition 1: Let f (a) = − abln 2 + log2a + 1

ln 2 and a be apositive real number, we have

maxa>0

f (a) = −log2b, (35)

where the optimal value of a is ao = 1b .

According to Proposition 1, we can rewrite (34) as

Rg,m = maxcg,m

maxag,m>0

(

−ag,meg,m

ln 2+ log2ag,m +

1ln 2

)

. (36)

As a result, the optimization problem (24) can be reformu-lated as

max{pg,m},{βg,m}

G∑

g=1

|Sg|∑

m=1

maxcg,m

maxag,m>0

(−ag,meg,m

ln 2+ log2ag,m

)

s.t. C1, C2, C3, C4. (37)

To solve (37), the iterative optimization algorithm is intro-duced to optimize {cg,m}, {ag,m}, and {pg,m} as wellas {βg,m}, separately. Specifically, given the optimal powerallocation solution {p(t−1)

g,m } and the power splitting solution{β(t−1)

g,m } in the (t − 1)th iteration, the optimal solution

of {c(t)g,m} in the tth iteration can be obtained according to (31),

i.e.,

c(t)g,m

=(√

p(t−1)g,m hH

g,mdg

)∗(p(t−1)

g,m

∥∥hH

g,mdg

∥∥2

2+ ξ(t−1)

g,m

)−1

,

(38)

where

ξg,m(t−1) =

∥∥hH

g,mdg

∥∥2

2

m−1∑

j=1

p(t−1)g,j

+∑

i�=g

∥∥hH

g,mdi

∥∥2

2

|Si|∑

j=1

p(t−1)i,j

+ σ2v +

σ2u

β(t−1)g,m

. (39)

In the meanwhile, the optimal solution of {a(t)g,m} in the tth

iteration can be calculated by

a(t)g,m =

1

eo(t)g,m

, (40)

where

eo(t)g,m

= 1 − p(t−1)g,m

∥∥hH

g,mdg

∥∥2

2

(p(t−1)

g,m

∥∥hH

g,mdg

∥∥2

2+ ξ(t−1)

g,m

)−1

.

(41)

Then, the optimization problem (37) can be simplified as

min�p(t)g,m

�,�

β(t)g,m

�G∑

g=1

|Sg|∑

m=1

a(t)g,me(t)

g,m

s.t. C(t)1 : p(t)

g,m ≥ 0, ∀g, m,

C(t)2 :

G∑

g=1

|Sg|∑

m=1

p(t)g,m ≤ Pt,

C(t)3 : R(t)

g,m ≥ Rming,m, ∀g, m,

C(t)4 : PEH(t)

g,m ≥ Pming,m , ∀g, m, (42)

where

e(t)g,m = 1 − 2Re

(

c(t)g,m

√

p(t)g,mhH

g,mdg

)

+∣∣∣c(t)

g,m

∣∣∣2 (

p(t)g,m

∥∥hH

g,mdg

∥∥2

2+ ξ(t)

g,m

). (43)

Furthermore, we introduce the variables {τ (t)g,m} such that

τ(t)g,m ≥ 1

β(t)g,m

, and rewrite the objective function in (42) as

min�p(t)g,m

�,�

β(t)g,m

�G∑

g=1

|Sg|∑

m=1

a(t)g,me(t)

g,m, (44)

where

e(t)g,m = 1 − 2Re

(c(t)g,mhH

g,mdg

)√

p(t)g,m

+∣∣∣c(t)

g,m

∣∣∣2

⎛

⎝∥∥hH

g,mdg

∥∥2

2

m∑

j=1

p(t)g,j

+∑

i�=g

∥∥hH

g,mdi

∥∥2

2

|Si|∑

j=1

p(t)i,j + σ2

uτ (t)g,m + σ2

v

⎞

⎠ , (45)


with the additional constraint

C(t)5 : τ (t)

g,m ≥ 1

β(t)g,m

, ∀g, m. (46)

Intuitively, the objective function (44) becomes convex forthe optimization variables {p(t)

g,m} and {τ (t)g,m}. At the same

time, the constraint C(t)3 in (42) can be also transformed into

a convex constraint as

C(t)3 :

