Energy Efficient Space Time Line Coded Regenerative Two-Way Relay Under Per-Antenna Power Constraints

Transcription

1 SPECIAL SECTION ON GREEN SIGNAL PROCESSING FOR WIRELESS COMMUNICATIONS AND NETWORKING Received July 29, 2018, accepted August 20, 2018, date of publication August 23, 2018, date of current version Septeber 21, Digital Object Identifier /ACCESS Energy Efficient Space Tie Line Coded Regenerative Two-Way Relay Under Per-Antenna Power Constraints JINGON JOUNG, Senior Meber, IEEE) School of Electrical and Electronics Engineering, Chung-Ang University, Seoul 06974, South Korea e-ail: This research was supported by the National Research Foundation of Korea NRF) grant funded by the Korea Governent MSIT) 2018R1A4A ). ABSTRACT In ultiple-input ultiple-output MIMO) systes, per-antenna power constraint PAPC) has been considered to enhance the power efficiency of the ultiple power aplifiers. Under PAPC, however, a conventional space-division ultiple access SDMA)-based two-way relay TWR) ethod suffers a significant bit-error-rate BER) perforance degradation due to the seriously down-scaled transit power to fulfill the PAPC, which results in energy-efficiency EE) degradation. In this paper, a new space tie line code STLC)-based TWR ethod is proposed to iprove the EE. The proposed ethod can utilize axiu power budget with a low peak-to-average power ratio so that can achieve a better BER perforance at the cost of higher power consuption, as verified in nuerical siulation results. The benefit of the proposed STLC-based TWR ethod is justified in ters of EE. The STLC-based TWR syste achieves higher EE than the conventional SDMA-based TWR when the axiu transit power is low, such as a sall base station with 23-dB axiu transit power. Furtherore, copared with the SDMA-based TWR, the proposed STLC-based TWR can reduce coputational coplexity by order of agnitude two; therefore, it can be readily extended to a TWR syste with a large nuber of antennas, e.g., a assive MIMO syste, which is one of the proising candidates for 5G counications. INDEX TERMS Energy efficiency, peak-to-average power ratio, per-antenna power constraint, spacedivision ultiple access, space-tie line code, two-way relay. I. INTRODUCTION Multiple-input ultiple-output MIMO) two-way relay TWR) syste effectively supports data exchange between two source nodes SNs) within two phases. Various TWR precoders adapted by channel conditions have been rigorously studied, e.g., zero-forcing ZF)-based spatial-division ultiple access SDMA) precoders in [1] [4]. In the MIMO TWR precoder design, a su power constraint SPC) is typically considered at a relay node RN), in which the average su power of all transit antennas is liited due to the available whole transit power budget. The SPC allows very unbalanced power over the transit antennas. In other words, the transit power of certain antennas can be uch greater than that of the others, depending on the channel condition, because an SDMA-based precoding atrix is designed based on the MIMO channel atrix. Since the channels vary over tie, the SDMA-based TWR signals have a high peak-to-average power ratio PAPR). Here, the power aplifiers PAs) practically have a liit on the output power i.e., a nonlinear characteristic with a saturation [5]. Thus, severe signal distortion is inevitable [5], [6]. In addition to the PA nonlinearity, several hardware ipairents, such as phase noise and I/Q ibalance, were studied for TWR systes [7]. On the other hand, to enhance the power efficiency of the ultiple PAs, a per-antenna power constraint PAPC) see [8] and the references therein) can be considered in the TWR precoder design. However, the transit power of SDMAbased TWR signals is significantly scaled down in order to fulfill the PAPC sustaining an orthogonal property of SDMAbased precoding atrix. Therefore, the counication perforance is seriously deteriorated when PAPC is involved as reported in [9]. In this paper, to resolve the issues fro the inherent nature of high PAPR and significantly down-scaled signals of the SDMA-based TWR syste under PAPC, we propose a space-tie line code STLC) based TWR schee IEEE. Translations and content ining are peritted for acadeic research only. Personal use is also peritted, but republication/redistribution requires IEEE perission. See for ore inforation. VOLUME 6, 2018

