digital object identifier 10.1109/access.2017.2766079 ... · province under grant 2016c33036, and...

Received September 20, 2017, accepted October 18, 2017, date of publication October 24, 2017,date of current version November 14, 2017.

Digital Object Identifier 10.1109/ACCESS.2017.2766079

Massive MIMO for Full-Duplex Cellular Two-WayRelay Network: A Spectral Efficiency StudyZHAOXI FANG 1, (Member, IEEE), WEI NI2, (Senior Member, IEEE),FENG LIANG1, PENGFEI SHAO1, AND YAOHUI WU11School of Electronics and Computer, Zhejiang Wanli University, Ningbo 315100, China2Commonwealth Scientific and Industrial Research Organization, Sydney, NSW 2122, Australia

Corresponding author: Zhaoxi Fang ([email protected])

The work was supported in part by the Natural Science Foundation of China under Grant 61401400, in part by the Natural ScienceFoundation of Zhejiang Province under Grant LY17F010002 and Grant LY18F010001, in part by the public welfare project of ZhejiangProvince under Grant 2016C33036, and in part by the Natural Science Foundation of Ningbo City under Grant 2016A610225 andGrant 2017A610101.

ABSTRACT This paper presents the new analysis of the applications of massive multiple-input-multiple-output (MIMO) in full-duplex (FD) cellular two-way relay networks, and sheds valuable insights on theinteractions between massive MIMO, and relay and duplex modes. Practical scenarios are considered,where massive MIMO is deployed at the base station and the relay station. Based on generic relaymodes, namely, antenna-selection-based decode-and-forward (DF) relay and signal-space alignment basedamplify-and-forward (AF) relay, closed-form expressions for the asymptotic signal-to-interference-plus-noise ratios (SINRs) are derived. The difference between AF and DF in the FD mode is quantified, and sois that between FD and half-duplex (HD) under the two relay modes. With massive MIMO, the superiorityof DF in the FD mode is confirmed in terms of spectral efficiency. The sufficient conditions for the FDmode to outperform the HD mode are identified. The effectiveness of massive MIMO in terms of self-loopinterference cancellation and inter-user interference suppression is proved. All these insightful findings arecorroborated by simulations.

INDEX TERMS Cellular two-way relay networks, massive MIMO, full-duplex, spectral efficiency.

I. INTRODUCTIONBeing the key enabling technologies for next-generationwireless networks, full-duplex (FD) radios [1]–[8] andmassive multiple-input-multiple-output (MIMO) [9], [10]have attracted extensive attention. FD radios can double thespectral efficiency of existing half-duplex (HD) radios bytransmitting and receiving at the same time and frequency,attributing to recent advances in self-loop interference can-cellation [11], [12]. For instance, the self-loop interference,i.e., the transmit signals of a node coupled back to the receiverof the node, has been recently suppressed by 70 to 100 dBthrough analog and/or digital cancellations [13]–[15]. On theother hand, massive MIMO is able to compensate forpoor propagation conditions, facilitate implementing cel-lular networks in millimeter wave (mmWave) frequencies,and address the scarcity of communication spectrum. Thisis through the integration of large numbers (e.g., up tohundreds) of miniaturized antennas with significantlyimproved array gains [16], [17].

An important application of FD and massive MIMO istwo-way relay (TWR), which has shown great potential

to improve spectral efficiency at the edge of wireless sys-tems [18]–[20]. Particularly, a cellular two-way relay network(cTWRN) is of practical interest, where a base station (BS)exchanges data with a number of remote mobile sta-tions (MSs) outside its coverage with the assistance of atwo-way relay station (RS) [21]–[24]. The BS and RS canbe equipped with massive MIMO, allowing all the MSs toaccess the BS simultaneously and improving spectral effi-ciency [23], [24].

Extensive studies have been conducted on TWR in theHD mode, where a RS receives and forwards messagesin two separate time slots or frequency bands [19], [20].Recently, FD has been increasingly studied for relay, first forone-way relay (OWR) [25], [26] and then TWR [27], [28].In the case of OWR, only the RS works in the FDmode, while the source(s) and destination(s) operate in theHD mode [25], [26]. In the case of TWR, all of the source(s),destination(s) and the relay(s) operate in the FD mode.Amplify-and-forward (AF), decode-and-forward (DF), andcompress-and-forward (CF) have been considered inFD TWR networks. Unfortunately, excessive self-loop

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VOLUME 5, 2017

https://orcid.org/0000-0001-8298-6720

Z. Fang et al.: Massive MIMO for FD cTWRN: Spectral Efficiency Study

interference and inter-stream interference (ISI) would sub-stantially compromise the spectral efficiency [27], [28].

Lately, massive MIMO has been applied to suppress theinterference in FD relay networks [26], [27], [29]–[31].In [26], the authors maximized the energy efficiency of amulti-pair one-way FD relay network, where a FD relaywas equipped with a large number of antennas to suppressthe interference. In [27] and [31], the spectral and energyefficiencies of multi-pair FD TWR networks with massiveMIMO were studied, showing that the use of massive MIMOat the relay can help mitigating the self-loop interference.Both the spectral and energy efficiencies increase with thenumber of antennas. The conditions were identified for FDTWR to outperform its HD counterpart [31]. However, theseresults are not applicable to cTWRNs, due to distinct networkarchitectures. To the best of our knowledge, FD-cTWRNwithmassive MIMO has not yet to be studied in spite of its greatpotential in practice.

This paper presents analysis on the applications of massiveMIMO in FD-cTWRNs, and sheds valuable insights on theinteractions between massive MIMO, as well as the relayand duplex modes. Our analysis is based on generic relaymodes, namely, antenna-selection based DF relay and signal-space alignment based AF relay. Closed-form expressionsare derived for the asymptotic signal-to-interference-plus-noise ratios (SINRs) of the relay modes, as the numbers ofantennas at the BS and RS increase. The difference betweenthe relay modes is quantified in the FD mode, and so arethose between FD and HD under each of the two relay modes.Corroborated by simulations, our analysis reveals that theSINRs increase linearly to the numbers of antennas at the BSor RS, and inversely proportionally to the number of MSs.Our analysis also shows that the use of massiveMIMO allowsfor eliminating the self-loop interference. The sufficient con-ditions are identified for the DF mode (referred to as FD-DF)to outperform the AF mode (referred to as FD-AF) in termsof spectral efficiency in the FD mode. We show the supe-riority of FD-cTWRNs over HD-cTWRNs, and derive theconditions for FD relaying schemes to outperform their HDcounterparts.