∥∥hH

g,mdg

∥∥2

2p(t)

g,m − ωg,m

∥∥hH

g,mdg

∥∥2

2

m−1∑

j=1

p(t)g,j

−ωg,m

∑

i�=g

∥∥hH

g,mdi

∥∥2

2

|Si|∑

j=1

p(t)i,j − ωg,mσ2

uτ (t)g,m

≥ ωg,mσ2v , (47)

where ωg,m = 2Rming,m − 1. Nevertheless, the constraints

C(t)4 and C

(t)5 in (42) are still non-convex due to the

multi-variable coupling. To make it solvable, another variables{μ(t)

g,m} are introduced such that

C(t)6 : μ(t)

g,m ≥ Pming,m

η(1 − β

(t)g,m

) , ∀g, m. (48)

Then, the constraint C(t)4 in (42) can be rewritten as

C(t)4 :

G∑

i=1

|Si|∑

j=1

∥∥hH

g,mdi

∥∥2

2p(t)i,j + σ2

v ≥ μ(t)g,m, ∀g, m, (49)

which becomes a convex constraint.To deal with the non-convex constraints C

(t)5 in (46) and

C(t)6 in (48), we transform them into matrix form according

to the Schur complement lemma [29], i.e.,

C(t)5 :

[τ

(t)g,m 11 β

(t)g,m

]

≥ 0, ∀g, m, (50)

and

C(t)6 :

⎡

⎣μ

(t)g,m

√Pmin

g,m

/η

√Pmin

g,m

/η 1 − β

(t)g,m

⎤

⎦ ≥ 0, ∀g, m. (51)

As a result, the optimization problem (42) can be reformu-lated as

min�p(t)g,m

�,�

β(t)g,m

�G∑

g=1

|Sg|∑

m=1

a(t)g,me(t)

g,m

s.t. C(t)1 , C

(t)2 , C

(t)3 , C

(t)4 , C

(t)5 , C

(t)6 , (52)

which is a standard convex optimization problem, and can besolved by numerical convex program solvers [38].

By iteratively solving the optimal values of {cg,m}, {ag,m},and {pg,m} as well as {βg,m} via (38), (40), and (52),separately, we can obtain the final power allocation solution{po

g,m} and power splitting solution {βog,m} with the max-

imum iteration times Tmax. Particularly, since the obtained{c(t)

m,n}, {a(t)m,n}, and {p(t)

m,n} as well as {β(t)m,n} are opti-

mal solutions in the tth iteration, iteratively updating thesevariables will increase or maintain the value of the objective

function in (37) [34]. As a result, the proposed iterativeoptimization algorithm for joint power allocation and powersplitting will converge to at least a local optimal solution.

In the meanwhile, the proposed joint optimization algorithmenjoys a polynomial complexity. Specifically, in each iteration,the complexity for obtaining the optimal {cm,n} in (38) and{am,n} in (40) is linear to the number of users, i.e., O(K). Theconvex optimization problem (52) can be solved with a worst-case complexity of O(TmaxK

4.5log2(1/ε)) given a solutionaccuracy ε > 0 [39]. Therefore, the computational complexityof the proposed iterative optimization algorithm is at mostO(TmaxK

4.5log2(1/ε)).

V. SIMULATION RESULTS

The performance in terms of spectrum efficiency and energyefficiency of the mmWave massive MIMO-NOMA systemswith SWIPT, including both the fully-connected HP andthe sub-connected HP, proposed in this paper is evaluatedvia simulations. Specifically, the simulation parameters aredescribed as follows: The system bandwidth is assumed tobe 1 Hz, which coincides to the achievable rate in (12). TheBS is equipped with an ULA of N = 64 antennas and NRF =4 RF chains to simultaneously serve K ≥ NRF users. All theK uses are grouped into G = NRF = 4 beams, and there aremore than one user in each beam. For the mth user in thegth beam, the channel vector is generated based on (4), wherewe assume: 1) Lg,m = 3, including one line-of-sight (LoS)component and two non-line-of-sight (NLoS) components;2) α

(1)g,m ∼ CN (0, 1), and α

(l)g,m ∼ CN (0, 10−1) for 2≤

l ≤ Lg,m; 3) ϕ(l)g,m and θ

(l)g,m follow the uniform distribution

U(−π, π) for 1 ≤ l ≤ Lg,m. B = 4 bits quantized phaseshifters are adopted, and the signal-to-noise ratio (SNR) isdefined as Pt

/σ2

v [8]. The maximum transmitted power Pt =30 mW, the minimal achievable rate for each user is Rfm/10,where Rfm is the minimal achievable rate among all users byusing fully digital ZF precoding, and the minimal harvestedenergy for each user is 0.1 mW.