2 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs FIGURE 1. Phase-1 transission fro SnA and SnB having two antennas each to a TWR node having M antennas by using an STBC schee. The STLC schee is recently proposed in [10] and [11]. The STLC can provide full rate i.e., one sybol delivery per transission) and full-spatial-diversity gain like a spacetie block code STBC) schee [12]. Moreover, the STLC can be readily applied to a large nuber of transit antennas because it can be independently processed for each transit antenna in parallel [11]. Exploiting the STLC characteristic enabling independent operation per transit antenna, the PAPC can be directly applied to each STLC signal sustaining the full spatial diversity gain and reducing the PAPR. Furtherore, the STLC-based TWR requires low coputational coplexity that is linearly proportional to the nuber of transit antennas, i.e., OM), where M is the nuber of transit antennas. On the other hand, the conventional ZF-based SDMA precoders require OM 3 ). Siulation results under the PAPC and the nonlinear PA odel verify that the STLC-based TWR can significantly reduce the PAPR by around 5 db, and at the sae tie, can iprove biterror-rate BER) perforance, at the cost of ore power consuption. To justify the benefit of the proposed STLCbased TWR, energy efficiency EE) of the TWR systes is evaluated. Fro the nuerical results, it is shown that the proposed STLC-based TWR is ore energy efficient than the conventional SDMA-based TWR for a low-power syste whose axiu transit power is low, such as a sall base station and a relay station with transit power up to 23 db. To the best of our knowledge, this study is the first attept to iprove TWR perforance under PAPC by using an STLC schee. A part of the ain contributions of this paper are suarized as follows: A new STLC-based TWR schee is proposed for lowcoplex TWR precoding, spatial diversity gain, and high energy efficiency iproveent. High PAPR issue of the conventional SDMA-based TWR schee is investigated. Coprehensive experients are conducted to justify the high energy efficiency of the proposed STLC-based TWR schee, by coparing to an existing SDMA-based TWR schee. The rest of the paper is organized as follows. Section II briefly describes the existing TWR syste using STBC and SDMA in the first and second phases, respectively, and exaines the high PAPR and significantly down-scaled signal power issues of the conventional SDMA-based TWR schee. In Section III, an STLC-based TWR schee is proposed in the second phase and its PAPR and coputational coplexity are investigated. In Sections IV and V, the perforance of BER and EE is evaluated to justify the proposed STLC-based TWR syste. Section VI concludes this paper. Notations: Superscripts T, H,, and 1 denote transposition, Heritian transposition, coplex conjugate, and inversion, respectively, for any scalar, vector, or atrix. The notation x and x denote the absolute value of x and the 2-nor of vector x, respectively; I and 0 represent an -by- identity and zero atrices, respectively; nullx) gives the span of nullspace of X; and x CN 0, σ 2 ) eans that a coplex rando variable x confors to a noral distribution with a zero ean and variance σ 2. E[x] stands for expectation of a rando variable x. II. TWO-WAY RELAY SYSTEM MODEL Consider a TWR syste, in which two SNs A and B SnA and SnB) with two antennas 1 each exchange their inforation through a two-way RN with M antennas. Here, no direct link between SnA and SnB is considered due to the obstacles as shown in Fig. 1. The channels fro the nth antennas of SnA and SnB to the th antenna of an RN are denoted by h n, = ρh h n, and g n, = ρ g ḡ n,, respectively, where n = {1, 2} and = M = {1,..., M}. Here, ρ h and ρ g are the largescale fading between SnA and RN and between SnB and RN, respectively; and sall-scale fading h n, and ḡ n, are independent and identically distributed i.i.d.) rando variables with CN 0, 1) distribution, i.e., Rayleigh fading channels. Considering a tie division duplex TWR syste, the channels fro SNs to RN and fro RN to SNs are assued 1 This configuration is erely for the siple description of a spatialdiversity transceiver. For the SNs with ore than two antennas, the nonorthogonal STBC and STLC schees can be applied with a rate lower than one during the first and second phases, respectively. VOLUME 6,

