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Efficient Transmission in Multiantenna Two-Way AFRelaying NetworksDOI:10.1109/TVT.2018.2791472

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Citation for published version (APA):Yang, J., Chen, L., Lei, X., Ding, Z., Fan, P., & Gao, X. (2018). Efficient Transmission in Multiantenna Two-Way AFRelaying Networks. IEEE Transactions on Vehicular Technology. https://doi.org/10.1109/TVT.2018.2791472

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https://doi.org/10.1109/TVT.2018.2791472https://www.research.manchester.ac.uk/portal/en/publications/efficient-transmission-in-multiantenna-twoway-af-relaying-networks(0fee79cd-69df-442a-8640-215abef99d3e).html/portal/zhiguo.ding.htmlhttps://www.research.manchester.ac.uk/portal/en/publications/efficient-transmission-in-multiantenna-twoway-af-relaying-networks(0fee79cd-69df-442a-8640-215abef99d3e).htmlhttps://www.research.manchester.ac.uk/portal/en/publications/efficient-transmission-in-multiantenna-twoway-af-relaying-networks(0fee79cd-69df-442a-8640-215abef99d3e).htmlhttps://doi.org/10.1109/TVT.2018.2791472

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2018 1

Efficient Transmission in Multi-Antenna Two-WayAF Relaying Networks

Jing Yang, Member, IEEE, Lei Chen, Student Member, IEEE, Xianfu Lei, Senior Member, IEEE,Zhiguo Ding, Senior Member, IEEE, Pingzhi Fan, Fellow, IEEE, and Xiqi Gao, Fellow, IEEE

Abstract—In this paper, an efficient transmission scheme,termed the joint antenna selection and data exchange (AS-DE)scheme, is proposed for a two-way amplify-and-forward relayingnetwork, where two single-antenna source terminals exchangeinformation via a multi-antenna relay station. For the proposedscheme, the best antenna at the relay for each source terminal isfirst selected separately, following the max-max scheme. Then,from the set of the previously selected antennas, either oneantenna is selected, in a similar fashion as well-known max-min and max-sum schemes, or two antennas exchange theirrespective received signals, which are then coded, amplifiedand broadcasted to the source and destination terminals. Tightlower and upper bounds on the outage probability (OP) for theproposed scheme have been derived assuming independent andidentically distributed Rayleigh fading channels. Furthermore,our analysis reveals that the proposed joint AS-DE schemecan achieve full diversity. Finally, it is shown that under thesame resource constraints, i.e., in terms of the number of theutilized time slots and transmit power, the proposed joint AS-DE scheme outperforms the max-min, the max-sum and themax-max schemes. Extensive numerical results accompaniedwith computer simulations, are further provided to validate thedeveloped analytical results.

Index Terms—Two-way relaying networks, outage probabili-ties, antenna selection, max-min, max-sum, max-max.

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

Manuscript received Jan. 22, 2015; revised Apr. 6, 2015, Jul. 1, 2015,Jan. 21, 2016 and Sep. 18, 2016; accepted Dec. 20, 2017. This work ofJ. Yang was supported in part by National Natural Science Foundation ofChina under Grant 61472343, and China Postdoctoral Science Foundation(Grant No. 2014M560374). The work of X. Lei was supported in part bythe Sichuan International Science and Technology Cooperation Project underGrant 2017HH0035, in part by the National Natural Science Foundation ofChina under Grant 61501382, and in part by the open research fund of theNational Mobile Communications Research Laboratory, Southeast University,under Grant 2017D15. The work of Z. Ding was supported by the UKEPSRC under grant number EP/N005597/1 and by H2020-MSCA-RISE-2015under grant number 690750. The work of P. Fan was supported by NSFCNo.61471302. The work of X. Gao was supported by National Natural ScienceFoundation of China under Grants 61320106003, 61471113, 61521061 and61631018, the China High-Tech 863 Plan under Grants 2015AA01A701 and2014AA01A704, National Science and Technology Major Project of Chinaunder Grant 2017ZX03001002-004, and the Huawei Cooperation Project. Thereview of this paper was coordinated by Prof. Jayaweera Sudharman.

This work was presented in part at 2012 International Conference onWireless Communications and Signal Processing (WCSP 2012), Nanjing,China, Oct., 2012.

J. Yang and L. Chen are with Yangzhou University, Yangzhou, China(e-mails: jingyang@yzu.edu.cn, leichen092@163.com). J. Yang is also withSoutheast University, Nanjing, China.

X. Gao is with Southeast University, Nanjing, China (e-mail: xq-gao@seu.edu.cn).

X. Lei and P. Fan are with Southwest Jiaotong University, China (e-mails:xflei81@gmail.com, pzfan@swjtu.edu.cn).

Z. Ding is with Lancaster University, UK (e-mail: z.ding@lancaster.ac.uk).

I. INTRODUCTION

Recently, two-way relaying networks (TWRNs) have beenenvisioned as a promising transmission technology to signifi-cantly improve the reliability and transmission rate of wirelesssystems [1], [2]. The performance of TWRNs can be furtherimproved by integrating multiple-input multiple-output (MI-MO) transmission technology [3]–[5]. Antenna selection (AS),i.e., optimally choosing a subset of the available antennas, isan attractive low-cost and low-complexity technique, but stillretains many of the advantages of conventional MIMO systems[6]. In the open technical literature, three antenna selectionschemes for MIMO amplify-and-forward (AF) and decode-and-forward (DF) TWRNs have been proposed, namely themax-min [7], [8], the max-sum [9] and the max-max schemes[10], [11].

The performance achieved by such schemes has been as-sessed in several past research works. For example, the outageprobability (OP) performance of the max-min and the max-sum schemes has been evaluated in [7]–[9]. These works haveshown that both schemes can achieve full diversity. In [10],antenna selection in a DF relaying network based on the max-max scheme was investigated, assuming that decoding at therelay is error-free. In [11], the so-called double-max schemewas proposed. In that work, relay selection based on the max-max scheme was addressed, assuming the use of an error-freedecoding relay.

Motivation: For the purpose of illustration, consider twosingle-antenna sources T1 and T2 exchanging information viaa relay station R which is equipped with N = 3 antennas, de-noted by antenna R1, antenna R2 and antenna R3, respectively.For example, let the channel gains from T1 and T2 to R at agiven time instant be h = {h1, h2, h3} = {0.35, 0.46, 0.59}and g = {g1, g2, g3} = {0.72, 0.54, 0.32}, respectively. Ac-cording to the max-min scheme, the best antenna at the relayis selected to maximize the end-to-end signal-to-noise ratio ofthe worse source [7], [8]. In this example, the antenna antennaR2 will be chosen with h2 = 0.46 and g2 = 0.54. However,it can be observed that the links having the largest channelgains, i.e., h3 = 0.59 and g1 = 0.72, have not been utilized.