In this paper, the spectrum efficiency is defined as theachievable sum rate in (13), and the energy efficiency isdefined as the ratio between the achievable sum rate and thetotal power consumption [7], i.e.,

EE =Rsum

Ptr + NRFPRF + NPSPPS + PBB(bps/Hz/W),

(53)

where Ptr =G∑

g=1

|Sg|∑

m=1pg,m is the total transmitted power,

PRF is the power consumed by each RF chain, PPS isthe power consumption of each phase shifter, and PBB isthe baseband power consumption. Particularly, we adopt thetypical values PRF = 300 mW, PPS = 40 mW (4-bit phaseshifter), and PBB = 200 mW [8]. NPS is the number of phaseshifters, which is equal to NNRF for the fully-connected HPand N for the sub-connected HP.

In the simulations, we consider the following five typicalmmWave massive MIMO systems with SWIPT for compar-ison: (1) “SWIPT-Fully digital ZF Precoding”, where each


Fig. 2. Spectrum efficiency of fully-connected architecture against thenumber of iterations for the joint power allocation and power splittingoptimization.

Fig. 3. Spectrum efficiency of sub-connected architecture against the numberof iterations for the joint power allocation and power splitting optimization.

antenna is connected to one RF chain, and ZF precod-ing is adopted; (2) “SWIPT-Fully-Connected HP-NOMA”,where fully-connected HP architecture is used in the pro-posed mmWave massive MIMO-NOMA systems with SWIPT;(3) “SWIPT-Fully-Connected HP-OMA”, where the systemmodel is similar with “SWIPT-Fully-Connected HP-NOMA”,while OMA is performed for users in each beam. Particularly,we represent OMA with FDMA, where users in the samebeam are allocated with equal bandwidth; (4) “SWIPT-Sub-Connected HP-NOMA”, where sub-connected HP architectureis used in the proposed mmWave massive MIMO-NOMAsystems with SWIPT; (5) “SWIPT-Sub-Connected HP-OMA”,where the system model is similar with “SWIPT-Sub-Connected HP-NOMA”, while OMA is performed for usersin each beam.

Fig. 2 and Fig. 3 show the convergence of the proposediterative algorithm for joint power allocation and power split-ting optimization in Section IV for the fully-connected HP andsub-connected HP, separately, where the number of users is setas K = 6, and SNR = 0 dB. As shown in Fig. 2 and Fig. 3,the spectrum efficiency tends to be stable after 10 timesof iteration, which verifies the convergence of the proposediterative algorithm as discussed in Section IV. In the followingsimulations, the number of iteration times for the proposediterative optimization algorithm is set as 10.

Fig. 4. Spectrum efficiency against SNR.

Fig. 5. Energy efficiency against SNR.

Fig. 4 shows the spectrum efficiency against SNR ofthe considered five schemes, where the number of users isK = 6. We can find that the proposed mmWave massiveMIMO-NOMA systems with SWIPT can achieve higher spec-trum efficiency than that of mmWave massive MIMO-OMAsystems with SWIPT, either for the fully-connected HP or thesub-connected HP, since NOMA can achieve higher spectrumefficiency than that of OMA [15]. It is intuitive that the fullydigital MIMO can achieve the best spectrum efficiency asshown in Fig. 4, since N RF chains are used to serve allusers to fully exploit the multiplexing gains. On the other hand,the fully-connected HP can achieve higher spectrum efficiencythan that of the sub-connected HP as discussed in Section II,since the full array gain can be exploited by every RF chainin the fully-connected HP.