3 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs to be syetric. To obtain full channel state inforation CSI), a typical channel estiation ethod that uses tieorthogonal training sequences/pilots is considered. Here, SN requires at least M-tie slots to estiate the channels fro RN to SN, while RN does only four-tie slots to estiate the channels fro SNs to RN. Considering M 2, full CSI assuption is ore reasonable at the RN rather than SNs. A. FIRST PHASE: STBC-BASED TRANSMISSION FROM SOURCE NODES Following the spatial-diversity transceiver structure introduced in [10], an STBC transission is considered during the first phase, as shown in Fig. 1. Note that the proposed schee in this paper later is for TWR in the second phase, and that any type of transission schees can be applied to the first phase without affecting the proposed schee. For the first tie slot t 1, SnA transits two inforation sybols [a 1, a 2 ] to the RN by using two antennas. At the sae tie, SnB transits [b 1, b 2 ] by using two antennas. Subsequently, SnA and SnB transit [a 2, a 1 ] and [b 2, b 1 ], respectively, at the second tie slot t 2. Here, without loss of generality, the average sybol power is assued to one, i.e., E[ a 2 ] = E[ b 2 ] = 1, and the transit power of SNs is liited per transit antenna by P S, i.e., PAPCs [8]. Thus, under the PAPCs, each inforation sybol is scaled by PS before the transission. The received signals r 1, and r 2, at the th antenna of the RN at t 1 and t 2, respectively, are then written as follows: [ a1 a r1, r 2, = h1, h ] 2, PS 2 a 2 a 1 + [ b1 b g 1, g ] 2, PS 2 b 2 b 1 n1, + 1) n 2, where n t, is the additive white Gaussian noise AWGN) at the th antenna at tie slot t with i.i.d. eleents, each of which follows a noral distribution CN 0, σ 2 ). The RN reconstructs two consecutively received signals r 1, and r 2, at the th antenna to a vector for as follows: r1, r = = P S H a + P S G b + n, 2) where r 2, h1, h H = 2, h 2, h 1, g1, g G = 2, g 2, g, 1, a1 a =, a 2 b1 b =, b 2 n1, n =. n 2, Then, the RN ultiplies H H and GH to the r in order to detect [a 1, a 2 ] and [b 1, b 2 ], respectively, as follows: H H r = γ h, PS a + P S H H G b + H H n, G H r = P S G H H a + γ g, PS b + G H n, where = 1,..., M, and γ h, = h 1, 2 + h 2, 2, γ g, = g 1, 2 + g 2, 2. 3a) 3b) 4a) 4b) By suing all the resultant signals through M antennas in 3a), the RN obtains H H r = P S γ h, a + P S H H G b + G H r = P S + H H n, G H H a + P S G H n. γ g, b 5a) 5b) The RN then reconstructs the signals in 5a) as follows: [ HH r ] [ [ a GH r = Ɣ + b] HH n ] GH n, 6) where Ɣ is the effective channel atrix fro SNs to RN that is written as [ PS Ɣ = γ h,i 2 PS HH G ] PS GH H PS γ. 7) g,i 2 Applying a linear detector to 6), the RN obtains the estiates of a and b as follows: [ã ] [ = Ɣ b 1 HH r ] GH r [ [ a = + Ɣ b] 1 HH n ] GH n. 8) Fro the estiates in 8), RN detects and regenerates â and ˆb to relay the to SNs in the second phase. B. SECOND PHASE: SDMA-BASED TRANSMISSION FROM TWR NODE The second phase of counication is shown in Fig. 2. A TWR node forwards â and ˆb to SnB and SnA, respectively, by using a conventional ZF-based SDMA technique [1] [4], under PAPC by P R. The channels fro an RN to antenna n of SnA and SnB are syetric to the channels fro SNs to RN, and thus, they are represented as the row vectors and h n = [h n,1 h n, h n,m ] g n = [g n,1 g n, g n,m ], VOLUME 6, 2018

4 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs FIGURE 2. Phase-2 transission fro a TWR node to two SNs by using conventional SDMA and channel inversion schees. respectively. The channel atrices fro RN to SnA and SnB are represented by h1 H = C 2 M g1 and G = C 2 M, h 2 g 2 respectively. Full CSI, i.e., H and G, is assued to be available at the RN through the channel estiation during the first phase. The RN forwards â and ˆb after SDMA and channel inversion precodings. The received signals at SnA and SnB at t 3 are then written as follows: ) y A = HD W G T A ˆb + W H T B â + z A, 9a) ) y B = GD W G T A ˆb + W H T B â + z B, 9b) where D R M M is a real-value diagonal atrix for PAPCs; W G = nullg) C M 2 and W H = nullh) C M 2 are SDMA precoding atrices such that GW G = 0 2 and HW H = 0 2 ; T A = HW G ) 1 C 2 2 and T B = GW H ) 1 C 2 2 are ZF-based channel inversion precoding atrices; and z A C 2 1 and z B C 2 1 are the AWGN vectors at SnA and SnB, respectively. Here, for the ZF-based SDMA precoding, M 4. Note that if full CSI is unavail at the SNs when M is very large, a ZF-based channel inversion strategy at RN