The rest of the paper is organized as follows. In Section II,the system model is presented. In Section III, FD-DF andFD-AF are described and analyzed with closed-form asymp-totic spectral efficiency derived. In Section IV, the superiorityof FD-cTWRNs over their HD counterparts is analyti-cally proved. Numerical results are presented in Section V,followed by the conclusions in Section VI.Notation: Boldface fonts denote vectors or matrices; the

i-th row, the j-th column, and the (i, j)-th element of amatrix A are denoted by a(i), aj, and a(i, j), respectively;CK×M stands for the K × M complex space. (·)∗, (·)T ,(·)H and (·)† denote complex conjugate, transpose, conjugatetranspose and pseudo inverse, respectively; tr(·) denotes trace;‖ · ‖ denotes the Euclidean norm, and | · | denotes magni-tude; 0K×M is the K × M all-zero matrix; IK denotes theK × K identity matrix; x ∼ CN (x̄,6) is a circularly

symmetric complex Gaussian random vector x with mean x̄and covariance matrix 6; the notation

a.s.−→ stands for ‘‘

almost surely converge to’’; E[·] and Var[·] stand for expec-tation and variance, respectively.

II. SYSTEM MODELFig. 1 illustrates a FD-cTWRN, where there is a BS, a RS,and K MSs, all operating in the FD mode. There is no directlink between the BS and the MSs. Each MS is equippedwith a single antenna. The BS is equipped with NB antennas.The relay is equipped with NR antennas. NR � K andNB � K . The maximum transmit powers of the BS, RSand each MS are PB, PR and PM , respectively. All the BSand MSs transmit to the RS simultaneously, while the RS istransmitting previously received signals. After proper signalprocessing, the RS forwards the signals to the BS and MSsconcurrently, while the BS and MSs are transmitting newsignals to the RS.

FIGURE 1. A full-duplex cellular two-way relay network with K mobilestations.

At any time slot n, let sB(n) = [sB,1(n), . . . , sB,K (n)]T ∈CK×1 collect the symbols of the BS to MSs withE[sB(n)sHB (n)] = IK . The transmit signals of the BS are givenby

xB(n) = FBsB(n), (1)

where FB ∈ CNB×K is the beamforming matrix of the BS,satisfying the total power constraint E

[tr(FB(n)FHB (n)

)]=

PB. The transmit signal of the k-th MS is given by

xM ,k (n) =√PM sM ,k (n), (2)

where sM ,k (n) is the unit-power symbol of MS k .The received signal of the RS can be written as

yR(n) = HBRxB(n)+HMRxM (n)+HRRx̃R(n)+ zR(n), (3)

where HBR ∈ CNR×NB and HMR = [h1,R, . . . ,hK ,R] ∈CNR×K are the channel matrices from the BS and MSs to theRS, respectively;HRR ∈ CNR×NR is the self-loop interferencechannel at the relay. xM (n) =

√PM sM (n) with sM (n) =

[sM ,1(n), . . . , sM ,k (n)]T , x̃R(n) is the self-loop interference at

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the relay, and zR(n) ∼ CN (0, σ 2INR ) is the additive whiteGaussian noise (AWGN) at the RS.HBR =

√`BH̃BR with `B being the path loss from the BS

to the RS and H̃BR collecting small-scale fading coefficients.Likewise, HMR =

√`M H̃MR with `M being the path loss

from the MSs to the RS,1 and HRR =√`RLH̃RR with `RL

being the path loss of the self-loop interference channel at theRS. H̃MR and H̃RR collect small-scale fading coefficients.

With analog and/or digital cancellation [12], [13], the self-loop interference can be substantially reduced and x̃R(n) canbe modeled as an AWGN [31], i.e., x̃R(n) ∼ CN (0, σ 2RLINR ),where σ 2RL = PR/NR.At the same time slot n, the transmit signal of the RS can

be given by

xR(n) = f(yR(n− τ )

), (4)

where f (x) is a relay signal processing function to be speci-fied later, and τ is the signal processing delay at the relay (innumbers of time slots).

We consider two relay modes, namely, DF and AF.In FD-DF, the RS decodes and then recodes the received sig-nals. In FD-AF, the FD RS delays and forwards the receivedsignals without decoding.

The received signals at the BS and MSs are respectivelygiven by

yB(n) = HRBxR(n)+HBBx̃B(n)+ zB(n); (5)

and

yM ,k (n) = hTR,kxR(n)+ hk,k x̃M ,k (n)

+

∑i 6=k

hi,kxM ,i(n)+ zM ,k (n); (6)

where HRB ∈ CNB×NR is the channel matrix from the RSto the BS; hR,k ∈ CNR×1 is the channel vector from theRS to MS k; HBB =

√`BLH̃BB and hk,k =

√`k,k h̃k,k

are the self-loop interference channels of the BS and MS k ,respectively, and hi,k =

√`i,k h̃i,k is the channel coefficient

from MS i to MS k (i 6= k). zB(n) ∼ CN (0, σ 2INB ) andzM ,k (n) ∼ CN (0, σ 2) are the AWGN at the BS and MSk , respectively. x̃B(n) is self-loop interference at the BS andx̃M ,k (n) ∼ CN (0, σ 2ML) is the self-loop interference at MS kwith σ 2ML = PM . Note that HBB and x̃B(n) depends on thespecific relaying scheme, and will be given in the following.

III. ANALYSIS OF MASSIVE MIMO ENABLED FD-cTWRNsIn this section, we individually study and compare the spec-tral efficiency of FD-DF and FD-AF with massive MIMOenabled at the BS and RS. Asymptotic SINRs and spectralefficiencies are inferred in closed-formwith critical thresholdidentified for FD-DF to outperform FD-AF.

1For presentation clarity, we assumed that the path losses are the samefor all the MSs. However, the results in this paper can be extended toFD-cTWRNs with different path losses between the MSs and the RS.

A. FD-DFWith a large antenna array, the RS has enough degrees of free-dom to suppress the inter-stream interference and to detectthe messages from the BS and the MSs. For the sake ofpracticality, this work adopts antenna-selection at the BS,i.e., K of the NB antennas at the BS are selected to send Kmessages destined for theK MSs.2 We assume that the firstKantennas are selected, and the transmit beamforming matrixat the BS can therefore be given by

FDFB = [√PB/K IK ,0K×(NB−K )]

T . (7)

As will be discussed later (in Proposition 1), the spectralefficiency of FD-DF with such simple antenna selection isindependent of small-scale fading in the case that NB → ∞and NR→∞.

LetH′

BR denote the firstK rows ofHBR. By substituting (1)and (7) into (3), the received signal at the RS can be writtenas

yR(n) =√PB/KH

′

BRsB(n)+√PMHMRsM (n)

+HRRx̃R(n)+ zR(n)

= HSRsBM (n)+HRRx̃R(n)+ zR(n), (8)

where HSR = [H′

BR,HMR] ∈ CNR×2K , and sBM (n) =[√PB/K sTB (n),

√PM sTM (n)]

T∈ C2K×1. Here, HSR can be

further rewritten as

HSR = H̃SR3SR, (9)

where H̃SR ∈ CNR×2K collects small-scale fading coeffi-cients, and 3SR = diag(

√`BIK ,

√`M IK ) ∈ C2K×2K collects

the path losses from the BS and MSs to the RS.Consider zero-forcing beamforming (ZFBF) at the RS to

receive yR(n). We have

ỹR(n) = WHRRyR(n)

= sBM (n)+WHRR (HRRx̃R(n)+ zR(n)) . (10)

whereWHRR = H†SR ∈ C

2K×NR is the beamforming matrix.As the result of ZFBF, the ISI is completely removed and

the RS is able to detect the messages form the BS and theMSs separately. The received SINR of sB,k (n) at the RS, i.e.,the signals from the BS towards MS k , can be given by

γ FD-DFBR,k =PB

K(δR,k + Var

[wHRR,kzR(n)

]) ,k = 1, · · · ,K , (11)

where wRR,k is the k-th column of WRR, and δR,k =Var

[wHRR,kHRRx̃R(n)

]is the power of the self-loop interfer-

ence after ZFBF.