When the max-sum scheme is utilized, the best antenna atthe relay is selected to maximize the sum-rate [9]. In theconsidered test case, the antenna R1 will be chosen withh1 = 0.35 and g1 = 0.72. However, as it can be observed thismethod does not exploit the channel coefficient h3 = 0.59,i.e., the maximum channel gain in all his, i ∈ {1, 2, 3}.

2 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2018

The max-max scheme selects at a given time instanceeither one or two antennas at the relay, corresponding tothe maximum channel coefficients [10], [11]. If the antennaindices are the same, one antenna is selected, otherwise twoantennas are selected. In the previously described example,two antennas are selected, namely the antenna R1 and antennaR3 corresponding to the links with h3 = 0.59 and g1 = 0.72.Consider, however, the following data transmission scenariofrom T1 to T2. Specifically, assume that information flowsfrom the links T1 → R1, R1 → T2 and T1 → R3, R3 → T2,characterized by channel gains h1 = 0.35, g1 = 0.72 andh3 = 0.59, g3 = 0.32, respectively. As can be observed,during the transmission through the antenna R1, link T1 → R1experiences the worse channel conditions since h1 is theminimum channel coefficient in his. On the other hand, linkR1 → T2 experiences the best channel conditions because g1is the maximum channel coefficient in gis. Similar findingscan be found when transmission through the links T1 → R3,R3 → T2 is considered. In such scenarios, the combinations of“small-maximum” and “maximum-small” channel coefficientsresult in a small received end-to-end (e2e) SNR at T2. Notethat when one antenna is selected, i.e., when the selectedantennas’ indices are identical, data transmission will exploitthe best links in an optimal way. In such a case, the max-maxscheme exhibits the best performance. However, this is a smallprobability event.

Motivated by this key observation, in this paper, an efficienttransmission scheme which can exploit the unutilized linkscharacterized by the best channel coefficients, termed thejoint antenna selection and data exchange (AS-DE) scheme, isproposed for multi-antenna AF TWRNs. The key idea in thejoint AS-DE scheme is to combine max-max antenna selectionscheme along with data exchange to transmit data throughthe links characterized by “maximum-maximum” and “small-small” channel coefficients. Consequently, the joint AS-DEscheme outperforms the max-min, the max-sum and the max-max schemes because its e2e SNR is significantly larger thanthat achieved by the aforementioned AS schemes. It shouldbe emphasized that the previously reported works on the max-max scheme, such as those presented in [10], [11], ignore thepossible transmission error due to the aforementioned “small-maximum” and “maximum-small” combinations of channelcoefficients, since they consider DF relaying networks andassume decoding at the relay is error-free.

The performance of the joint AS-DE scheme is assessed byderiving the tight upper and lower bounds on the e2e OP, as-suming Rayleigh fading conditions. The tightness of the newlyderived bounds is verified by means of computer simulation.Extensive numerical results are further presented revealingthat the joint AS-DE scheme can achieve full diversity. Inaddition, it is shown that under the same resource consumptionconstraints, such as in terms of the utilized time slots andtransmit power, the joint AS-DE scheme also outperforms theexisting max-min, max-sum and max-max schemes.

The remainder of this paper is organized as follows: SectionII presents the system model and the joint AS-DE scheme.Section III investigates the OP and diversity gain performancefor the joint AS-DE scheme. Numerical and simulation results

are presented in Section IV. Finally, Section V concludes thepaper.

Notation: E {·} and IM denote the expectation operationand an M ×M identity matrix, respectively. Kv(·) and Ei(·)denote the v order modified Bessel function of the secondkind [12, Eq. (8.407)] and the Exponential integral function[12, Eq. (8.211)], respectively. The notations CN (0, σ2), fX(·)and FX(·) represent a circularly symmetric complex Gaussianrandom variable (RV) with zero mean and variance σ2, theprobability density function (PDF) and cumulative distribu-tion function (CDF) of RV X, respectively. Pr(·) returns theprobability.

II. SYSTEM MODEL AND THE PROPOSED JOINT AS-DESCHEME

In this section, the system model and the joint AS-DEscheme are introduced.

A. System Model

Consider a TWRN, where two single-antenna source termi-nals T1 and T2 exchange information by using an AF relaystation R equipped with N ≥ 2 antennas. Assume that allthe links experience independent and identically distributed(i.i.d.) Rayleigh fading, following CN (0,Ω), and channelsare reciprocal. Assume that the i-th antenna Ri is selectedto help the communication between T1 and T2. The wholecommunication takes place in two times slots. In the firsttime slot, T1 and T2 transmit their signals to R. The receivedsignal at the antenna Ri after M successive symbol durationscan be written as

yi =√Phis1 +

√Pgis2 + ni, (1)

where sj = [sj(1), · · · , sj(M)]T , j = 1, 2, denotes thetransmitted symbol of Tj with E[sjs†j ] = IM , P is the transmitpower of Tj , hi and gi denote the channel coefficients betweenT1 and antenna Ri, and between T2 and the antenna Ri,respectively, ni ∼ CN (0, N0IM ) represents additive gaussianwhite noise (AWGN) at the antenna Ri.

In the second time slot, the selected antenna Ri amplifiesits received signal with gain α and then broadcasts it to Tj .The received signals at T1 and T2 are given by

yT1 =√

Prhiαyi + nT1 , and yT2 =√Prgiαyi + nT2 ,

respectively, where Pr denotes the transmit power of the i-thantenna at R and nTj ∼ CN (0, N0IM )) is AWGN at terminalTj . Assuming that fixed gain relaying is used, the amplificationfactor is expressed as [1], [13],

α =

√1

2PΩ+N0. (2)

After the self-interference cancellation is performed, assum-ing Pr = 2P , the received SNR at T1 and T2 via the help ofthe antenna Ri is given as [13],

γT1i =2γliγ

ri

2γli + c, and γT2i =

2γliγri

2γri + c, (3)

JING YANG et al.: EFFICIENT TRANSMISSION IN MULTI-ANTENNA TWO-WAY AF RELAYING NETWORKS 3

where γli = P |hi|2/N0, γri = P |gi|

2/N0, γ = PΩ/N0, and

c = 2γ + 1.In the following, the three conventional AS schemes, i.e.,

the max-min, the max-sum and the max-max schemes, areintroduced.