can be a reasonable approach to eliinate the self-interference. Here, the structure of D should be αi M to sustain the orthogonal property of SDMA, i.e., GDW G = 0 2 and HDW H = 0 2. At the sae tie, D = αi M fulfills the PAPCs, such that E α [ ] W G T A ˆb + W H T B â 2) P R, M, 10) where [x] is the th eleent of a vector x. Therefore, the α is upper bounded as follows: α α ax = in E PR [ ] W G T A ˆb + W H T B â 11) 2). The PAPC in 11) is a stringent constraint copared to the conventional SPC that is derived as follows: MPR α E W G T A ˆb + W H T B â. 12) By virtue of the orthogonal property of SDMA, naely HW H = 0 2 and GW G = 0 2, the self-interferences disappear fro the received signals in 9a) as follows: ) y A = αh W G T A ˆb + W H T B â + z A 13a) = αhw G T A ˆb + z A 13b) = αˆb + z A, 13c) ) y B = αg W G T A ˆb + W H T B â + z B 13d) = αgw H T B â + z B 13e) = αâ + z B. 13f) Dividing the received signals in 13a) by α, the SNs obtain the estiates of â and ˆb as follows: â = â + z B α, 14) ˆb = ˆb + z A α. 15) To axiize the SNRs of the received signals in 14), obviously, α = α ax and it can be known at all SNs through broadcasting it fro RN, which is a arginal signaling overhead. C. TRANSMIT POWER PER ANTENNA OF SDMA-BASED TWR NODE In Fig. 3, the transit power over 10 4 sybols of each antenna of an SDMA-based TWR is shown when M = 40 and P R = 4 db. As shown, the transit power across 40 antennas changes significantly. The highly dynaic transit power across the transit antennas for one channel realization iplies that high PAPR per antenna for varying channels, resulting in the PA ipairent due to the nonlinearity of the PA [5]. Furtherore, PAPC suppresses the transit power exceeding the liit P R. Thus, if the largest transit power i.e., the first antenna in the exaple in Fig. 3) exceeds the liit, it is scaled down to fulfill the PAPC. Here, the transit VOLUME 6,

5 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs y A,1,2 = h 1, α h 2, ˆb 1 h 1, ˆb 2 ) + g 2,â 1 g 1,â2) )) + z A,1,2, 17b) y A,2,1 = h 2, α h 1, ˆb 1 + h 2, ˆb 2 ) + g 1,â1 + g 2,â 2 ))) + z A,2,1, 17c) y A,2,2 = h 2, α h 2, ˆb 1 h 1, ˆb 2 ) + g 2,â 1 g 1,â2) )) + z A,2,2, 17d) FIGURE 3. Transit power per antenna of SDMA under PAPC when M = 40 and P R = 4 db. The transit power is averaged for 10 4 sybols with one channel realization. power of all other antennas, even though whose transit power already eets the PAPC, will be scaled down with the sae scaling factor to sustain the SDMA property as stated in the previous subsection. Therefore, the low-power transission ay degrade the counication perforance severely. This conjecture is true as verified by siulation in Section IV. To resolve these issues, in the next section, we propose an STLC-based TWR ethod, which allows for RN to exploit high-power around its axiu) transission with low PAPR. III. PROPOSED STLC-BASED TWR SYSTEM In this section, we proposed an STLC-based TWR schee in the second phase counications as shown in Fig. 4. Note that the first phase is the sae as that described in Section II.A. In the second phase, the RN encodes â and ˆb, which are obtained through the first phase counications, to an STLC sybol vector as follows: s 1, h1, h = α 2, [ˆb ] s 2, h 2, h 1 1, ˆb 2 [â ]) g1, g + 2, 1 g 2, g, 16) 1, â 2 where s t, is the STLC sybol that is transitted through the th transit antenna at tie t {t 3 = 1, t 4 = 2}, and α is a scaling factor obtained as α = P R / γ h, + γ g,, such that E[ α s t, 2 ] = P R to satisfy PAPCs. Then, during the second phase, to relay â and ˆb, the RN broadcasts s 1, and s 2, through the th antenna at the first- and second-tie slots, respectively and sequentially. Consequently, the received signals fro all M antennas at SnA are written as follows: y A,1,1 = h 1, α h 1, ˆb 1 + h 2, ˆb 2 ) +g 1,â1 + g 2,â 2 ))) + z A,1,1, 17a) where y A,1,t and y A,2,t are the received signals at the first and second antennas of SnA, respectively, at tie slot t {t 3, t 4 }, and z A,1,t and z A,2,t are the corresponding AWGNs. Now, SnA cobines the received signals, i.e., STLC decoding [10], [11], and then divides the cobined signals by the effective channel gain fro RN to SnA, that is derived as γ h = α γ h,, to obtain the estiates ˆb 1 and ˆb 2 of ˆb 1 and ˆb 2 as follows: ˆb 1 = y A,1,1 + y A,2,2 γ h = ˆb α h1, g 1, γ + h 2, g 2,)â 1 h + h 1, g 2, h 2, g 1,)â 2 ) ) + z A,1,1 + z A,2,2, 18a) γ h ˆb 2 = y A,1,2 + y A,2,1 γ h = ˆb α h1, g 2, γ + h 2, g 1,)â 1 h + h 1, g 1, + h 2, g ) ) 2,)â 2 z A,1,2 z A,2,1. 