Fig. 5 shows the energy efficiency against SNR, where thenumber of users is also K = 6. We can find that the proposedmmWave massive MIMO-NOMA systems with SWIPT canachieve higher energy efficiency than both mmWave massiveMIMO-OMA systems with SWIPT and fully digital MIMOsystems with SWIPT. Particularly, the number of RF chainsis equal to the number of BS antennas in fully digitalMIMO systems, which leads to very high energy consumption,e.g., 300 mW for each RF chain. On the contrary, the numberof RF chains is much smaller than the number of antennasin the proposed mmWave massive MIMO-NOMA systemswith SWIPT. Therefore, the energy consumption caused by


Fig. 6. Energy efficiency against the number of users.

the RF chains can be significantly reduced compared to thefully digital MIMO systems. In addition, we can see fromFig. 5 that the sub-connected HP can achieve higher energyefficiency than that of the fully-connected HP, since a lessnumber of phase shifters is adopted in the sub-connected HP.

The performance comparison in terms of energy efficiencyagainst the number of users is shown in Fig. 6, where SNRis set as 10 dB. We can see that when the sub-connected HPis adopted, the energy efficiency of the proposed mmWavemassive MIMO-OMA systems with SWIPT is higher than allof other schemes even the number of users is very large.

VI. CONCLUSIONS

In this paper, we propose to apply SWIPT in HP-basedmmWave massive MIMO-NOMA systems to achieve atrade-off between spectrum efficiency and energy efficiency.To enable the spectrum- and energy-efficient systems, usergrouping, hybrid precoding, power allocation, and power split-ting are carefully designed. Specifically, the CHS algorithm isfirst proposed to select one user for each beam as the clusterhead, and then the analog precoding is designed accordingto the selected cluster heads for all beams. After that, usergrouping is performed based on the correlation of users’equivalent channels. Then, the digital precoding is designedby selecting users with the strongest equivalent channel gainin each beam. Furthermore, the joint optimization of powerallocation and power splitting is proposed to maximize theachievable sum rate, and an iterative optimization algorithmis developed to solve the non-convex optimization problem.Simulation results show that the proposed mmWave mas-sive MIMO-NOMA systems with SWIPT can achieve higherspectrum and energy efficiency compared with mmWavemassive MIMO-OMA systems with SWIPT. In the future,we will consider more sophisticated hybrid precoding designfor the proposed mmWave massive MIMO-NOMA systemswith SWIPT to further improve the performance.

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Linglong Dai (M’11–SM’14) received the B.S.degree from Zhejiang University in 2003, the M.S.degree (Hons.) from the China Academy ofTelecommunications Technology in 2006, and thePh.D. degree (Hons.) from Tsinghua University,Beijing, China, in 2011. From 2011 to 2013, he wasa Post-Doctoral Research Fellow with the Depart-ment of Electronic Engineering, Tsinghua Univer-sity, where he was an Assistant Professor from2013 to 2016 and has been an Associate Professorsince 2016. He has co-authored the book mmWave

Massive MIMO: A Paradigm for 5G (Academic Press, Elsevier, 2016).He has published over 60 IEEE journal papers and over 40 IEEE con-ference papers. He holds 16 granted patents. His current research interestsinclude massive MIMO, millimeter-wave communications, NOMA, sparsesignal processing, and machine learning for wireless communications. He hasreceived five conference Best Paper Awards at the IEEE ICC 2013, the IEEEICC 2014, the IEEE ICC 2017, the IEEE VTC 2017-Fall, and the IEEEICC 2018. He has also received the Tsinghua University Outstanding Ph.D.Graduate Award in 2011, the Beijing Excellent Doctoral Dissertation Awardin 2012, the China National Excellent Doctoral Dissertation NominationAward in 2013, the URSI Young Scientist Award in 2014, the IEEE TRANS-ACTIONS ON BROADCASTING Best Paper Award in 2015, the Second Prizeof Science and Technology Award of the China Institute of Communicationsin 2016, the Electronics Letters Best Paper Award in 2016, the IEEECOMMUNICATIONS LETTERS Exemplary Editor Award in 2017, the NationalNatural Science Foundation of China for Outstanding Young Scholars in 2017,the IEEE ComSoc Asia-Pacific Outstanding Young Researcher Award in 2017,and the IEEE ComSoc Asia-Pacific Outstanding Paper Award in 2018.He currently serves as an Editor of the IEEE TRANSACTIONS ON COM-MUNICATIONS, the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,and the IEEE COMMUNICATIONS LETTERS.