• In the max-min scheme, the i∗-th antenna is selectedaccording to [7], [8],

i∗ = arg max1≤i≤N

min(γT1i , γT2i ). (4)

• In the max-sum scheme, the selected antenna i∗ follows[9]

i∗ = arg max1≤i≤N

((1 + γT1i )(1 + γ

T2i )). (5)

From (4) and (5), it can be observed that only one antennacan be selected for relaying between T1 and T2 in boththe max-min and max-sum schemes.

• In the max-max scheme, the l∗-th and r∗-th antennas areselected according to [10], [11],

l∗ = arg max1≤i≤N

hi, and r∗ = arg max1≤j≤N

gj . (6)

From (6), it can be observed that if the antenna indicesl∗ = r∗, only one antenna can be used for relayingbetween T1 and T2 in the max-max scheme. Otherwise,two antennas can be used. Besides, it can be seen thatthe selected l∗-th and r∗-th antennas have the largestchannel gain to T1 and T2, respectively.

B. The Joint AS-DE Scheme

The proposed joint AS-DE scheme includes two procedures,i.e., antenna selection and data exchange. Antenna selection isperformed based on the max-max scheme in a similar fashionas in (6). During the data exchange phase, the l∗-th antenna atR transmits its signal yl∗ to the r∗-th antenna at R, and the r∗-th antenna at R transmits its signal yr∗ to the l∗-th antennaat R. We note that data exchange is started only when twoantennas are selected, i.e., the antenna indices l∗ ̸= r∗. Thewhole communication takes place in two times slots.

Let us now rearrange hi and gi, i = 1, · · · , N , in anascending order. We define the channel coefficients h(i) andg(i), respectively, such that h(1) ≤ h(2) ≤ · · · ≤ h(N) = hl∗and g(1) ≤ g(2) ≤ · · · ≤ g(N) = gr∗ . Note that hl∗ and gr∗ arethe N -th largest channel gain in his and gis, respectively, buthr∗ and gl∗ are the w-th largest channel gain, 1 ≤ w ≤ N−1,and q-th largest, 1 ≤ q ≤ N − 1, in his and gis, respec-tively. We denote γl(N) = P |hl∗ |

2/N0, γl(w) = P |hr∗ |2/N0,

γr(N) = P |gr∗ |2/N0, and γr(q) = P |gl∗ |

2/N0.In the following, data transmission in the joint AS-DE

scheme is presented when either one or two antennas areselected.

1) If One Antenna is Selected: In this case, the antennaindices are the same, i.e., l∗ = r∗. In the first time slot, T1and T2 broadcast their information to R. In the second timeslot, the selected antenna amplifies its received signal in thefirst time slot by a gain α, and broadcasts to T1 and T2 withfull power Pr = 2P .

Similar to (3), the received SNR at T2 can be obtained as

γ1,T2 =2γl(N)γ

r(N)

2γr(N) + c. (7)

2) If Two Antennas are Selected: In this case, the antennaindices are different, i.e., l∗ ̸= r∗. In the first time slot, thereceived signals at R via the antennas l∗ and r∗, which havebeen selected based on (6), are given by

yl∗ =√Phl∗s1 +

√Pgl∗s2 + nl∗ ,

and

yr∗ =√Phr∗s1 +

√Pgr∗s2 + nr∗ ,

respectively. The nl∗ , nr∗ ∼ CN (0, N0IM ) represent theAWGN at the l∗-th and r∗-th antennas, respectively.

Following [13], the durations of both time slots are consid-ered to be the same. Data exchange between the l∗-th and r∗-thantennas occurs in the second time slot. Then, the selected l∗-th antenna transmits its signal yl∗ to the r∗-th antenna, andthe r∗-th antenna transmits its signal yr∗ to the l∗-th antenna.In the same time slot, the l∗-th and r∗-th antennas process yr∗and yl∗ to generate the space time coded symbol xl∗ and xr∗ ,respectively. The transmitted signals xl∗ and xr∗ are designedto be linear functions of yr∗ and yl∗ and their conjugates,namely [13]–[16],

xl∗ = Al∗yr∗ +Bl∗y∗r∗ , and xr∗ = Ar∗yl∗ +Br∗y

∗l∗ , (8)

where Ap and Bp, p ∈ {l∗, r∗}, are M × M precodingmatrices, designed using guidelines for the construction ofdistributed space-time coding schemes, and y∗p denotes theconjugate of yp. For simplicity, in this paper, we considerM = 2, and the orthogonal matrices are used at the twoselected antennas as in [16], namely

Al∗ = I2,Bl∗ = 02,Ar∗ = 02,Br∗ =(

0 −11 0

)(9)

Therefore, (8) becomes

xl∗ = Al∗(√

Phr∗s1 +√Pgr∗s2 + nr∗

),

and

xr∗ = Br∗(√

Phl∗s1 +√Pgl∗s2 + nl∗

)∗.

Then, the l∗-th and r∗-th antennas broadcast xl∗ and xr∗after amplification, respectively, each with half power Pr/2 =P . Let ỹT2 denote the received signals after self-interferencecancellation at T2, given by

ỹT2 =

√Pr2gr∗α

′Br∗

(√Phl∗s1 + nl∗

)∗+

√Pr2gl∗α

′Al∗

(√Phr∗s1 + nr∗

)+ nT2 . (10)

The average transmit power at each antenna is constrained to

E{∥α

′xp∥2F

}= 1. (11)

4 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2018

When orthogonal matrices in (9) are employed, α′= α/

√2,

and the received SNR at T2 can be obtained, based on (10),as follows

γASDE2,T2

=α2PP |hl∗ |2|gr∗ |2∥Br∗∥2 + α2PP |hr∗ |2|gl∗ |2∥Al∗∥2

α2P |gr∗ |2∥Br∗∥2N0 + α2P |gl∗ |2∥Al∗∥2N0 + 2N0.