2Aswill be shown in SectionV, the performance gap between the proposedsimple antenna-selection based FD-DF scheme and the cut-set bound issmall.

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Likewise, the received SINR ofMS k’s signal at the RS canbe given by

γ FD-DFMR,k =PM

δR,K+k + Var[wHRR,K+kzR(n)

] ,k = 1, · · · ,K , (12)

where δR,K+k = Var[wHRR,K+kHRRx̃R(n)

]is the power of the

self-loop interference after ZFBF.With a large number of antennas at the RS, we have

δR,k = σ2RLE

[wHRR,kHRRH

HRRwRR,k

]= `RLNRσ 2RLE

[‖wRR,k‖2

]=

`RLPR(NR − K )`B

, (13)

which is due to the fact that 1NRHRRHHRR ' `RLINR for

NR→∞. Likewise, for NR→∞, we have

δR,K+k =`RLPR

(NR − K )`M. (14)

Note that (13) and (14) reveal that δR,k → 0 andδR,K+k → 0, as NR → +∞; i.e., the self-loop interferencecan be cancelledwhen the RS is equippedwith a large numberof antennas.

Now, based on (10), the RS can estimate the symbolsfrom the BS and MSs as ŝB,k (n) and ŝM ,k (n), respectively,k = 1, . . . ,K . Then, it recodes the signals into sR(n) =[sR,1(n), . . . , sR,K (n)]T , and forwards them using ZFBF tosuppress ISI among the MSs, where sR,k (n) = ŝB,k (n) ⊕ŝM ,k (n), k = 1, . . . ,K . The transmit signal of the RS is givenby

xR(n) = αDFR H†RM sR(n− τ ), (15)

where αDFR is an adjustable coefficient for meeting the trans-mit power constraint of the RS, and can be given by

αDFR =

√√√√ PRE[tr(H†RMH

†HRM

)] . (16)The received signals at the BS and MS k are respectively

given by

yB(n) = αDFR HRBH

†RM sR(n− τ )+HBBx̃B(n)+ zB(n);

(17)

and

yM ,k (n) = αDFR sR(n− τ )+ hk,k x̃M ,k (n)

+

∑i 6=k

hi,kxM ,i(n)+ zM ,k (n). (18)

The second term on the right-hand side (RHS) of (17) is theself-loop interference at the BS, where HBB ∈ CNB×K andx̃B(n) ∼ CN (0, σ 2BLIK ) denotes the self-loop channel andthe self-loop interference with σ 2BL = PB/K , respectively.

The second and third terms on the RHS of (18) are the self-loop interference and ISI at MS k , respectively.

Consider ZFBF for the reception at the BS. The beamform-

ing matrix is WHB =(HRBH

†RM

)†. From (17), the receive

SINR of MS k’s signal at the BS can be given by

γ FD-DFRB,k =(αDFR )

2

δB,k + Var[wHB,kzB(n)

] , (19)where wB,k is the k-th column of WB, and δB,k =Var

[wHB,kHBBx̃B(n)

]is the power of the self-loop interfer-

ence after ZFBF. With a large number of receive antennas atthe BS, i.e., NB→∞, δB,k can be written as

δB,k = σ2BLE

[wHB,kHBBH

HBBwB,k

]=`M`BLNRPB

`BNB. (20)

From (20), we have

δB,k

(αDFR )2=K`BLPB`BNB

→ 0, as NB→+∞. (21)

In other words, the self-loop interference at the BS becomesnegligible, and a large number of antennas in massive MIMOis able to eliminate the self-loop interference at the BS.

From (18), the receive SINR at MS k can be given by

γ FD-DFRM ,k =(αDFR )

2

|hk,k |2σ 2ML + PM∑

i6=k |hi,k |2 + σ 2

. (22)

where the ISI and self-loop interference cannot be mitigated,since each MS has only a single antenna.

By combining (11), (12), (19) and (22), the achievablespectral efficiency of FD-DF can be given by

RFD-DFsum =K∑k=1

[C(min(γ FD-DFBR,k , γFD-DFRM ,k ))

+ C(min(γ FD-DFMR,k , γFD-DFRB,k ))], (23)

where C(x) = log2(1+ x).Proposition 1: In the case that NB → +∞ and NR →+∞, the receive SINRs of FD-DF almost surely converge to

γ FD-DFBR,k

NR

a.s.−→

`BPBKσ 2R; (24a)

γ FD-DFMR,k

NR

a.s.−→

`MPMσ 2R; (24b)

γ FD-DFRB,k

NB

a.s.−→

`BPRKσ 2B; (24c)

γ FD-DFRM ,k

NR

a.s.−→

`MPRKσ 2k

; (24d)

where k = 1, . . . ,K , σ 2B = σ2+ `BLPB; σ 2R = σ

2+ `RLPR;

and σ 2k = σ2+ PM

∑Ki=1 `i,k ,∀k .

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Proof: This proposition can be proved using the lawof large numbers and the assumption of independent fadingchannels. For details, see Appendix A.

Proposition 1 reveals that the small-scale fading does notaffect the spectral efficiency of FD-DF if both the BS andRS are equipped with massive MIMO. Despite the existenceof self-loop interference and ISI, the receive SINRs at theRS and MSs increase with NR, and the receive SINRs at theBS increases with NB. To this end, the spectral efficiency ofFD-DF improves with the numbers of antennas at the BSand RS in cTWRNs. This confirms the effectiveness of thesimple antenna selection described at the beginning of thissection.

B. FD-AFTo allow the RS to forward signals without decoding, signalspace alignment based linear precoding [24] is considered atthe BS to align the received signals from the BS and MSsat the RS. The beamforming matrix at the BS can be givenby

FAFB = αB(H†MRHBR

)†, (25)

where αB is an adjustable coefficient to guarantee the powerconstraint at the BS, i.e., E

[tr(FAFB

(FAB)H)]

= PB.Without decoding, the RS retransmits the received signal:

xR(n) = αAFR H†RMH

†MRyR(n− τ ), (26)

where αAFR is an adjustable coefficient to guarantee the powerconstraint at the RS.