18b) γ h In 18a), the effective channel gain γ h can be readily estiated at the SnA. Here, we note that the self-interferences, which are the second ters in the right-hand side of 18a) and 18b), are difficult to be eliinated at the SNs, because it is difficult to estiate the coupled interference channels without the additional signaling overhead. However, by virtue of the sufficiently large effective channel gain γ h, the self-interferences can be suppressed as verified in Section IV. Concurrently, the received signals at SnB are written as follows: y B,1,1 = g 1, α h 1, ˆb 1 + h 2, ˆb 2 ) + g 1,â1 + g 2,â 2 ))) + z B,1,1, 19a) y B,1,2 = g 1, α h 2, ˆb 1 h 1, ˆb 2 ) + g 2,â 1 g 1,â2) )) + z B,1,2, 19b) VOLUME 6, 2018

6 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs FIGURE 4. Phase-2 transission fro a TWR node to two SNs by using the proposed STLC-based TWR schee. y B,2,1 = g 2, α h 1, ˆb 1 + h 2, ˆb 2 ) + g 1,â1 + g 2,â 2 ))) + z B,2,1, 19c) y B,2,2 = g 2, α h 2, ˆb 1 h 1, ˆb 2 ) + g 2,â 1 g 1,â2) )) + z B,2,2, 19d) where y B,1,t and y B,2,t are the received signals at the first and second antennas of SnB, respectively, at tie slot t {t 3, t 4 }, and z B,1,t and z B,2,t are corresponding AWGN. Following the sae procedure as the SnA, the SnB obtains the estiates of â 1 and â 2, denoted by â 1 and â 2, respectively, as follows: â 1 = y B,1,1 + y B,2,2 γ g = â α g1, h 1, γ + g 2, h 2,)ˆb 1 g +g 1, h 2, g 2, h 1,)ˆb 2 ) ) + z B,1,1 + z B,2,2 γ g, 20a) â 2 = y B,1,2 + y B,2,1 γ g = â α g1, h 2, γ + g 2, h 1,)ˆb 1 g + g 1, h 1, + g 2, h 2,)ˆb 2 ) ) z B,1,2 z B,2,1 γ g, 20b) where γ g = α γ g, is the effective channel gain fro RN to SnB. Reark 1: The proposed STLC-based TWR ethod transits two sybols per transission i.e., a 1, a 2, b 1, and b 2 for t 3 and t 4 ), while the SDMA-based TWR ethod in Section II.B transits four sybols per transission i.e., a 1, a 2, b 1, and b 2 for t 3 ). Thus, the spectral efficiency of the proposed STLC-based TWR syste is half that of the conventional SDMA-based TWR syste. The spectral efficiency decrease of the proposed STCL-based TWR ethod FIGURE 5. Average transit power per antenna of an STLC-based syste with PAPC when M = 40 and P R = 4 db. The average is perfored for 10 4 sybols with one channel realization. will be considered for the fair coparison with the SDMAbased TWR ethod, in Section IV. Reark 2: The iniu nuber of required antennas at TWR is four for the ZF-based SDMA precoding to transit two sybols per transission through rank-2 null-space, i.e., M 4, while it is only one, i.e., M 1, for the proposed STLC-based TWR. A. TRANSMIT POWER PER ANTENNA OF STLC-BASED TWR NODE Fig. 5 shows the average transit power over 10 4 sybols of each antenna of STLC-based TWR node when M = 40 and P R = 4 db. As observed, the transit power is alost evenly distributed across 40 antennas under PAPC. Fro the evenly distributed transit power, lower PAPR and efficient PA operation are expected copared to the SDMAbased TWR syste in Section II.C. Fig. 6 shows the copleentary cuulative distribution function CCDF) of PAPR. Here, it is observed that the proposed STLC-based TWR can reduce PAPR ore than around 5 db. Coparing the results VOLUME 6,

7 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs FIGURE 6. PAPR perforance coparison between SDMA-based and STLC-based TWR ethods when M = 40 and P R = 4 db. FIGURE 7. BER perforance across transit power when M = 8 and d = 500, under PAPC. in Figs. 3 and 5, it is clear that the proposed STLC-based TWR transitter consues ore power than the SDMAbased TWR. Here, it should be reephasized that the proposed STLC-based schee fully utilizes the axiu transit power of PAs efficiently, with low PAPR. B. COMPLEXITY COMPARISON Since the first phase is coon for the proposed STLC-based and bencharking SDMA-based schees, we copare the encoding and decoding coplexity in the second phase, which is a coplexity bottleneck. The coplexity order of the proposed STLC encoding at RN is OM) and that of the decoding at SNs is O1). Thus, the coplexity order of the proposed STLC-based TWR is OM). Since the coplexity increases linearly proportional to the nuber of transit antennas, the proposed STLC-based TWR is applicable to a syste with a large nuber of transit antennas, e.g., assive MIMO systes. On the other hand, the