(12)

Furthermore, (12) can be re-expressed as

γASDE2,T2 =γr(N)γ

l(N) + γ

r(q)γ

l(w)

γr(q) + γr(N) + c

. (13)

Eq. (13) can be upper- and lower-bounded as

γASDET2,ub ≥ γASDE2,T2 ≥ γ

ASDET2,lb , (14)

where

γASDET2,lb =γr(N)γ

l(N)

γr(q) + γr(N) + c

, (15)

γASDET2,ub =γl(N)(γ

r(q) + γ

r(N))

γr(q) + γr(N) + c

. (16)

To compare the joint AS-DE scheme with the max-maxscheme, here, we present the received SNR at T2 in the max-max scheme. In the max-max scheme, since it does not utilizethe “data exchange”, in the second time slot, the transmittedsignal x′l∗ at the l

∗-th antenna and the transmitted signal x′r∗at the r∗-th antenna are given as

x′l∗ = Al∗(√

Phl∗s1 +√Pgl∗s2 + nl∗

),

and

x′r∗ = Br∗(√

Phr∗s1 +√Pgr∗s2 + nr∗

)∗,

respectively.Following similar arguments as to (13), the received SNR

at T2 in the max-max scheme can be obtained as

γMaxMax2,T2 =γr(q)γ

l(N) + γ

r(N)γ

l(w)

γr(q) + γr(N) + c

. (17)

Remark 1: Comparing (13) with (17), it can be seen thatthe difference between the two SNR results is in their numer-ators. In the numerator of (13), there exists the “maximum-maximum”, i.e. γr(N)γ

l(N), and “small-small”, i.e., γ

r(q)γ

l(w),

channel coefficient combinations for the joint AS-DE scheme,but “small-maximum” and “maximum-small”, i.e., γr(q)γ

l(N)

and γr(N)γl(w), link combinations in (17) for the max-max

scheme. This is because both γr(N) and γl(N) are the maximal

effective channel gain, due to the fact that gr∗ and hl∗ arethe N -th maximum among gis and his; and, γr(q) and γ

l(w)

are small, due to the fact that gl∗ and hr∗ are the q-thmaximum and w-th maximum in gis and his, respectively. The“maximum-maximum” and “small-small” link combinationsin the joint AS-DE scheme, result in a larger received SNRthan in the case of the max-max scheme, where the “small-maximum” and “maximum-small” link combinations are used.Although the max-max scheme exploits the best links with

the largest channel gains, it does not utilize them in the bestmanner. Recalling the example described in the introductionsection, one can find that the max-min and the max-sumschemes may not exploit the best links. However, in the jointAS-DE scheme data transmission from T1 to T2 uses the linksT1 → R3, R1 → T2 and T1 → R1, R3 → T2, having gainsh3 = 0.59, g1 = 0.72 and h1 = 0.35, g3 = 0.32, respectively.From this and (13), we conclude that the joint AS-DE schemeexploits the strong channel links in the best manner, byutilizing “maximum-maximum” and “small-small” channelcoefficients combinations. Because of this, it outperforms themax-max, the max-min and the max-sum schemes.

Remark 2: Despite the fact that the joint AS-DE schemeoutperforms the conventional AS schemes, it requires a sec-ond RF chain for its practical implementation. Moreover, itsbaseband implementation is more complicated than the one ofconventional schemes, as it requires data exchange betweenthe selected antennas. Recently, novel MIMO transmissionschemes have been reported, such as spatial modulation andMIMO electronically steerable passive array radiator (ESPAR)[17]–[19]. Such schemes can minimize complexity and thecosts while attaining the advantages of the MIMO system.

Remark 3: Hereafter some issues regarding the implementa-tion of the data exchange phase of the joint AS-DE scheme arediscussed. Such a scheme can be implemented in an efficientmanner in baseband, by employing digital hardware, insteadof exchanging analog signals between antennas. Specializeddevices, such as digital signal processors (DSP) or fieldprogrammable gate arrays (FPGA) can be used to this purpose.Such devices are equipped with specialized direct memory ac-cess (DMA) controllers, thus rendering them capable of trans-ferring large amounts of data, stored in buffers. Sophisticatedtechniques, such as multiple buffering, can be also employedto increase the efficiency of data transmission. Data exchangebetween two antennas can be implemented without significantcomputational complexity by exchanging the contents of theircorresponding buffers. For a given hardware platform, one canperform such a task in an optimzied way, i.e., by minimizingthe number of the required clock cycles.

III. PERFORMANCE ANALYSIS

In this section, the OP performance at T2 will be analyzed.The performance analysis at T1 can be obtained in a similarfashion and thus mathematical derivations are omitted forbrevity. For writing simplicity, some definitions are given asfollows.

Definition 1:∑̂1,ki

,N∑

ki=0

(N

ki

)(−1)ki ,

∑̂2,ki

, 1γ

N∑ki=0

(N

ki

)(−1)ki+1ki,

and ∑̂3,ki,kj

=1

γ2N !

(q − 1)!(N − 1− q)!

q−1∑ki=0

N−1−q∑kj=0

(q − 1ki

)×(N − q − 1

kj

)(−1)ki+kj .

JING YANG et al.: EFFICIENT TRANSMISSION IN MULTI-ANTENNA TWO-WAY AF RELAYING NETWORKS 5

The distributions of γ1,T2 and γASDE2,T2

will be firstly presentedin the following theorems, which lay the foundation forperformance analysis.

A. Distribution of the received SNR

Theorem 1: When one antenna is selected for relayingbetween T1 and T2, i.e., the antenna indices l∗ = r∗, theCDF of the received SNR at terminal T2, i.e., γ1,T2 , can beexpressed in closed-form as

Fγ1,T2 (z)=1 +∑̂

1,k1 ̸=0

∑̂2,k2 ̸=0

√2k1zc

k2e−

k1γ zK1

(√2k1k2zc

γ

).

(18)

Proof: See Appendix A.Theorem 2: When two antennas are selected for relaying

between T1 and T2, i.e., the antenna indices l∗ ̸= r∗, theCDF of the upper bound on γASDE2,T2 , i.e., FγASDET2,ub

(z), is given as

FγASDET2,ub(z) =

{L1, a = bL2, a ̸= b

(19)

wherea =

k2 + 1

γ, b =

N + k1 − q − k2γ

,

L1 =∑̂

3,k1,k2

1a(a+ b)

+∑

1,k3 ̸=0

k3cz

aγe−

k3zγ K2

(2

√k3acz

γ

) ,and

L2=∑̂

3,k1,k2

1a(a+ b)

+∑

1,k3 ̸=0

2ce−k3zγ

b− a

√k3z

acγK1

(2

√k3acz

γ

)

−

√2k3z

(a+ b)cγK1

(√2k3(a+ b)cz

γ

)].