From (5), (25) and (26), the received signals at the BS andMSs can be given respectively by

yB(n)

= αAFR HRBH†RM

[αBsB(n− τ )+

√PM sM (n− τ )

]+αAFR HRBH

†RM

[H†MR (HRRx̃R(n− τ )+ zR(n− τ ))

]+HBBx̃B(n)+ zB(n); (27)

and

yM ,k (n) = αAFR

[αBsB(n− τ )+

√PM sM (n− τ )

]+αAFR

[vHRR,k (HRRx̃R(n− τ )+ zR(n− τ ))

]+ hk,k x̃M ,k (n)+

∑i 6=k

hi,kxM ,i(n)+ zM ,k (n); (28)

where vRR,k is the k-th column of(H†MR

)H, HBB ∈ CNB×NB

denotes the self-loop channel, and x̃B(n) ∼ CN (0, σ 2BLINB )denotes self-loop interference with σ 2BL = PB/NB, respec-tively. The term involving sB(n − τ ) in (27) is the self-interference at the BS, which is known to the BS and canbe self-canceled prior to signal detection at the BS. Aftercanceling the self-interference, the BS can employ ZFBF, i.e.,

WHB =(HRBH

†RM

)†, to detect the signals from the MSs.

From (27), the receive SINR ofMS k’s signal at the BS canbe given by

γ FD-AFB,k =(αAFR )

2PM

(αAFR )2(µR,k + ρR,k )+ δB,k + Var

[wHB,kzB(n)

] ,(29)

where µR,k = Var[vHRR,kHRRx̃R(n− τ )

]is the power of the

self-loop interference propagated from the RS, and ρR,k =Var

[vHRR,kzR(n− τ )

]is the power of the noise propagated

from the RS.From (28), after canceling the self-interference at MS k ,

the receive SINR is given by

γ FD-AFM ,k =(αAFR )

2α2B

(αAFR )2(µR,k + ρR,k )+ PM

∑Ki=1 |hi,k |

2 + σ 2.

(30)

By combining (29) and (30), the achievable spectral effi-ciency of FD-AF can finally be given by

RFD-AFsum =K∑k=1

[C(γ FD-AFB,k )+ C(γFD-AFM ,k )]. (31)

Proposition 2: In the case of NR→∞ and NB→∞, thereceive SINRs at the BS and MSs of FD-AF almost surelyconverge to

γ FD-AFB,k

NR

a.s.−→

α`M`BPRPMα`BPRσ 2R + (α`BPB + `MKPM )σ

2B

; (32a)

γ FD-AFM ,k

NR

a.s.−→

α`M`BPBPRK[`MPRσ 2R + (α`BPB + `MKPM )σ

2k

] ; (32b)where k = 1, . . . ,K , and α specifies the BS-to-RS antennaratio, i.e., α = NB/NR.

Proof: See Appendix B.From Proposition 2, we see that small-scale fading can be

suppressed in the presence of massiveMIMO, and the receiveSINR increases with the numbers of antennas as it does inFD-DF (as revealed in Proposition 1).

C. COMPARISON BETWEEN FD-DF AND FD-AFIn the following, a comparison study is carried out betweenFD-DF and FD-AF, and critical conditions are identified forFD-DF to outperform FD-AF in terms of spectral efficiency.Proposition 3: In the case that NB → ∞ and NR →∞, FD-DF is able to achieve higher spectral efficiency thanFD-AF if the following condition holds:

PB ≥`Mσ

2

`Bσ2min

PR, (33)

where σ 2min = mink=1,··· ,K {σ2k }.

Proof: We can start with the downlink transmission, i.e.,from the BS to the MSs. If (33) holds, PB ≥

`Mσ2

`Bσ2kPR,∀k .

Then, we have γ FD-DFBR,k ≥ γFD-DFRM ,k ,∀k , i.e., the bottleneck of

the transmission of FD-DF is the hop from the RS to theMSs.

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Therefore, in the downlink, the achievable spectral efficiencyis given by

RFD-DFsum,DL =K∑k=1

C(min(γ FD-DFBR,k , γFD-DFRM ,k ))

=

K∑k=1

C(γ FD-DFRM ,k ). (34)

For FD-AF, it is easy to show that the downlink SINRsγ FD-AFM ,k < γ

FD-DFRM ,k ,∀k . Hence, FD-DF achieves a higher

spectral efficiency than FD-AF in the downlink of cTWRNs.Proceed with the uplink. We can show that γ FD-AFB,k <

γ FD-DFMR,k ,∀k , and γFD-AFB,k < γ

FD-DFRB,k ,∀k , always hold. As a

result, we can conclude that FD-DF bypasses FD-AF as longas (33) withstands.It is worth mentioning that in practical cellular networks,

the transmit power of the BS is typically much higher thanthat of the RS. Moreover, the RS is generally placed witha line-of-sight (LoS) towards the BS. For these reasons,(33) can be typically satisfied, and FD-DF can outperformFD-AF in most practical cases. On the other hand, FD-DF hasa higher complexity and cost than FD-AF, since no decodingor recoding operation is involved in FD-AF.

D. POWER SCALING CASEWe proceed to show the power savings at the MSs offeredby massive MIMO in FD-cTWRNs. Particularly, the transmitpower of the MSs can decrease inversely proportionally withthe spectral efficiency unaffected, as the number of antennasincreases at the RS.Proposition 4: Consider a power scaling case that PB and

PR are fixed, while the transmit power of each MS PM scaleswith the number of RS antennas as PM = P0M/NR, where P

0M

is a constant. In the case that NB → +∞ and NR → +∞,the receive SINRs of FD-DF almost surely converge to

γ FD-DFBR,k

NR

a.s.−→

`BPBKσ 2R; (35a)

γ FD-DFMR,ka.s.−→

`MP0Mσ 2R; (35b)

γ FD-DFRB,k

NB

a.s.−→

`BPRKσ 2B; (35c)

γ FD-DFRM ,k

NR

a.s.−→

`MPRKσ 2

. (35d)

The receive SINRs of FD-AF at the BS andMSs almost surelyconverge to

γ FD-AFB,ka.s.−→

`MPRP0MPRσ 2R + PBσ

2B

; (36a)

γ FD-AFM ,k

NR

a.s.−→

α`M`BPBPRK[`MPRσ 2R + α`BPBσ

2] . (36b)

From (35b) and (36a), we see that the receive SINRsγ FD-DFMR,k and γ

FD-AFB,k , k = 1, . . . ,K , only depend on P

0M ,

not on NR. In other words, the reduction of PM can becompensated for by increasing NR inversely proportionally,while the receive SINRs at the RS, or the spectral efficiency,remain unaffected in the uplink for both FD-DF and FD-AF.This suggests that with the numbers of antennas at the BS andRS approaching infinite, the transmit power of theMSs can bemade arbitrary small, while preserving the spectral efficiencyin the uplink.

IV. COMPARISON BETWEEN HD AND FD cTWRNsIn this section, comparison studies are carried out betweenFD-cTWRNs and their HD counterparts which necessi-tate two successive time slots to accomplish a cycle ofTWR [21], [22]. The superiority of the FD mode to the HDmode is proved in terms of spectral efficiency.