coputational coplexity of the SDMA-based schee is OM 3 ) due to the null ) operation and inversion of an M-by-2 coplex-valued atrix. The significant coputational coplexity of the conventional SDMA-based TWR hinders the TWR systes fro being eployed to the MIMO systes with assive antennas. IV. BER PERFORMANCE EVALUATION AND COMPARISON Now, the BER perforances of the proposed STLC-based and conventional SDMA-based TWR ethods are copared under PAPC. For the first phase, 200 quadrature phase-shift keying QPSK) odulated sybols are transitted fro each SN. In the second phase, for the fair coparison of the STLC- and SDMA-based TWR ethods, the data transission rates are set to be identical to each other. Concretely, the STLC-based TWR forwards the QPSK sybols, while the SDMA-based TWR forwards binary phase-shift keying BPSK) sybols, for the sae transission tie. Note that the spectral efficiency of the STLC-based ethod is half that of the SDMA-based ethod as stated in Section III.A. The path loss is odeled as ρ h = ρ g ρ = log 10 d µ ) on db scale, where G includes the transceiver feeder loss and antenna gains, d µ is the path loss for the distance d between nodes in eter), and µ is a path loss exponent. The sall-scale fading is odeled as Rayleigh fading with a zero ean and a unit variance. In our siulation, we set G = 5 db and µ = The su transit power of SN and that of RN is identical to each other, i.e., 2P S = MP R, and the noise figure is set by 174 db. In Fig. 7, the BER perforance is evaluated across transit power when the nuber of transit antennas is eight, i.e., M = 8. An ideal PA odel and a practical nonlinear PA odel are considered. The ideal PA linearly aplifies the input signals for a whole range of transitting power. The nonlinear PA is odeled as a soft liiter, in which the transit signal is clipped, such that its power to be equal to the axiu transit power of the PA if the signal power exceeds the axiu power of the PA [5]. In general, the BER perforance of both SDMA- and STLC-based TWR schees obviously iproved as the transit power budget i.e., P S and P R ) increases. Since the proposed STLC-based TWR syste perfors alost always full-power transission see Fig. 5), it is sensitive against the PA odels, resulting in nonnegligible perforance degradation due to the clipping effect when a nonlinear PA odel is involved. However, the proposed STLC-based TWR under PAPC is clearly superior to the SDMA-based TWR schee, regardless of the PA odels. Here, it should be reephasized that the proposed STLC-based TWR achieves saller PAPR around 5 db copared to the SDMA-based TWR syste see Fig. 6). The proposed STLC-based TWR perforance is saturated at a high power regie due to the residual selfinterferences. The residual self-interference effect can be reduced by increasing the effective channel gain γ h and γ g VOLUME 6, 2018

8 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs FIGURE 8. BER perforance across transit power when M = 40 and d = 500, under PAPC. FIGURE 9. BER perforance across the nuber of transit antennas when 2P S = MP R = 26 db and d = 500, under PAPC. in 18a) and 20a), respectively, with ore transit antennas as shown in Fig. 8. Here, no saturation is observed up to MP R = 40 db, which is oitted in the results. As discussed in Sections II.C and shown in Fig. 3, the transit power of SDMA-based TWR is significantly scaled down in order to fulfill the PAPC sustaining the orthogonal property of the SDMA-based precoding atrices. Therefore, the SDMAbased TWR systes under PAPC are robust against the PA odels. In other words, the SDMA-based TWR signals are linearly aplified. However, the BER perforance of the SDMA-based TWR under PAPC is worse than that of the proposed STLC-based TWR schee due to the inherently low-power SDMA signals. As the transit power increases, the BER perforance of the SDMA-based TWR keeps being iproved without saturation since the self-interferences are perfectly canceled out. In Fig. 9, the BER perforance is evaluated for various M. As expected, the perforance is iproved as M increases due to the suppressed interference for the STLC-based TWR case) and increased effective channel gain for both STLC- and SDMA-based TWR cases). The nonlinear PA effect, i.e., perforance degradation, increases as M increases for the STLC-based TWR syste. However, the proposed STLC-based TWR syste outperfors the conventional SDMA-based TWR