Proof: See Appendix B.Theorem 3: When two antennas are selected, i.e., l∗ ̸= r∗,

the CDF of the lower bound on γASDE2,T2 , i.e., FγASDET2,lb(z), is given

as,

FγASDET2,lb(z) =

∑̂3,k1,k2

∑̂1,k3

(∫ 10

e−k3zγζ A

′

1dζ +

∫ 0.50

e−k3zγζ A

′

2dζ

)(20)

where

A′

1 = −[1 + (ac− 1)ζ + bc(1− ζ)]

(ζ − 1)[(a− b)ζ + b]2e

acζζ−1 , (21)

and

A′

2 = −e

(a+b)cζ−1+2ζ (−1 + bc(−1 + ζ) + (2− ac)ζ)

(−1 + 2ζ)(b+ (a− b)ζ)2. (22)

Proof: See Appendix C.Remark 4: Theorem 3 involves the computation of the

integrals with integrands composed of elementary functions.Although such integrals are not in closed-form, they canbe easily evaluated numerically by employing standard tech-niques available in the most common mathematical softwarepackages, such as Matlab, Maple, or Mathematica.

B. Outage Probability

The OP is defined as the probability that the instantaneousSNR falls below a given threshold γth, i.e.,

Pout(γth) = Pr[γ < γth] = Fγ(γth). (23)

We note that the OP at Tj , j = 1, 2 is given by

Pr(outage at Tj) = Pr[one antenna selected]× Pr[outage at Tj |one antenna selected]

+ Pr[two antennas selected]× Pr[outage at Tj |two antennas selected].

The OP results are presented in the following corollaries.Corollary 1: In the joint AS-DE scheme, the tight upper

and lower bounds on the OP at T2 can be calculated as

PASDEout,ub (γth) = pNFγ1,T2 (γth) + p′

N

N−1∑q=1

FγASDET2,lb(γth), (24)

and

PASDEout,lb (γth) = pNFγ1,T2 (γth) + p′

N

N−1∑q=1

FγASDET2,ub(γth), (25)

respectively, where pN = p′

N = 1/N , Fγ1,T2 (γth), FγASDET2,ub(γth)

and FγASDET2,lb(γth) are presented in Theorem 1, Theorem 2 and

Theorem 3, respectively.Remark 5: The probabilities pN in (24) and (25) are for the

event that one antenna is selected. From (6), it can be seen thatamong the N×N pairs (hi, gj) (i, j = 1, 2 · · ·N), there are Npairs (hl∗ , gr∗) with l∗ = r∗ = 1, · · · , N . We note that eachpair is selected with the same probability, since we assumeall his and gjs are i.i.d. distributed. Therefore, the probabilitythat one antenna is selected, is pN = N/(N × N) = 1/N .In (24) and (25), p

′

N equals to (1− 1/N) /(N − 1), where1 − 1/N is the probability that two different antennas havebeen selected, i.e., l∗ ̸= r∗, and 1/(N − 1) is the probabilitythat q takes a specific value in {1, · · · , N − 1}.

C. Diversity Order

Corollary 2: The proposed joint AS-DE scheme canachieve full diversity, i.e., the diversity order is N .

Proof: See Appendix D.

IV. SIMULATION AND NUMERICAL RESULTS

In this section, computer simulations are carried out todemonstrate the performance of the joint AS-DE scheme withγth = 3, P = 1 and Pr = 2P = 2 in all figures, Ω = 1in Figs. 1-3, and Ω = 1/(1 − d)−3 in Fig. 4 where d and3 denote the distance between T1 and R and the path-lossexponent, respectively. In addition, numerical results obtainedfrom Corollary 1 are also used to show the accuracy of thedeveloped analytical results. We note that in order to guaranteecomparison fairness, the same power consumption used bythe joint AS-DE scheme as in the max-min, the max-sumand the max-max schemes is considered. For the max-minand max-sum schemes which select a single antenna at R,

6 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2018

5 10 15 20 2510

-6

10-5

10-4

10-3

10-2

10-1

100

.(dB)

Out

age

Pro

babi

lity

max-max scheme

max-min scheme

max-sum scheme

Proposed AS-DE scheme

N=2

N=4

Fig. 1. OP comparisons of different AS schemes under different γ.

2 3 4 5 6 7 8 9 1010

-4

10-3

10-2

10-1

100

The number of antennas, N

Out

age

Pro

babi

lity

max-max scheme

max-min scheme

max-sum scheme

Proposed AS-DE scheme

. = 10 dB

Fig. 2. OP comparisons of different AS schemes under different N andγ = 10 dB.

the whole transmit power at R is Pr = 2. For the proposedAS-DE and max-max schemes, if one antenna is selected,the transmit power of the selected antenna at R is Pr = 2;otherwise, each selected antenna broadcasts the signal withpower Pr/2 = 1, indicating that the whole transmit power atR is Pr/2 + Pr/2 = 2.

Fig. 1 illustrates the Monte-Carlo simulation results on theOP performance of the joint AS-DE scheme in comparisonto the max-min, max-sum, max-max schemes versus γ underN = 2, 4. It clearly illustrates that under arbitrary N andγ, our proposed joint AS-DE scheme performs much betterthan the other three AS schemes. For example, when N = 4and at 10−4 OP, the joint AS-DE scheme provides a nearly3 dB gain over those of the max-min and max-sum schemes,about a 10 dB gain over that of the max-max scheme. Thisresult is expected because the joint AS-DE scheme utilizes the

5 10 15 20 25 30 3510

-6

10-5

10-4

10-3

10-2

10-1

100

. (dB)

OP

simLb, AnlysisUb, Analysis

N=2,3,4

Fig. 3. OP versus γ under different relay antenna number N in the jointAS-DE scheme .

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.910

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

The distance between T1 and R, d

OP

Ub AnalysisLb AnalysisSim

N=2,3,4

. = 0dB

Fig. 4. OP versus the distance between T1 → R under different relayantenna number N in the joint AS-DE scheme .

“maximum-maximum” and “small-small” channel coefficientscombinations, resulting in a larger received SNR. Furthermore,it can also be seen that the joint AS-DE scheme can achievefull diversity as the max-min, max-sum schemes.

Fig. 2 compares the OP performance of the joint AS-DEscheme with the max-min, max-sum and max-max schemesversus the relay antenna number N with γ = 10 dB. It canbe also clearly seen that the joint AS-DE scheme outperformsthe other three schemes under an arbitrary N . Besides, as thenumber of relay antennas N increases, the SNR gain that thejoint AS-DE scheme achieves over the other three schemescounterpart is further enlarged.

In Fig. 3, the developed analytical results presented inCorollary 1 for the joint AS-DE schemes are compared tothe simulation results with N = 2, 3 and 4. As can be

JING YANG et al.: EFFICIENT TRANSMISSION IN MULTI-ANTENNA TWO-WAY AF RELAYING NETWORKS 7

observed from the figure, under an arbitrary N , the upperand lower bounds on OP are quite close to the simulationcounterparts which verifies our analysis. Furthermore, thelower and upper bound outage curves verify our diversity orderanalysis, indicating that the joint AS-DE scheme can achievefull diversity.