A. FD-DF VERSUS HD-DFConsider HD-DF in cTWRNs. The achievable spectral effi-ciency is given by [23]

RHD-DFsum =K2log2

[1+

min (`BNRPB, `MNRPR)Kσ 2

]+K2log2

[1+

min (KNR`MPM , `BNBPR)Kσ 2

], (37)

where the coefficient 1/2 is due to the use of the HD mode.From (23), (24) and (37), we conclude that:Proposition 5: FD-DF can always outperform HD-DF in

cTWRNs in the case that NB→∞ and NR→∞.Proof: Let σ 2k,max = max{σ

2R, σ

2k } and σ

2DL,max =

maxk=1,··· ,K {σ 2k,max}. In the downlink, the achievable spectralefficiency of FD-DF is lower bounded by

RFD-DFsum,DL =K∑k=1

C(min(γBR,k , γRM ,k ))

≥ K log2

[min (`BNRPB, `MNRPR)

Kσ 2DL,max

]. (38)

Likewise, let σ 2UL,max = max{σ2R, σ

2B}. In the uplink, the

achievable spectral efficiency of FD-DF is lower bounded by

RFD-DFsum,UL =K∑k=1

C(min(γMR,k , γRB,k ))

≥ K log2

[min (KNR`MPM , `BNBPR)

Kσ 2UL,max

]. (39)

From (37), (38) and (39), we see that the gain of FD-DFover HD-DF in spectral efficiency is lower bounded by

1RDFsum = RFD-DFsum − R

HD-DFsum

≥ RFD-DF,LBsum,DL + RFD-DF,LBsum,UL − R

HD-DFsum

=K2log2

[σ 2min (`BNRPB, `MNRPR)

Kσ 4DL,max

]

+K2log2

[σ 2min (KNR`MPM , `BNBPR)

Kσ 4UL,max

]. (40)

VOLUME 5, 2017 23293


which is positive, i.e., 1RDFsum > 0, if NB → +∞ andNR→+∞. Here, R

FD−DF,LBsum,DL and R

FD−DF,LBsum,UL are the RHSs

of the inequalities in (38) and (39), respectively.The above result shows that FD-DF can always achieve a

higher spectral efficiency than HD-DF even if the self-loopinterference cannot be perfectly canceled, in the presence ofmassive MIMO at the BS and RS.

From (23), (24) and (37), we can also show that:Proposition 6: FD-DF achieves a higher spectral effi-

ciency than HD-DF when the number of antennas at the BSand the RS satisfies:

NR ≥ max

{Kσ 4R`BPBσ 2

,σ 4R

`MPMσ 2,max

k

Kσ 4k`MPRσ 2

},

NB ≥Kσ 4B`BPRσ 2

. (41)

B. FD-AF VERSUS HD-AFIn the case that NB → ∞ and NR → ∞, the achievablespectral efficiency of HD-AF is given by [24]

RHD-AFsum =12

K∑k=1

[C(γHD-AFB,k )+ C(γHD-AFM ,k )], (42)

where the coefficient 1/2 is due to the use of the HD mode,and the receive SINRs are given by

γHD-AFB,k

NR

a.s.−→

α`M`BPRPM(α`B(PR + PB)+ `MKPM )σ 2

,

γHD-AFM ,k

NR

a.s.−→

α`M`BPBPRK (`MPR + α`BPB + `MKPM )σ 2

, (43)

k = 1, . . . ,K .From (31), (32), (42) and (43), the gain of FD-AF over

HD-AF is lower bounded by

1RAFsum= RFD-AFsum − R

HD-AFsum

≥K2log2

[ασ 2NR`M`BPBPR

K (`MPR + α`BPB + `MKPM ) σ 4DL,max

]

+K2log2

[ασ 2NR`M`BPRPM

(α`BPR + α`BPB + `MKPM )σ 4UL,max

]. (44)

where we can show that 1RAFsum > 0 if NB → +∞ andNR→+∞. As a result, we can conclude that:Proposition 7: FD-AF can always outperform HD-AF in

cTWRNs in the case that NB→∞ and NR→∞.From (32) and (43), we can also show that:Proposition 8: FD-AF achieves a higher spectral effi-

ciency than HD-AF when the number of antennas at the BSand the RS satisfies:

NR ≥

(PRσ 2R + PBσ

2B

)2`MPRPM (PB + PR)σ 2

,

NB ≥KNR`MPRσ 4DL,max

`BPB(NR`MPRσ 2 − Kσ 4DL,max

) . (45)

V. NUMERICAL RESULTSIn the simulations, the path losses are modeled as `B = d

−3BR ,

`M = d−3MR, and `i,k = d

−3i,k ,∀i, k(i 6= k), where dBR is the

distance between the BS and RS, dMR is the distance betweenthe RS and MSs, and di,k is the distance between MS i andMS k . All the small-scale fading coefficients are indepen-dently drawn from a circularly symmetric complex Gaussiandistribution with zero mean and unit variance. The transmitpower budgets of the BS, RS and the MSs are PB = 30 dBm,PR = 20 dBm, and PM = 0 dBm, respectively. For the self-loop interference channel, we introduce a residual self-loopinterference level factor ξ , which defines the ratio of the resid-ual self-loop interference power to the noise power at eachnode, i.e., ξ = `RLσ 2RL/σ

2= `BLσ

2BL/σ

2= `MLσ

2ML/σ

2.Unless otherwise specified, we assume that there are K = 8MSs; dBR = dMR = 50m, and di,k = 30m, ∀i, k(i 6= k),respectively; the noise variance σ 2 = −50 dBm; and residualself-loop interference level factor ξ = 0 dB. We also plotthe results of cut-set bound and a FD relaying scheme withmaximum ratio combining and maximum ratio transmission(MRC/MRT) [31] for performance comparison.

Fig. 2 shows the achievable spectral efficiency of theproposed FD-DF and FD-AF under different numbers ofantennas at the RS, i.e., NR. The number of antennas at theBS is fixed to be NB = 200. We also plot the spectralefficiency of HD-DF and HD-AF for comparison purpose.It is observed that the analytical results for FD-DF and FD-AF schemes asymptotically approach the simulation results.The FD-DF scheme is able to closely approaching the cut-setupper bound. For instance, the spectral efficiency gap is lessthan 3 bps/Hz when both the BS and the RS are equippedwith 200 antennas. It can also be seen that despite theexistence of residual self-loop interference, both FD-DF andFD-AF outperform their HD counterparts when the numbersof antennas are sufficient large, and their gains grow withNR. For instance, FD-DF can achieve 70% higher spectral

FIGURE 2. Spectral efficiency of FD-DF and FD-AF with K = 8 MSs. The BSis equipped with NB = 200 antennas.

23294 VOLUME 5, 2017


efficiency than HD-DF, when the RS is equipped withmore than 100 antennas. Fig. 2 also confirms that FD-DFoutperforms FD-AF. This is due to the fact that self-loopinterference and noise at the RS propagate to the BS andMSsin FD-AF.