regardless of M. V. ENERGY EFFICIENCY COMPARISON Note that the BER perforance iproveent of the proposed STLC-based TWR can be achieved at the cost of ore power consuption as discussed in Section III.A. Thus, in order to justify the benefit of the proposed STLC-based TWR ethod, the energy efficiency EE) should be copared. The EE, denoted by η, is fundaentally defined as a ratio of spectral efficiency bits/sec/hz) to the power consuption Watt) as follows [13] [15]: η = Spectral Efficiency [bits/sec/hz/watt], 21) Power Consuption and its unit turns to be bits/hz/joule. In the following siulation, η is easured by the ratio of the nuber of transit bits reliably relayed without error to the SNs during the second phase to the total power consuption for the retransissions in the second phase as follows [14], [16]: Tt=1 1 ɛ)n) η = Tt=1 c M P + MP fix T [bits/hz/joule], 22) where ɛ is BER for N-bit data transission for T ties; c represents syste inefficiency c > 1) that is caused by overhead power consuption at radio frequency circuits; P is the transit power of antenna ; P fix is the fixed power consuption per tie slot. In the siulation, N = 100 and T = The paraeters related to the power consuption are set as follows [13] [15]: c = 5.26 and P fix = 45 db. Nonlinear PA is considered and other paraeters are the sae as the paraeters used in Section IV. In Fig. 10, EE perforance bits/hz/j) across the transit power of TWR is shown. When the nuber of transit antenna increases fro eight to 40, the EE decreases because the power consuption increases faster than the increase of the transission rate. Note that spectral efficiency is a logarithic function with respect to the transit power, while the power consuption is linearly proportional to the transit power. Due to the siilar reason, as the transit power of TWR, i.e., P R, increases, the EE increases up to a certain point and turns to decrease. It is observed that the EE of the proposed STLC-based TWR is greater than that of the conventional SDMA-based TWR when the transit power is low, i.e., MP R < 32 db, which is clearer when M = 8. However, when the transit power is large, i.e., MP R > 32 db, the conventional SDMA-based TWR outperfors the proposed STLC-based TWR ethod. To further clearly copare the EEs, the EE perforance iproveent %) of the proposed STLC-based TWR copared to the VOLUME 6,

9 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs FIGURE 10. EE perforance across transit power P R of TWR. FIGURE 12. EE perforance across the nuber of transit antennas M. FIGURE 11. EE iproveent %) of the proposed STLC-based TWR syste copared to the SDMA-based TWR syste across transit power P R of TWR. SDMA-based TWR is shown in Fig. 11. Fro the results, it is clearly observed that the proposed STLC-based TWR has EE benefit when MP R < 29 db for M = 40 and when MP r < 32 db for M = 8. The axiu EE iproveent is around 12% when M = 40. In Fig. 12, EE perforance is evaluated across the nuber of transit antennas M when the total transit power of each node is 23 db i.e., 2P S = MP r = 26 db) and 43 db i.e., 2P S = MP r = 46 db). The case when the total transit power is 23 db can be interpreted as a case for a low-power syste including a sall base station. On the other hand, the case when the total transit power is 43 db can be interpreted as a case for a high-power syste including a acro base station. Fro the results, it is observed that the EE decreases as M increases owing to the reason discussed in Fig. 10. Clearly, for a low-power syste, the proposed STLC-based TWR schee provides higher EE than the conventional SDMA-based TWR schee, regardless of the nuber of transit antennas. However, the proposed schee is inferior FIGURE 13. EE iproveent %) of the proposed STLC-based TWR syste copared to the SDMA-based TWR syste across the nuber of transit antennas M. to the conventional schee for a high-power syste. This result is further clearly observed in Fig. 13. For the lowpower systes with P S = {3, 13, 23} db, the proposed STLC-based TWR outperfors the conventional SDMAbased TWR in ters of EE. VI. CONCLUSION In this paper, an STLC-based TWR ethod with M antennas is proposed. Under PAPC and with nonlinear PAs, coparing to a conventional SDMA-based TWR syste, we verify that the proposed ethod achieves three erits, at the cost of higher power consuption: i) PAPR reduction by around 5 db, ii) coplexity reduction fro OM 3 ) to OM), iii) EE iproveent for the low-power systes. REFERENCES [1] J. Joung and A. H. Sayed, Multiuser two-way aplify-and-forward relay processing and power control ethods for beaforing systes, IEEE Trans. Signal Process., vol. 58, no. 3, pp , Mar VOLUME 6, 2018

