wireless diversity OFDM systems

Electric Power Systems Research 121 (2015) 200–206

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Optimal subcarrier pairing for MRC in powerline/wireless diversity OFDM systems Yu-Suk Sung a , Yong-Hwa Kim b , Illsoo Sohn c , Seong-Cheol Kim a , Jong-Ho Lee c,∗ a Institute of New Media and Communications, Department of Electrical and Computer Engineering, Seoul National University, Seoul 151-742, Republic of Korea b Department of Electronic Engineering, Myongji University, Yongin, Gyeonggi 449-728, Republic of Korea c Department of Electronic Engineering, Gachon University, Seongnam, Gyeonggi 461-701, Republic of Korea

a r t i c l e

i n f o

Article history: Received 7 August 2014 Received in revised form 20 November 2014 Accepted 17 December 2014 Keywords: Subcarrier pairing Maximal ratio combining (MRC) Orthogonal frequencydivision multiplexing (OFDM) Powerline/wireless diversity

a b s t r a c t In this paper, we consider the parallel use of powerline/wireless orthogonal frequency division multiplexing (OFDM) systems for robust smart grid communication, where the powerline and wireless subcarriers are paired to perform maximal ratio combining (MRC). An optimal subcarrier pairing scheme is proposed to maximize the data rate for MRC reception in powerline/wireless diversity OFDM systems. We verify the performance enhancement of the proposed optimal subcarrier pairing scheme by varying the system and channel parameters. Numerical results show that the proposed scheme provides about 15–30 Mbps of higher data rate, which corresponds to a capacity gain of about 5–22%, compared to the pairing scheme without specific intelligence. Performance improvement in terms of outage probability is also shown. © 2014 Elsevier B.V. All rights reserved.

1. Introduction In recent years, smart grid techniques have attracted growing attention owing to their inherent capacity to realize a future energy management system by using intelligent grids [1]. Smart grid systems require an interactive, bi-directional communication network between power grid companies and consumers for enhancing the energy efficiency, safety, and reliability of electricity transmission. The communication network for smart grids must be highly reliable, because the distribution grid should possess robustness and stability to respond to changes. Therefore, the parallel use of different communication networks is expected to play a significant role in the realization of a robust smart grid communication, because the probability of different communication links simultaneously shutting down is extremely low. As described in [2–5], the powerline communication network collaborates with the wireless network, which enhances the robustness and link quality even though the powerline/wireless

∗ Corresponding author. Tel.: +82 31 750 5321. E-mail addresses: [email protected] (Y.-S. Sung), [email protected] (Y.-H. Kim), [email protected] (I. Sohn), [email protected] (S.-C. Kim), [email protected] (J.-H. Lee). http://dx.doi.org/10.1016/j.epsr.2014.12.016 0378-7796/© 2014 Elsevier B.V. All rights reserved.

collaboration requires additional installation cost. A wireless relaying system assisted by the powerline network in an indoor environment has been studied in [2]. In [3], it has been proven that by combining the powerline and wireless networks, the physical layer performance can be improved and the resulting spatial diversity gain can increase the whole system throughput. It is described in [4] that a wireless/powerline combined network outperforms a single wireless or powerline network, in smart home networking, in terms of the network energy cost, network overhead, and average latency. Furthermore, it is described in [5] that the hybrid powerline/wireless architecture forms a reliable, high-capacity, and cost-effective access network, and so has been installed in rural environments to provide both broadband services and smart grid services. Let us consider the parallel use of powerline/wireless orthogonal frequency division multiplexing (OFDM) networks [3]. Since multiplexing approach to increase the data rate in two distinct powerline and wireless channels is relatively simple as noted in [3], it is assumed that a data symbol is simultaneously transmitted through both the powerline and wireless subcarriers to enhance reliability by using the powerline/wireless diversity combining. The receiver is assumed to perform maximal ratio combining (MRC) or saturated metric combining (SMC), which are considered to be practical schemes. It can be noted that, in [3], an OFDM signal is

Y.-S. Sung et al. / Electric Power Systems Research 121 (2015) 200–206 Table 1 Summary of the notations used in the paper. Notation