In Fig. 3, the spectral efficiency of FD-cTWRNs underdifferent number of MSs is plotted, where NB = 200 andNR = 100. The other simulation parameters are the same asthose in Fig. 2. As the number of MSs increases, each MSsuffers from growing inter-user interference. Nevertheless,Fig. 3 demonstrates that the large antenna array is able tocombat the growing ISI and improve the spectral efficiencyof both FD-DF and FD-AF. It can also be seen that theperformance gap between the proposed FD-DF scheme andthe FD-MRC/MRT scheme enlarges as the number of usersincreases. This is due to the fact that MRC/MRT based linearprocessing suffers from ISI at all nodes, while the ISI iscompletely removed with zero-forcing receiving/precodingin FD-DF scheme.

FIGURE 3. Spectral efficiency of FD-DF and FD-AF under different numberof MSs. NB = 200 and NR = 100.

Fig. 4 investigates the impact of relay location on thespectral efficiency of the proposed two schemes. Fromthe figure, we see that a higher spectral efficiency canbe achieved for these schemes when the relay is close tothe MSs. This is due to the fact that with large antennaarrays, the system throughput is bottlenecked by the RS-MS links in the FD-cTWRNs. It can be also seen that thegap between FD-DF and the cut-set bound is small in mostcases.

Fig. 5 shows the impact of the residual self-loop interfer-ence on the spectral efficiency of FD-DF and FD-AF, whereK = 8, and the other systems parameters are the same asthose in Fig. 2. We see that in the case that the residual self-loop interference is weak, the spectral efficiencies of FD-DFand FD-AF can bypass those of HD-DF and HD-AF, respec-tively. In the case that the residual self-loop interference isstrong, i.e., ξ ≥ 9 dB, it is possible that FD-DF and FD-AF

FIGURE 4. The impact of relay location on the spectral efficiency of FD-DFand FD-AF, NB = 200 and NR = 100.

FIGURE 5. Spectral efficiency of FD-DF and FD-AF under different levelsof residual self-loop interference, NB = 200 and NR = 100.

perform worse than their respective HD counterparts, for agiven pair of NB and NR. Nonetheless, it is noted that onecan increase NR and/or NB to improve the robustness ofFD-cTWRNs against self-loop interference. As long as thenumbers of antennas at the BS and RS are sufficient large,the FD schemes is superior to their HD counterparts in termsof spectral efficiency.

Finally, Figs. 6 and 7 investigate the spectral efficiency ofthe two FD schemes in both the downlink and uplink, wherepower scaling is taken into account. Particularly, the transmitpower of each MS is set to be inversely proportional to thenumber of antennas at the RS, i.e., PM = 1 mW/NR, whilethe transmit powers of the BS and RS are fixed to be 30 dBmand 20 dBm, respectively. From the figures, we see that theachievable spectral efficiency in the downlink increases as thenumber of antennas increases at the RS. In contrast, the uplinkspectral efficiency flats out and converges for both FD-DFand FD-AF. These results suggest that with FD and massive

VOLUME 5, 2017 23295


FIGURE 6. Downlink spectral efficiency of FD-DF and FD-AF under powerscaling. The BS is equipped with NB = 200 antennas.

FIGURE 7. Uplink spectral efficiency of FD-DF and FD-AF under powerscaling. The BS is equipped with NB = 200 antennas.

MIMO, the transmit power of the MSs can be substantiallyreduced, while a prescribed data rate can be preserved, asrevealed in Proposition 4.

VI. CONCLUSIONSIn this paper, we analyzed the impact of FD and mas-sive MIMO on the spectral efficiency of cTWRNs. Closed-from expressions were derived as the number of antennasbecome large. It was shown that massive MIMO is ableto suppress self-loop interference and small-scaling fading,thereby improving the spectral efficiency of cTWRNs. Wealso proved that FD-cTWRNs can always outperform theirHD counterparts in the presence of massive MIMO at theBS and RS. In our future work, we will extend these resultsto the case where channel state information is imperfectat both the BS and RS. The proposed FD-DF and FD-AFrelaying protocols can also be applied to energy-harvestingnetworks [33]–[35].

APPENDIX APROOF OF PROPOSITION 1First, given the receive SINR γBR,k , the variance of the noisewHRR,kzR in (11) can be given by

Var[wHRR,kzR

]= σ 2E[‖wRR,k‖2]

= σ 2E[(

(HHSRHSR)−1)kk

]=

σ 2

K`BE[tr((H̃

HSRH̃SR)

−1)]

=σ 2

(NR − K )`B, (46)

where k = 1, . . . ,K , and the identity E[tr(X−1)

]=

MN−M

in the case that X is a M × M central Wishart matrix withN degrees-of-freedom [32], are used in the last equality.Substituting (13) and (46) into (11), we achieve (24a).

Likewise, the variance of the noise in (12) can be given by

Var[wHRR,K+kzR(n)

]=

σ 2

(NR − K )`M, k = 1, . . . ,K . (47)

Substituting (14) and (47) into (12), we obtain (24b).Next, consider the receive SINRs at the BS. With large

antenna arrays at the BS and RS, from (16), αDFR can bedetermined by [24]

αDFR =

√√√√ PRK`ME

{tr[(HRMHHRM

)−1]}=

√(NR − K )`MPR

K. (48)

For the receive SINRs at the BS, the variance of the noisewHB,kzB(n) in (19) can be given by

Var[wHB,kzB(n)

]= σ 2E

[‖wB,k‖2

]= σ 2E

{[((HRBH

†RM

)H (HRBH

†RM

))−1]k,k

}

=`MNRσ 2

`BNB. (49)

Substituting (48), (49) and (20) into (19), we achieve (24c).For the receive SINRs at the MSs, in the case that there are

a large number of MSs, we have

|hk,k |2σ 2ML + PM∑i6=k

|hi,k |2 ' PMK∑i=1

`i,k . (50)

Finally, we can obtain (24d) by substituting (48) and (50)into (22).

23296 VOLUME 5, 2017


APPENDIX BPROOF OF PROPOSITION 2With large antenna arrays at the BS and RS, from (25), αB canbe determined by

αB =

√√√√√√PB

E

{tr

[(H†MRHBR

)† ((H†MRHBR

)†)H]}

=

√`BNBPB`MKNR

. (51)

From (3) and (26), αAFR can be given by

αAFR =

√√√√ PR(α2B + PM +11 +12)E

{tr[H†RMH

†HRM

]} .(52)

where

11 = σ2E{tr[H†MRH

†HMR

]}, (53)

and

12 = σ2RLE

{tr[H†MRHRRH

HRRH

†HMR

]}(54)

are the powers of the noise and self-loop interference afterZFBF, respectively.