10 J. Joung: Energy-Efficient Space Tie Line-Coded Regenerative TWR Under PAPCs [2] J. Joung and A. H. Sayed, User selection ethods for ultiuser two-way relay counications using space division ultiple access, IEEE Trans. Wireless Coun., vol. 9, no. 7, pp , Jul [3] J. Joung, Beaforing vector design for regenerative wired two-way relay systes, Electron. Lett., vol. 53, no. 9, pp , Apr [4] J. Joung and J. Choi, Linear precoder design for an AF two-way MIMO relay node with no source node precoding, IEEE Trans. Veh. Technol., vol. 66, no. 11, pp , Nov [5] J. Joung, C. K. Ho, K. Adachi, and S. Sun, A survey on power-aplifiercentric techniques for spectru- and energy-efficient wireless counications, IEEE Coun. Surveys Tuts., vol. 17, no. 1, pp , 1st Quart., [6] S. B. Sliane, Reducing the peak-to-average power ratio of OFDM signals through precoding, IEEE Trans. Veh. Technol., vol. 56, no. 2, pp , Mar [7] K. Guo, D. Guo, and B. Zhang, Perforance analysis of two-way ultiantenna ulti-relay networks with hardware ipairents, IEEE Access, vol. 5, pp , [8] J. Choi, S. Han, and J. Joung, Low-coplexity ultiuser MIMO precoder design under per-antenna power constraints, IEEE Trans. Veh. Technol., to be published. [Online]. Available: [9] A. Wiesel, Y. C. Eldar, and S. Shaai, Zero-forcing precoding and generalized inverses, IEEE Trans. Signal Process., vol. 56, no. 9, pp , Sep [10] J. Joung, Space tie line code, IEEE Access, vol. 6, pp , [11] J. Joung, Space tie line code for assive MIMO and ultiuser systes with antenna allocation, IEEE Access, vol. 6, pp , [12] S. M. Alaouti, A siple transit diversity technique for wireless counications, IEEE J. Sel. Areas Coun., vol. 16, no. 8, pp , Oct [13] J. Joung, C. K. Ho, and S. Sun, Spectral efficiency and energy efficiency of OFDM systes: Ipact of power aplifiers and countereasures, IEEE J. Sel. Areas Coun., vol. 32, no. 2, pp , Feb [14] J. Joung and S. Sun, EMA: Energy-efficiency-aware ultiple access, IEEE Coun. Lett., vol. 18, no. 6, pp , Jun [15] J. Joung, Y. K. Chia, and S. Sun, Energy-efficient, large-scale distributedantenna syste L-DAS) for ultiple users, IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp , Oct [16] Y. Sankarasubraania, I. F. Akyildiz, and S. W. McLaughlin, Energy efficiency based packet size optiization in wireless sensor networks, in Proc. 1st IEEE Int. Workshop Sensor Netw. Protocols Appl., Anchorage, AK, USA, May 2003, pp JINGON JOUNG S 03 M 07 SM 15) received the B.S. degree in radio counication engineering fro Yonsei University, Seoul, South Korea, in 2001, and the M.S. and Ph.D. degrees in electrical engineering and coputer science fro the Korea Advanced Institute of Science and Technology KAIST), Daejeon, South Korea, in 2003 and 2007, respectively. He was a Scientist with the Institute for Infoco Research, Agency for Science, Technology and Research, Singapore. He joined Chung-Ang University CAU), Seoul, in He was a Post-Doctoral Research Scientist with KAIST in 2017 and a Postdoctoral Fellow with the University of California at Los Angeles, Los Angeles, CA, USA, in He is currently an Assistant Professor with the School of Electrical and Electronics Engineering, CAU, and a Principal Investigator with the Wireless Systes Laboratory. His research activities are in the areas of ultiuser systes, ultiple-input ultiple-output counications, and cooperative systes. His current research area/interests include energy-efficient ICT, IoT, and achine learning algoriths. Dr. Joung was recognized as the Exeplary Reviewer fro the IEEE COMMUNICATIONS LETTERS in 2012 and the IEEE WIRELESS COMMUNICATIONS LETTERS in 2012 and He was a recipient of the Best Paper Award at the Korean Institute of Counications and Inforation Sciences conference in 2018 and 2018 and the First Prize at the Intel-ITRC Student Paper Contest in He has been serving as an Associate Editor for the IEEE TRANSACTIONS VEHICULAR TECHNOLOGY since He served as a Guest Editor for the IEEE ACCESS for special section Recent Advanced in Full- Duplex Radios and Networks in He has been serving on the Editorial Board of the APSIPA Transactions on Signal and Inforation Processing since VOLUME 6,