Definition

NP NW 

The number of subcarriers of the powerline system The number of subcarriers of the wireless system The set of the indices of the powerline subcarriers to be paired with the wireless subcarriers Subcarrier index of powerline system Subcarrier index of wireless system which is paired with pi th subcarrier Subcarrier pairing for pi th powerline subcarrier. For pi ∈ , i = (pi , qi ) and for pi ∈ / , i = pi Received signal by the powerline system at the pi th subcarrier Powerline complex channel coefficient at the pi th subcarrier Data symbol transmitted at the pi th subcarrier Transmit power of the powerline system at each subcarrier Colored background noise of the powerline at the pi th subcarrier Variance of the zP [pi ] Received signal by the wireless system at the qi th subcarrier Wireless complex channel coefficient at the qi th subcarrier Transmit power of the wireless system at each subcarrier AWGN of the wireless system at the qi th subcarrier with a variance of ZW SNR of the powerline system at the pi th subcarrier SNR of the wireless system at the qi th subcarrier Received signal after the MRC over the subcarrier pair i Additive noise after the MRC over the subcarrier pair i SNR after the combining through the subcarrier pair i

pi qi i yP HP [pi ] s[pi ] PP zP [pi ] ZP [pi ] yW [qi ] HW [qi ] PW zW [qi ]  P [pi ]  W [qi ] yMRC [i ] zMRC [i ]  MRC [i ]

generated by a single OFDM modulator and two identical copies of the OFDM signal are transmitted via both the powerline and wireless channels. This implies that the powerline and wireless networks should use the same OFDM parameters. The powerline and wireless OFDM systems considered in this study have different numbers of subcarriers. Further, two independent OFDM modulators are used so different OFDM signals are transmitted via the powerline and wireless channels. Since SMC requires additional parameters to characterize the impulsive noise in powerline channels and is specialized for maximum-likelihood (ML) detection [3], we focus on MRC powerline/wireless diversity OFDM systems. In [6], we proposed an optimal subcarrier pairing scheme for MRC considering PLC system only where the pairing occurs within powerline subcarriers in order to improve the reliability of the powerline networks. In this study, similar approach is extended to the powerline/wireless diversity systems. A narrowband PLC over medium voltage (MV) distribution networks is gaining the attention for the application of smart grid [7,8]. It is expected that a broadband PLC over MV networks also can be a consideration for future smart grids as described in [9]. We consider the broadband powerline OFDM with a 30 MHz bandwidth [10], and the MV powerline channel model described in [11]. It is assumed that the powerline noise is composed of colored background noises [11] and impulsive noises [12]. The rest of this paper is organized as follows. Section 2 describes powerline/wireless diversity channels and analyzes the information theoretic performance. In Section 3, we propose an optimal subcarrier pairing scheme to maximize the data rate for MRC diversity reception. Numerical results are presented in Section 4 to verify the performance enhancement of the proposed scheme. Finally, conclusions are drawn in Section 5. The notations used in the paper are listed in Table 1.

alternatively as or cooperatively with a powerline network. In this study, we assume that the objective of the wireless network is to cooperate with the powerline network, and thereby the wireless network assists the powerline network. All the powerline subcarriers are assumed to carry different data symbols, and one of the wireless subcarriers is paired with a powerline subcarrier. The paired powerline and wireless subcarriers are modulated using the same data symbol and thereby the wireless connection achieves network survivability in the case where the powerline connection is lost [5]. The number of subcarriers for the powerline and wireless OFDM systems are denoted as NP and NW , respectively. In this study, we consider two different scenarios as follows: • When NP > NW , NW powerline subcarriers among NP subcarriers are paired with NW wireless subcarriers and NP − NW powerline subcarriers are used without pairing. • When NP ≤ NW , NP wireless subcarriers among NW subcarriers assist NP powerline subcarriers and the remaining NW − NP wireless subcarriers are assumed to be used for other wireless services. Let us define  as a set of indices of the powerline subcarriers to be paired with the wireless subcarriers with a cardinality of || ≤ NP . The signal received by the powerline receiver at the pi th subcarrier can be expressed as



yP [pi ] = H P [pi ]

P P s[pi ] + z P [pi ],

(1)

where s[pi ] denotes the data symbol transmitted at the pi th subcarrier with E[|s[pi ]|2 ] = 1, HP [pi ] is the powerline complex channel coefficient at the pi th subcarrier, PP denotes the transmit power of the powerline transmitter at each subcarrier, and zP [pi ] is the colored background noise at the powerline receiver with a variance of ZP [pi ]. For pi ∈ , we assume the subcarrier pairing of i = (pi , qi ), where both the pi th powerline subcarrier and the qi th wireless sub/ , the subcarrier pairing carrier carry the same data symbol. For pi ∈ is simply expressed as i = pi . The signal received by the wireless receiver at the qi th subcarrier is expressed as



yW [qi ] = H W [qi ]