Given a large number of antennas at the RS, we have

11 = σ2E{tr(H†MRH

†HMR

)}=

KNR − K

`−1M σ2, (55)

which becomes negligible (11→ 0 if NR→+∞).Similarly, we have

12 = σ2RL`RLPRE

{tr(H†MRH

†HMR

)}=

KNR − K

`−1M `RLPR, (56)

which can also be negligible when NR→+∞.Then, αAFR in (52) can be approximated by

αAFR '

√√√√ PR(α2B + PM )E

{tr[H†RMH

†HRM

]}=

√(NR − K )`MPRK (α2B + PM )

. (57)

For the receive SINR at MS k , the variance of the noisein (30) can be given by

ρR,k = σ2E[(

(HHMRHMR)−1)kk

]=

σ 2

(NR − K )`M. (58)

The variance of the self-loop interference at MS k can begiven by

µR,k = `RLPRE[(

(HHMRHMR)−1)kk

]=

`RLPR(NR − K )`M

. (59)

Substituting (51) and (57)-(59) into (30), we obtain (32b).For the receive SINRs at the BS, the variance of the noise

wHB,kHBBx̃B(n) in (29) can be given by

σ̃ 2B,k = σ2BLE

[wHB,kHBBH

HBBwB,k

]= σ 2BLNB`BLE

[‖wB,k‖2

]=`MNR`BLPB

`BNB. (60)

Substituting(49), (51), (57) and (60) into (29), we can finallyobtain (32a).

REFERENCES[1] J. Choi, M. Jain, K. Srinivasan, P. Levis, and S. Katti, ‘‘Achieving

single channel, full duplex wireless communication,’’ in Proc. Mobicom,New York, NY, USA, Sep. 2010, pp. 1–12.

[2] D. Bharadia, E. McMilin, and S. Katti, ‘‘Full duplex radios,’’ in Proc.ACM SIGCOMM, Hong Kong, Aug. 2013, pp. 375–386.

[3] D. Kim, H. Lee, and D. Hong, ‘‘A survey of in-band full-duplextransmission: From the perspective of PHY and MAC layers,’’ IEEECommun. Surveys Tuts., vol. 17, no. 4, pp. 2017–2046, 4th Quart., 2015.

[4] G. Liu, F. R. Yu, H. Ji, V. C. M. Leung, and X. Li, ‘‘In-bandfull-duplex relaying: A survey, research issues and challenges,’’ IEEECommun. Surveys Tuts., vol. 17, no. 2, pp. 500–524, 2nd Quart., 2015.

[5] Z. Zhang, K. Long, A. V. Vasilakos, and L. Hanzo, ‘‘Full-duplex wirelesscommunications: Challenges, solutions, and future research directions,’’Proc. IEEE, vol. 104, no. 7, pp. 1369–1409, Jul. 2016.

[6] T.-X. Zheng, H.-M. Wang, Q. Yang, and M. H. Lee, ‘‘Safeguardingdecentralized wireless networks using full-duplex jamming receivers,’’IEEE Trans. Wireless Commun., vol. 16, no. 1, pp. 278–292, Jan. 2017.

[7] Q. Cui, Y. Zhang, W. Ni, M. Valkama, and R. Jantti, ‘‘Energy efficiencymaximization of full-duplex two-way relay with non-ideal poweramplifiers and non-negligible circuit power,’’ IEEE Trans. WirelessCommun., vol. 16, no. 9, pp. 6264–6278, Sep. 2017.

[8] Q. Cui, T. Yuan, and W. Ni, ‘‘Energy-efficient two-way relaying undernon-ideal power amplifiers,’’ IEEE Trans. Veh. Technol., vol. 66, no. 2,pp. 1257–1270, Feb. 2017.

[9] T. L. Marzetta, ‘‘Noncooperative cellular wireless with unlimited numbersof base station antennas,’’ IEEE Trans. Wireless Commun., vol. 9, no. 11,pp. 3590–3600, Nov. 2010.

[10] H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, ‘‘Energy and spectralefficiency of very large multiuser MIMO systems,’’ IEEE Trans.Commun., vol. 61, no. 4, pp. 1436–1449, Apr. 2013.

[11] T. Riihonen, S. Werner, and R. Wichman, ‘‘Mitigation of loopback self-interference in full-duplex MIMO relays,’’ IEEE Trans. Signal Process.,vol. 59, no. 12, pp. 5983–5993, Dec. 2011.

[12] E. Ahmed and A. M. Eltawil, ‘‘All-digital self-interference cancellationtechnique for full-duplex systems,’’ IEEE Trans. Wireless Commun.,vol. 14, no. 7, pp. 3519–3532, Jul. 2014.

[13] M. Heino et al., ‘‘Recent advances in antenna design and interferencecancellation algorithms for in-band full duplex relays,’’ IEEE Commun.Mag., vol. 53, no. 5, pp. 91–101, May 2015.

[14] X. Zhang, W. Cheng, and H. Zhang, ‘‘Full-duplex transmission in PHYand MAC layers for 5G mobile wireless networks,’’ IEEE WirelessCommun., vol. 22, no. 5, pp. 112–121, May 2015.

[15] E. Hossain and M. Hasan, ‘‘5G cellular: Key enabling technologiesand research challenges,’’ IEEE Instrum. Meas. Mag., vol. 18, no. 3,pp. 11–21, Jun. 2015.

[16] F. Rusek et al., ‘‘Scaling up MIMO: Opportunities and challenges withvery large arrays,’’ IEEE Signal Process. Mag., vol. 30, no. 1, pp. 40–46,Jan. 2013.

VOLUME 5, 2017 23297


[17] E. G. Larsson, O. Edfors, F. Tufvesson, and T. L. Marzetta, ‘‘MassiveMIMO for next generation wireless systems,’’ IEEE Commun. Mag.,vol. 52, no. 2, pp. 186–195, Feb. 2014.

[18] B. Rankov and A. Wittneben, ‘‘Spectral efficient protocols for half-duplexfading relay channels,’’ IEEE J. Sel. Areas Commun., vol. 25, no. 2,pp. 379–389, Feb. 2007.

[19] H. J. Yang, J. Chun, and A. Paulraj, ‘‘Asymptotic capacity of the separatedMIMO two-way relay channel,’’ IEEE Trans. Inf. Theory, vol. 57, no. 11,pp. 7542–7554, Nov. 2011.

[20] X. Yuan, T. Yang, and I. B. Collings, ‘‘Multiple-input multiple-outputtwo-way relaying: A space-division approach,’’ IEEE Trans. Inf. Theory,vol. 59, no. 10, pp. 6421–6440, Oct. 2013.

[21] H. J. Yang, Y. Choi, N. Lee, and A. Paulraj, ‘‘Achievable sum-rate of MU-MIMO cellular two-way relay channels: Lattice code-aided linear precod-ing,’’ IEEE J. Sel. Areas Commun., vol. 3, no. 8, pp. 1304–1318, Sep. 2012.

[22] Z. Fang, X. Yuan, and X. Wang, ‘‘Towards the asymptotic sum capacity ofthe MIMO cellular two-way relay channel,’’ IEEE Trans. Signal Process.,vol. 62, no. 16, pp. 4039–4051, Aug. 2014.

[23] Z. Fang, F. Liang, J. Li, L. Jin, and Y. Liu, ‘‘Multiuser two-way relayingwith large-scale antenna arrays and energy harvesting,’’ Wireless Pers.Commun., vol. 95, no. 2, pp. 1299–1315, Jul. 2017.