Bichai Wang (S’15) received the B.S. degree inelectronic engineering from Tsinghua University,Beijing, China, in 2015, where she is currentlypursuing the Ph.D. degree with the Department ofElectronic Engineering. Her research interests arein wireless communications, with an emphasis onnon-orthogonal multiple access, mmWave massiveMIMO, and deep learning-based wireless communi-cations. She received the Freshman Scholarship ofTsinghua University in 2011, the Academic MeritScholarships of Tsinghua University in 2012, 2013,

and 2014, respectively, the Excellent Thesis Award of Tsinghua Universityin 2015, the National Scholarship in 2016, the IEEE VTC’17 Fall Best StudentPaper Award in 2017, the IEEE TRANSACTIONS ON COMMUNICATIONSExemplary Reviewer Award in 2017, the First Prize of the 13th ChinaGraduate Electronics Design Contest in 2018, and the IEEE ComSoc Asia-Pacific Outstanding Paper Award in 2018.

Mugen Peng (M’05–SM’11) received the Ph.D.degree in communication and information systemsfrom the Beijing University of Posts and Telecom-munications (BUPT), Beijing, China, in 2005.Afterward, he joined BUPT, where he has beena Full Professor with the School of Informa-tion and Communication Engineering since 2012.He leads a Research Group focusing on wirelesstransmission and networking technologies with theKey Laboratory of Universal Wireless Commu-nications, Ministry of Education, BUPT. He has

authored/coauthored over 100 refereed IEEE journal papers and over 200 con-ference proceeding papers. His main research areas include wireless commu-nication theory, radio signal processing, and convex optimizations, with aparticular interest in cooperative communication, self-organization network-ing, heterogeneous networking, cloud communication, and Internet of Things.

Dr. Peng was a recipient of the 2018 Heinrich Hertz Prize Paper Award,the 2014 IEEE ComSoc AP Outstanding Young Researcher Award, and theBest Paper Award in IEEE WCNC 2015, WASA 2015, GameNets 2014,IEEE CIT 2014, ICCTA 2011, IC-BNMT 2010, and IET CCWMC 2009.He received the First Grade Award of the Technological Invention Awardin the Ministry of Education of China, and the First Grade Award of theTechnological Invention Award from the China Institute of Communications.He is on the Editorial/Associate Editorial Board of the IEEE Communi-cations Magazine, IEEE ACCESS, IEEE INTERNET OF THINGS JOURNAL,IET Communications, and China Communications.

Shanzhi Chen (SM’04) received the bachelor’sdegree from Xidian University in 1991 and the Ph.D.degree from the Beijing University of Posts andTelecommunications, China, in 1997. He joined theDatang Telecom Technology and Industry Group andthe China Academy of Telecommunication Tech-nology (CATT) in 1994, and has been serving asthe EVP of Research and Development since 2008.He is currently the Director of the State Key Labo-ratory of Wireless Mobile Communications, CATT,where he conducted research and standardization

on 4G TD-LTE and 5G. He has authored and co-authored four books[among them the textbook Mobility Management: Principle, Technology andApplications (Springer Press)], 17 book chapters, approximately 100 journalpapers, 50 conference papers, and over 50 patents in these areas. He hascontributed to the design, standardization, and development of 4G TD-LTEand 5G mobile communication systems. His current research interests include5G mobile communications, network architectures, vehicular communicationnetworks, and Internet of Things. He served as a member and a TPC Chair ofmany international conferences. His achievements have received multiple topawards by China central government and honors, especially the Grand Prize ofthe National Award for Scientific and Technological Progress, China, in 2016(this Grand Prize is the highest category and in some years, it leaves with nowinners due to its high standard). He is the Area Editor of the IEEE INTERNETOF THINGS, the Editor of the IEEE NETWORK, and the Guest Editor of theIEEE WIRELESS COMMUNICATIONS, the IEEE Communications Magazine,and the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY.

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Hybrid Precoding-Based Millimeter-Wave Massive …oa.ee.tsinghua.edu.cn/dailinglong/publications/paper...IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 37, NO. 1, JANUARY 2019