P W s[pi ] + z W [qi ],

(2)

where HW [qi ] is the wireless complex channel coefficient, PW denotes the transmit power of the wireless transmitter at each subcarrier, and zW [qi ] is the additive white Gaussian noise (AWGN) at the wireless receiver with a variance of ZW . For pi ∈ , the received signals in (1) and (2) are combined using the MRC [3] expressed as √ √ ∗ ∗ P P (H P [pi ]) P P W (H W [qi ]) W y yMRC [i ] = [p ] + y [qi ] i P W Z [pi ] Z   (3) |H P [pi ]|2 P P |H W [qi ]|2 P W ˆ s[p ] + z [p ], + = i i Z P [pi ] ZW where √ zMRC [i ] =

∗

P P (H P [pi ]) P z [pi ] + Z P [pi ]

√ ∗ P W (H W [qi ]) W z [qi ]. ZW

(4)

When NP ≤ NW , pi ∈  for all i. When NP > NW , however, there exists pi ∈ /  and the received signal in (1) is demodulated without combining. The instantaneous signal-to-noise ratio (SNR) at the pi th subcarrier can be given as



2. Powerline/wireless diversity OFDM systems We consider a powerline/wireless diversity OFDM system as shown in Fig. 1. As described in [5], a wireless network operates

201

MRC [i ] =

 P [pi ] +  W [qi ],

pi ∈ 

 P [pi ],

pi ∈ / ,

(5)

202

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Transmitter

Receiver

Powerline OFDM modulator

Powerline Channel

Powerline OFDM demodulator

Subcarrier Pairing

Decoder MRC Wireless OFDM modulator

Wireless Channel

Wireless OFDM demodulator

Fig. 1. Block diagram of powerline/wireless diversity OFDM system.

where

 P [pi ]

=

  HP [pi ]2 P P Z P [pi ]

and

 W [qi ]

=

  HW [qi ]2 P W ZW

. For a given set

of subcarrier pairings  = {1 , 2 , . . ., N P }, the whole data rate is computed [13] as N  P

R() =

log2 (1 + MRC [i ])f,

(6)

i=1

where f denotes the subcarrier spacing. It can be noted that the MRC in (3) can be used even in the case where the powerline and wireless systems comprise different OFDM parameters. However, we assume that the subcarrier spacing is the same for the sake of analytical simplicity in (6). 3. Optimal subcarrier pairing In this section, we discuss on the determination of the subcarrier pairings  for maximizing (6), which is expressed as opt = argmax R().

(7)

For a simple pairing, we can set pi = qi = i with pi ∈  and the other /  is used without pairing. When NP = NW and a subcarrier with pi ∈ simple pairing is employed, the powerline/wireless OFDM system in Fig. 1 is identical to that in [3]. Therefore, it is obvious that the case considered in [3] is a special case of the powerline/wireless OFDM system shown in Fig. 1. In this study, let us assume that the channel quality of each of the subcarriers is fed back to the transmitter. Further, we can derive the optimal subcarrier pairing opt . Let us reexamine the inequality in [6] log2 (a1 + 2 ) − log2 (a1 + 1 ) > log2 (a2 + 2 ) − log2 (a2 + 1 ) (8) for all 0 < a1 < a2 and 0 < 1 < 2 . As described in [6], the logarithmic function is monotonically increasing, whereas the rate of change over a given interval is monotonically decreasing. In (5), i is defined as the ith smallest value among  P [i] with i = 1, 2, . . ., NP , and the corresponding subcarrier index is denoted as ˛i . Similarly,  i is defined as the ith largest value among  W [i] with i = 1, 2, . . ., NW and the corresponding subcarrier index is denoted as ˇi . Further, we consider 0 < 1 < 2 < · · · < N P and 1 > 2 > · · · > N W > 0. First, we consider that one of the two powerline subcarriers with the SNRs of i and j is paired with the wireless subcarrier with an SNR of  k and the other one is used without pairing. In (8), let us assume that a1 = i , a2 = j , 1 = 1, and 2 = 1 +  k . When i < j , (8) leads to log2 (1 + i + k ) + log2 (1 + j ) − log2 (1 + j + k ) − log2 (1 + i ) > 0.

(9)

This implies that the powerline subcarrier with a higher SNR should be used without pairing. As a result, the powerline subcarrier indices are sorted in ascending order of their SNRs and let  include the first NW of the sorted subcarrier indices. Now, let us consider the pairing between the powerline subcarriers in  and NW wireless subcarriers. When i < j and  k >  l , it is observed that the following inequality holds from (8) with a1 = i , a2 = j , 1 = 1 +  l , and 2 = 1 +  k : log2 (1 + i + k ) + log2 (1 + j + l ) − log2 (1 + i + l ) − log2 (1 + j + k ) > 0.