[24] Z. Fang, X. Yuan, X. Wang, and C. Li, ‘‘Nonregenerative cellular two-wayrelaying with large-scale antenna arrays,’’ IEEE Trans. Veh. Technol.,vol. 65, no. 7, pp. 4959–4972, Jul. 2016.

[25] L. Jimenez Rodriguez, N. H. Tran, and T. Le-Ngoc, ‘‘Optimal powerallocation and capacity of full-duplex AF relaying under residual self-interference,’’ IEEE Wireless Commun. Lett., vol. 3, no. 2, pp. 233–236,Apr. 2014.

[26] H. Q. Ngo, H. A. Suraweera, M. Matthaiou, and E. G. Larsson, ‘‘Multipairfull-duplex relaying with massive arrays and linear processing,’’ IEEEJ. Sel. Areas Commun., vol. 32, no. 9, pp. 1721–1737, Sep. 2014.

[27] H. Cui, M. Ma, L. Song, and B. Jiao, ‘‘Relay selection for two-way fullduplex relay networks with amplify-and-forward protocol,’’ IEEE Trans.Wireless Commun., vol. 13, no. 7, pp. 3768–3777, Jul. 2014.

[28] Q. Li and D. Han, ‘‘Sum secrecy rate maximization for full-duplextwo-way relay networks,’’ in Proc. ICASSP, Mar. 2016, pp. 3641–3645.

[29] X. Xia, W. Xie, D. Zhang, K. Xu, and Y. Xu, ‘‘Multi-pair full-duplexamplify-and-forward relaying with very large antenna arrays,’’ in Proc.WCNC, Mar. 2015, pp. 304–309.

[30] X. Jia, P. Deng, L. Yang, and H. Zhu, ‘‘Spectrum and energy efficienciesfor multiuser pairs massive MIMO systems with full-duplex amplify-and-forward relay,’’ IEEE Access, vol. 3, pp. 1907–1918, 2015.

[31] Z. Zhang, Z. Chen, M. Shen, and B. Xia, ‘‘Spectral and energy efficiencyof multipair two-way full-duplex relay systems with massive MIMO,’’IEEE J. Sel. Areas Commun., vol. 34, no. 4, pp. 848–863, Apr. 2016.

[32] A. M. Tulino and S. Verdú, ‘‘Random matrix theory and wirelesscommunications,’’ Found. Trends Commun. Inf. Theory, vol. 1, no. 1,pp. 1–182, 2004.

[33] X. Chen, W. Ni, X. Wang, and Y. Sun, ‘‘Provisioning quality-of-serviceto energy harvesting wireless communications,’’ IEEE Commun. Mag.,vol. 53, no. 4, pp. 102–109, Apr. 2015.

[34] Z. Nan, T. Chen, X. Wang, and W. Ni, ‘‘Energy-efficient transmissionschedule for delay-limited bursty data arrivals under nonideal circuit powerconsumption,’’ IEEE Trans. Veh. Technol., vol. 65, no. 8, pp. 6588–6600,Aug. 2016.

[35] X. Chen, W. Ni, X. Wang, and Y. Sun, ‘‘Optimal quality-of-servicescheduling for energy-harvesting powered wireless communications,’’IEEE Trans. Wireless Commun., vol. 15, no. 5, pp. 3269–3280, May 2016.

ZHAOXI FANG (M’15) received the B. Eng. incommunication engineering and the Ph.D. degreein electrical engineering from Fudan University,Shanghai, China, in 2004 and 2009, respectively.In 2009, he joined the School of Electronics andComputer, Zhejiang Wanli University, Ningbo,China, where he is currently a Professor. From2013 to 2014, he was a Post-Doctoral Researcherwith the Department of Electrical and ComputerEngineering, Michigan State University, USA. His

research interests include multiple-input multiple-output, communications,wireless relaying, and cooperative communications.

WEI NI (M’09–SM’15) received the B.E. andPh.D. degrees in electronic engineering fromFudan University, Shanghai, China, in 2000 and2005, respectively. He was a Deputy ProjectManager with the Bell Labs R&I Center,Alcatel/Alcatel-Lucent from 2005 to 2008, anda Senior Researcher with Devices Research andDevelopment, Nokia from 2008 to 2009. He iscurrently a Team Leader, a Project Leader, and aSenior Scientist with CSIRO, Australia. He also

holds adjunct position at Macquarie University, Sydney, and the Universityof Technology Sydney, Sydney. His research interests include radio resourcemanagement, software-defined networking, network security, and multiuserMIMO. He also served as the Publication Chair of BodyNet 2015, StudentTravel Grant Chair for WPMC 2014, Program Committee Member ofCHINACOM 2014, and TPC member of the IEEE ICC’14, the ICCC’15,the EICE’14, and the WCNC’10. He serves as an Editorial Board Memberfor Hindawi Journal of Engineering (2012–2014), Secretary of IEEE NSWVTS Chapter (2015–2016), Track Chair of the IEEE VTC-Spring 2017, andPHY Track Co-chair of the IEEE VTC-Spring 2016.

FENG LIANG received the B.S. and M.S. degreesin optical instruments from Zhejiang University,China, in 1989 and 1992, respectively, and Ph.D.degree in optical instruments from the ShanghaiInstitute of Optics and Fine Mechanics, ChineseAcademy of Sciences, in 1995. He is currently theDean with the School of Electronics and Com-puter, Zhejiang Wanli University, China. He hasauthored and co-authored over 30 technical papersin journals. His current interests focus on network

security, QoS of WLAN, network management systems, and multimediacommunications.

PENGFEI SHAO received the B.E. and M.S.degrees in communication and information systemfrom the Beijing University of Posts and Telecom-munications in 2000 and 2003, respectively, andthe Ph.D. degree in control theory and controlengineering from the Zhejiang University of Tech-nology in 2016. He is currently an AssociateProfessor with the School of Electronics and Com-puter, Zhejiang Wanli University, Ningbo, China.His research interests include wireless networking

and information fusion.

YAOHUI WU received the B.E. and M.S. degreesin communication engineering from the BeijingUniversity of Posts and Telecommunications,China in 2001 and 2004, respectively. He is cur-rently pursuing the Ph.D. degree in communica-tion engineering with Ningbo University. He isalso with the School of Electronics and Com-puter, Zhejiang Wanli University. His researchinterests include resource allocation and channelestimation.

23298 VOLUME 5, 2017

INTRODUCTIONSYSTEM MODELANALYSIS OF MASSIVE MIMO ENABLED FD-cTWRNsFD-DFFD-AFCOMPARISON BETWEEN FD-DF AND FD-AFPOWER SCALING CASE

COMPARISON BETWEEN HD AND FD cTWRNsFD-DF VERSUS HD-DFFD-AF VERSUS HD-AF

NUMERICAL RESULTSCONCLUSIONSREFERENCESBiographiesZHAOXI FANGWEI NIFENG LIANGPENGFEI SHAOYAOHUI WU

digital object identifier 10.1109/access.2017.2766079 ... · province under grant 2016c33036, and...

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