In Fig. 4, the impact of the relay location on OP for T2is studied in the joint AS-DE scheme. Specifically, the OP isplotted against the distance d between T1 and R by modelingthe path-loss dependent parameters Ω = 1/(1− d)−3. As canbe observed, the OP performance at T2 improves as the relaystation gets close to T2. Besides, the lower and upper boundswe derived are quite tight under an arbitrary d indicating theaccuracy of our analysis.

V. CONCLUSIONIn this paper, we proposed an efficient transmission scheme

for multi-antenna AF TWRNs, termed as the joint AS-DEscheme. Particularly, the joint AS-DE scheme utilized theantenna selection criterion in the max-max scheme along withdata exchange to transmit data through the links characterizedby “maximum-maximum” and “small-small” channel coeffi-cient combinations. We presented the tight lower and upperbounds on the OP for the proposed scheme. Furthermore, ouranalysis revealed that the joint AS-DE scheme can achievefull diversity. Finally, analysis and simulation results showedthat under the same time slots and power consumption, thejoint AS-DE scheme outperforms the existing schemes, i.e.,the max-min, max-sum and max-max ones. For example, whenN = 4 and at 10−4 OP, the joint AS-DE scheme provides anearly 3 dB gain when compared with the max-min and max-sum schemes, and about a 10 dB gain when compared withthe max-max scheme.

APPENDIX APROOF OF THEOREM 1

Since all links experience i.i.d. Rayleigh fading, the PDFand CDF of the instantaneous SNR of any links, γli or γ

ri

follow that

fγli(x) =1

γe−

xγ , Fγli(x) = 1− e

− xγ .

Based on the order statistics in [20], we have

Fγl(N)

(x) = (Fγli(x))N =

∑1,k1

e−k1xγ . (A-1)

The PDF of γl(N) can be obtained as,

fγl(N)

(x) =∑2,k2

e−k2xγ .

Similarly, we have

fγr(N)

(y) =∑2,k2

e−k2yγ .

From (7), Fγ1,T2 (z) can be expressed as

Fγ1,T2 (z) =

∫ ∞0

Pr(γl(N) ≤ z +

2cz

2y

)fγr

(N)(y)dy.

Utilizing [12, Eq.(3.471.9)], Theorem 1 can be achieved.

APPENDIX BPROOF OF THEOREM 2

We will firstly study the distribution of θ = γr(q)+γr(N), and

then the distribution of u = θ/(θ + c). Finally, the distributionof γASDET2,ub = γ

l(N)u will be obtained.

Now, let’s study the CDF of θ = γr(q) + γr(N). Based on

the order statistics in [20], the joint PDF of γr(q) and γr(N),

1 ≤ q < N , is

fγr(q)

,γr(N)

(s, v) =∑̂

3,k1,k2

e−bse−av, (B-1)

for 0 < s < v < ∞.Therefore, the CDF of θ, i.e., Fθ(ϑ), follows that

Fθ(ϑ) =

∫ ϑ2

0

∫ ϑ−ss

fγr(q)

,γr(N)

(s, v)dvds

=∑̂

3,k1,k2

1

a

∫ ϑ/20

[e−(a+b)s−e(a−b)s−aϑ

]ds. (B-2)

Utilizing [12, Eq. (2.311)], we have

Fθ(ϑ) =

−∑̂

3,k1,k2

1a

[ϑ2 e

−aϑ + e− (a+b)ϑ

2 −1a+b

], a− b = 0,∑̂

3,k1,k2

1a

[e−aϑ−e−

(a+b)ϑ2

a−b +1−e−

(a+b)ϑ2

a+b

], a− b ̸= 0.

(B-3)

From u = θ/(θ + c), we have θ = g(u), where g(u) =cu1−u . Therefore, fu(u) = fθ(g(u))|g

′(u)|, where g′(u) de-

notes the derivative of g(u).

Taking the derivative of (B-3), we can obtain the PDF of θ,i.e. fθ(ϑ). And then, fu(u) can be obtained as follows,

fu(u) =

∑̂3,k1,k2

c′2u2(1−u)3 e

− acu1−u , a = b∑̂3,k1,k2

c′

(b−a)(1−u)2

(e−

acu1−u − e−

(a+b)cu2(1−u)

), a ̸= b

0, u > 1.

(B-4)

The CDF of γASDET2,ub is given as follows

FγASDET2,ub(z) =

∫ ∞−∞

Fγl(N)

( zu

)fu(u)du. (B-5)

Substituting (A-1) and (B-4) into (B-5), with the aid of [12,Eq. (3.351.2)] and [12, Eq. (3.471.9)], Theorem 2 is deduced.

APPENDIX CPROOF OF THEOREM 3

We firstly study the distribution of ε =γr(N)/(γ

r(q) + γ

r(N) + c), and then the distribution of

γASDET2,lb = εγl(N).

The CDF of ε is given as

Fε(ζ) = Pr

(γr(N)

γr(q) + γr(N) + c

≤ ζ

). (C-1)

8 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2018

When 1/2 ≤ ζ ≤ 1, substituting (B-1) into (C-1), we have

Fε(ζ) =∑̂

3,k1,k2

∫ ∞0

∫ (s+c)ζ1−ζ

s

e−ave−bsdvds

=∑̂

3,k1,k2

1

a(a+ b)+

(−1 + ζ)eacζ

−1+ζ

a(b+ (a− b)ζ)︸ ︷︷ ︸A1

.

When 0 ≤ ζ ≤ 1/2, (C-1) becomes

Fε(ζ) =∑̂

3,k1,k2

∫ cζ1−2ζ

0

∫ (s+c)ζ1−ζ

s

e−ave−bsdvds

=∑̂

3,k1,k2

A1 + (−1 + ζ)e(a+b)cζ−1+2ζ

a(−b+ (b− a)ζ)− e

(a+b)cζ−1+2ζ

a(a+ b)︸ ︷︷ ︸A2

.Therefore, the PDF of ε can be obtained as,

fε(ζ) =

∑̂

3,k1,k2

A′1, 1/2 < ζ < 1,∑̂3,k1,k2

(A′1 +A

′

2

), 0 < ζ ≤ 1/2,

0, others.

(C-2)

where A′1 and A′

2 are given in (21) and (22), respectively.Therefore, the CDF of γASDET2,lb , i.e., FγASDET2,lb

(γth), is

FγASDET2,lb(γth) =

∫ ∞0

Fγl(N)

(γthζ

)fε(ζ)dζ. (C-3)

Substituting (A-1) and (C-2) into (C-3), Theorem 3 can bereached.

APPENDIX DPROOF OF COROLLARY 2

The following facts are utilized, i.e., limx→0

e−x = 1 − x,limx→0

K1(x) = 1/x and limx→0

K2(x) = 2/x2.

Recalling Theorem 1, (18) can be re-expressed as,

Fγ1,T2 (z) = 1 +N∑

k2=1

(N

k2

)(−1)k2+1

N∑k1=1

(N

k1

)(−1)k1e−

k1zγ

= 1 +

[(1− e−

zγ

)N− 1].

When γ → ∞, we have

Fγ1,T2 (z)γ→∞=

(z

γ

)N. (D-1)

Utilizing (A-1), (C-3) can be rewritten as

FγASDET2,lb(z) =

∫ ∞0

(1− e−zγζ )Nfε(ζ)dζ

γ→∞=

(z

γ

)N ∫ ∞0

1

ζNfε(ζ)dζ. (D-2)

We note that∫∞0

1ζN

fε(ζ)dζ is a constant, which is indepen-dent of γ.

Based on (D-1) and (D-2), at the high SNR regions, (24)can be asymptotically approximated by

PASDEout,ub (γth)γ→∞=

[1

N+

1

N

N−1∑q=1

∫ ∞0

1

ζNfε(ζ)dζ

](γthγ

)N.

(D-3)

Recalling Theorem 2, L1 in (19) can be deduced as, whenγ → ∞,

L1γ→∞=

∑̂3,k1,k2

[1

a(a+ b)+

1

2a2

N∑k3=1

(N

k3

)(−1)k3e−

k3zγ

]

=∑̂

3,k1,k2

{1

a(a+ b)+

1

2a2

[(1− e−

zγ

)N− 1]}

=∑̂

3,k1,k2

1

a(a+ b)

(z

γ

)N. (D-4)

Similarly, L2 in (19) can be obtained as follows, when γ → ∞,

L2γ→∞=

∑̂3,k1,k2

1

a(a+ b)

(z

γ

)N. (D-5)

Utilizing (D-4) and (D-5), when γ → ∞, (19) is deduced as,

FγASDET2,ub(z)

γ→∞=

∑̂3,k1,k2

1

a(a+ b)

(z

γ

)N. (D-6)

From (D-1) and (D-6), at the high SNR regions, (25) canbe asymptotically approximated by

PASDEout,lb (γth)γ→∞=

1N

+1

N

N−1∑q=1

∑̂3,k1,k2

1

a(a+ b)

(γthγ

)N.

(D-7)

Finally, Corollary 2 is proved from (D-7) and (D-3).

REFERENCES

[1] B. Rankov and A. Wittneben, “Spectral efficient protocols for half-duplex fading relay channels,” IEEE J. Sel. Areas Commun., vol. 25,no. 2, pp. 379–389, Feb. 2007.

[2] J. Yang, P. Fan, T. Duong, and X. Lei, “Exact performance of two-wayAF relaying in Nakagami-m fading environment,” IEEE Trans. WirelessCommun., vol. 10, no. 3, pp. 980–987, Mar. 2011.

[3] H. Gao, T. Lv, S. Zhang, C. Yuen, and S. Yang, “Zero-forcing based MI-MO two-way relay with relay antenna selection: Transmission schemeand diversity analysis,” IEEE Trans. Wireless Commun., vol. 11, no. 12,pp. 4426–4437, Dec. 2012.

[4] I. Krikidis, S. Sasaki, S. Timotheou, and Z. Ding, “A low complexityantenna switching for joint wireless information and energy transfer inMIMO relay channels,” IEEE Trans. on Commun., vol. 62, no. 5, pp.1577–1587, May 2014.

[5] P. Zhang, S. Chen, and L. Hanzo, “Two-tier channel estimation aidednear-capacity MIMO transceivers relying on norm-based joint transmitand receive antenna selection,” IEEE Trans. Wireless Commun., vol. 14,no. 1, pp. 122–137, Jan. 2015.

[6] C. Jiang and L. Cimini, “Antenna selection for energy-efficient MIMOtransmission,” IEEE Wireless Commun. Lett., vol. 1, no. 6, pp. 577–580,Dec. 2012.

JING YANG et al.: EFFICIENT TRANSMISSION IN MULTI-ANTENNA TWO-WAY AF RELAYING NETWORKS 9

[7] G. Amarasuriya, C. Tellambura, and M. Ardakani, “Two-way amplify-and-forward MIMO relay networks with antenna selection,” in Proc.IEEE Globecom, Houston, USA, Dec. 2011, pp. 1–5.

[8] K. Yang, N. Yang, C. Xing, and J. Wu, “Relay antenna selection inMIMO two-way relay networks over Nakagami-m fading channels,”IEEE Trans. Veh. Technol., vol. 63, no. 5, pp. 2349–2362, Jun. 2014.

[9] G. Amarasuriya, C. Tellambura, and M. Ardakani, “Two-way amplify-and-forward multiple-input multiple-output relay networks with antennaselection,” IEEE J. Sel. Areas Commun., vol. 30, no. 8, pp. 1513–1529,Sep. 2012.

[10] M. Eslamifar, W. H. Chin, C. Yuen, and Y. L. Guan, “Performanceanalysis of two-way multiple-antenna relaying with network coding,” inProc. IEEE VTC-Fall, Anchorage, Alaska, Sep. 2009, pp. 1–5.

[11] Y. Li, R. H. Y. Louie, and B. Vucetic, “Relay selection with networkcoding in two-way relay channels,” IEEE Trans. Wireless Commun.,vol. 59, no. 9, pp. 4489–4499, Nov. 2010.

[12] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, andProducts, 6th ed. San Diego, CA: Academic Press, 2000.

[13] T. Cui, F. Gao, T. Ho, and A. Nallanathan, “Distributed space-timecoding for two-way wireless relay networks,” IEEE Trans. SignalProcess., vol. 57, no. 2, pp. 658–671, Feb. 2009.

[14] W. Wang, S. Jin, X. Gao, K.-K. Wong, and M. McKay, “Power allocationstrategies for distributed space-time codes in two-way relay networks,”IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5331–5339, 2010.

[15] B. Maham, A. Hjorungnes, and G. Abreu, “Distributed gabba space timecodes in amplify-and-forward relay networks,” IEEE Trans. WirelessCommun., vol. 8, no. 4, pp. 2036–2045, Apr. 2009.

[16] Y. Jing and H. Jafarkhani, “Using orthogonal and quasi-orthogonaldesigns in wireless relay networks,” IEEE Trans. Inf. Theory, vol. 53,no. 11, pp. 4106–4118, Nov. 2007.

[17] M. D. Renzo, H. Haas, and P. M. Grant, “Spatial modulation formultiple-antenna wireless systems: a survey,” IEEE Commun. Mag.,vol. 49, no. 12, pp. 182–191, Dec. 2011.

[18] V. Barousis, A. Kanatas, A. Kalis, and C. Papadias, “A stochasticbeamforming algorithm for ESPAR antennas,” IEEE Antennas WirelessPropag. Lett., vol. 7, no. 1, pp. 745–748, Aug. 2008.

[19] R. Qian, M. Sellathurai, and D. Wilcox, “A study on MVDR beamform-ing applied to an ESPAR antenna,” IEEE Signal Process. Lett., vol. 22,no. 1, pp. 67–70, Jan. 2015.

[20] H. David, Order statistics. New York: Wiley, 1980.

Jing Yang was born in Shandong, China, in 1982.She received her Ph. D. degree in communicationsand information systems from Southwest JiaotongUniversity, Chengdu, in 2013. Since Mar. 2013, shehas been with the School of Information Engineer-ing, Yangzhou University, as a Associate Professor.From Sep. 2015 to Feb. 2016, she was a VisitingScholar in University of Victoria, Canada. Her re-search interests include 5G networks, cooperativeand energy harvesting networks, physical layer se-curity and massive MIMO.

Lei Chen was born in Jiangsu, China, in 1991. Shereceived the B.S. degree in communication engi-neering from Yangzhou University, Jiangsu, in 2009.She is currently working towards her M.S. degree inthe School of Information Engineering, YangzhouUniversity. Her research interests are in cooperativerelaying communications, cognitive radio networks,physical layer security.

Xianfu Lei was born in 1981. He received the Ph.D.degree in communication and information systemsfrom Southwest Jiaotong University, China, in 2012.From 2012 to 2014, he was a Research Fellow withthe Department of Electrical & Computer Engineer-ing, Utah State University, USA. Since 2015, hehas been an Associate Professor with SouthwestJiaotong University. His research interests include5G communications, cooperative communications,and energy harvesting. He has authored over 70research papers on these topics. He received the

Exemplary Reviewer Certificate of the IEEE Communications Letters andan Exemplary Reviewer Certificate of the IEEE Wireless CommunicationsLetters in 2013. He has been a TPC Chair of several international conferencesand workshops, including the most recently the IEEE ICC18 Symposiumon Ad-Hoc and Sensor Networking. He currently serves as an Editor ofthe IEEE COMMUNICATIONS LETTERS and the IEEE ACCESS. He hasserved as a Guest Editor of the IEEE JOURNAL ON SELECTED AREASIN COMMUNICATIONS.

Zhiguo Ding (S’03-M’05) received his B.Eng inElectrical Engineering from the Beijing Universityof Posts and Telecommunications in 2000, and thePh.D degree in Electrical Engineering from ImperialCollege London in 2005. From Jul. 2005 to Aug.2014, he was working in Queen’s University Belfast,Imperial College and Newcastle University. SinceSept. 2014, he has been with Lancaster Universityas a Chair Professor. From Oct. 2012 to Sept. 2019,he has also been an academic visitor in PrincetonUniversity. Dr Ding’ research interests are 5G net-

works, game theory, cooperative and energy harvesting networks and statisticalsignal processing. He is serving as an Editor for IEEE Transactions onCommunications, IEEE Transactions on Vehicular Technology, and Journalof Wireless Communications and Mobile Computing, and was an Editor forIEEE Wireless Communication Letters, IEEE Communication Letters from2013 to 2016. He received the best paper award in IET Comm. Conf.on Wireless, Mobile and Computing, 2009, IEEE Communication LetterExemplary Reviewer 2012, and the EU Marie Curie Fellowship 2012-2014.

PingzhiFan (M’93-SM’99-F’15) received his PhDdegree in Electronic Engineering from the HullUniversity, UK. He is currently a professor anddirector of the institute of mobile communications,Southwest Jiaotong University, China. He is a recip-ient of the UK ORS Award, the Outstanding YoungScientist Award by NSFC, and the chief scientist ofa national 973 research project. He served as generalchair or TPC chair of a number of internationalconferences, and is the guest editor-in-chief, guesteditor or editorial member of several international

journals. He is the founding chair of IEEE VTS BJ Chapter and IEEE ComSocCD Chapter, the founding chair of IEEE Chengdu Section. He also servedas a board member of IEEE Region 10, IET(IEE) Council and IET Asia-Pacific Region. He has over 200 research papers published in various academicEnglish journals (IEEE/IEE/IEICE, etc), and 8 books (incl. edited), and is theinventor of 22 granted patents. His research interests include high mobilitywireless communications, 5G technologies, wireless networks for big data,signal design & coding, etc. He is an IEEE VTS Distinguished Lecturer(2015-2019), and a fellow of IEEE, IET, CIE and CIC.

10 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. X, NO. XX, XXXXX 2018

XiqiGao (S’92-AM’96-M’02-SM’07-F’15) receivedthe Ph.D. degree in electrical engineering fromSoutheast University, Nanjing, China, in 1997. Hejoined the Department of Radio Engineering, South-east University, in April 1992. Since May 2001, hehas been a professor of information systems andcommunications. From September 1999 to August2000, he was a visiting scholar at MassachusettsInstitute of Technology, Cambridge, and Boston U-niversity, Boston, MA. From August 2007 to July2008, he visited the Darmstadt University of Tech-

nology, Darmstadt, Germany, as a Humboldt scholar. His current research

interests include broadband multicarrier communications, MIMO wirelesscommunications, channel estimation and turbo equalization, and multiratesignal processing for wireless communications. From 2007 to 2012, he servedas an Editor for the IEEE Transactions on Wireless Communications. From2009 to 2013, he served as an Associate Editor for the IEEE Transactionson Signal Processing. From 2015 to 2017, he served as an Editor for theIEEE Transactions on Communications. Dr. Gao received the Science andTechnology Awards of the State Education Ministry of China in 1998, 2006and 2009, the National Technological Invention Award of China in 2011, andthe 2011 IEEE Communications Society Stephen O. Rice Prize Paper Awardin the field of communications theory.