(10)

It is observed in (10) that the powerline subcarrier with a lower SNR should be paired with the wireless subcarrier with a higher SNR to increase the data rate. Therefore, we conclude that the wireless subcarrier indices are sorted in descending order of their SNRs and sequentially paired with the powerline subcarrier indices sorted in ascending order of their SNRs. With the above observation, we summarize the optimal subcarrier pairing scheme as follows. • The powerline subcarriers are sorted in ascending order of their SNRs, which yields the sorted subcarrier indices {˛1 , ˛2 , . . ., ˛N P } • When NP > NW , NW wireless subcarriers are sorted in descending order of their SNRs. The sorted subcarrier indices are expressed as {ˇ1 , ˇ2 , . . ., ˇN W } and  = {˛1 , ˛2 , . . ., ˛N W }. • When NP ≤ NW , NP wireless subcarriers with the highest SNRs are selected among NW wireless subcarriers. The selected subcarriers are sorted in a descending order of their SNRs. The sorted subcarrier indices are given as {ˇ1 , ˇ2 , . . ., ˇN P } and  = {˛1 , ˛2 , . . ., ˛N P }. • For ˛i ∈ , the subcarrier pairing is performed as opt = (˛i , ˇi ). i For ˛i ∈ / , the powerline subcarrier is used without pairing and opt i = ˛i . 4. Numerical results In this section, we present the evaluation results of the ergodic data rate and outage probability of the proposed subcarrier pairing scheme using the Monte Carlo simulation. The performance of the simple pairing scheme described in Section 3 is evaluated for the sake of comparison. The powerline OFDM system comprises NP = 1536 subcarriers with a 30 MHz bandwidth and the useful OFDM symbol duration is 51.2 ␮ s [10]. The transmit power of the powerline transmitter is assumed to be −60 dBm/Hz [11]. The wireless OFDM system is set to comprise the same subcarrier spacing with NW = 1024 and 2048 occupying a 20 MHz and 40 MHz bandwidth, respectively. For same transmit power per subcarrier, the total transmit power of the wireless system is setto be 40 dBm and

Y.-S. Sung et al. / Electric Power Systems Research 121 (2015) 200–206 Table 2 OFDM parameters for simulation.

Table 3 SUI-1 channel model parameters PLC

Wireless systems NW = 1024

NW = 2048

Value FFT size Sampling clock OFDM subcarrier spacing, f Useful OFDM symbol duration, 1/f Total number of subcarriers Occupied bandwidth

2048 40 [MHz] 19.5312 [kHz] 51.2 [␮s] 1536

1024

2048

30 [MHz]

20 [MHz]

40 [MHz]

43 dBm [14] for each value of NW . OFDM parameters for simulation are summarized in Table 2. 4.1. Channel models The power spectral density of the powerline noise can be expressed as Z P [i] = Z0P + 37 exp[−0.17 × 10−6 (fL + f · i)] +

 P Z m 1

(dBm/Hz),

(11)

where Z0P is the constant noise density, which varies from −90 dBm/Hz, in the worst case, to −120 dBm/Hz, in the moderate case [11]; fL is the lowest frequency, which corresponds to 3 MHz for the considered system; and i is the subcarrier index. The first and second terms on the right-hand side of (11) represent the colored background noise [15], whereas the third term represents the impulsive noise as in [16]. As FFT in OFDM receiver spreads impulsive energy over all tones, the impulsive noise causes the SNR in each subcarrier to decrease. In this study, we assume that  impulsive noises occur in one useful OFDM symbol duration and each impulsive noise sample follows an i.i.d. complex Gaussian with zero mean and Z1P f variance. As described in [17], the impulse events occur at a rate of approximately 165 impulses per second (imp/s). However, for MV powerlines, there are a few studies conducted to characterize the impulsive noise characteristic. In this study, we assume that  varies between 0 and 10, which implies that the impulse rate is between 0 imp/s, in the best case, and 195,312.5 imp/s, in the worst case. Moreover, m denotes the FFT size of the powerline OFDM and Z1P is assumed to be 30 dB greater than Z0P [18]. As described in [5] for hybrid wireless/PLC networks, where the WiFi units combined with BPL units were installed on MV poles, we also assume that the wireless system is mounted on the MV power grids. Therefore, we consider the IEEE 802.16j channel models of type D for suburban environments as the wireless channel model in this study, where the transmitter and receiver are assumed to be located above the rooftop [22]. In this model, the path loss exponent increases beyond the breakpoint, which is determined by the transmission frequency and the antenna height. With a carrier frequency of 2 GHz, which is one of the representative operating band of 3G/4G systems, and an antenna height of 15 m, the path loss exponent and the breakpoint are given by 4.86 and 194 m, respectively. The path loss can be calculated as following equation:

 PL (dB) = 20log10

4 d0

+ PLf + PLht

 + 10log10

 d

Delay Power K-factor Doppler

(12)

Tap 2

Tap3

Unit

0 0 4 0.4

0.4 −15 0 0.3

0.9 −20 0 0.5

␮s dB Hz

4.2. Performance comparison As mentioned in Section 3, the proposed optimal pairing scheme requires channel quality feedback. The feedback information should include channel coefficient and SNR for each subcarrier. We assume that the transmitter and the receiver agree to use same pairing scheme in advance, so actual subcarrier pairing information need not be exchanged. But in practical systems, the instantaneous feedback of the channel quality of each subcarrier at each OFDM symbol is not feasible. Therefore we consider two different feedback scenarios:

10 5 0 −5 −10 −15 −20 −25 −30 −35 −40

100

Tap 1

where d0 is the breakpoint, is the wavelength, d is the distance between the transmitter and the receiver, and PLf and PLht are correction factors, where each is a function of the frequency and the antenna height, respectively, and the values are given by 0 and −14 dB for the considered system. The statistical parameters such as tapped delay line, fading, and antenna directivity have been used based on three-tap SUI1 channel model [22] as summarized in Table 3. The magnitude of channel gains in frequency domain for several channel realizations is depicted in Fig. 2. The wireless channel coefficients are assumed to be stochastic, whereas the powerline channel model is assumed to be deterministic. We consider the deterministic powerline channel model which is preferred for simulating powerline networks with multiple nodes, as mentioned in [19]. In this study, we consider a powerline channel environment with typical suburban topologies [11]. The deterministic powerline channel coefficients are evaluated in the frequency band from 3 MHz to 33 MHz for the MV topologies [11,20,21]. As in [6], the distance between the transmitter and the receiver is considered to be 1000 m, and we consider the line length parameters mentioned in [11] for typical suburban topologies.

Magnitude of channel gain (dB)

Parameter

203

0

128

256

384

512 640 Subcarrier index

768

896

Fig. 2. Example of SUI-1 wireless channel realizations for NW = 1024.

1024

204

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Fig. 3. Ergodic data rates with respect to Z0P when  = 4.

(i) instantaneous feedback, where current channel realization is immediately reflected in subcarrier sorting/pairing process as well as current data transmission; (ii) outdated feedback, where the subcarrier sorting/pairing is based on the previous channel realization. Fig. 3 shows the ergodic data rate achieved by the proposed optimal pairing scheme in a typical suburban environment at varying Z0P when  = 4. Capacity gain compared to the case in which only powerline is used for transmission is depicted in Fig. 4. To illustrate the performance improvement through the proposed pairing scheme, capacity gain over simple pairing scheme also is presented in Fig. 5. Through the proposed scheme with instantaneous feedback, about 15–20 Mbps for NW = 1024 and 20–30 Mbps for NW = 2048 increase of data rates are achieved compared to the simple pairing case. The proposed scheme outperforms the simple pairing even with the outdated feedback where the increase of data rates is about 10–15 Mbps. When NW = 1024 (NP > NW ), performance degradation due to outdated feedback is small, but the degradation is more pronounced when NW = 2048 (NP ≤ NW ). By using auxiliary wireless channel for transmission, significant capacity gain can be achieved. When the powerline channel is bad with high noise density of Z0P = −90 dBm/Hz, almost 200%

Fig. 4. Capacity gain over powerline only transmission with respect to Z0P when  = 4.

of gain for NW = 1024 is shown in Fig. 4. This gain comes from that the subcarriers of powerline system having very low SNRs are compensated by the subcarriers of wireless system having relatively high SNRs. As the noise density of powerline channel is lowered, the capacity gain also decreases but still about 20% of gain is achieved when Z0P = −120 dBm/Hz. The gain is larger for NW = 2048 compared to that for NW = 1024, because more subcarriers of powerline systems are combined with those of wireless systems. Capacity gain due to optimal pairing scheme over simple pairing scheme is about 3–9% for outdated feedback case, and about 5–11% for instantaneous feedback case, when NW = 1024. With NW = 2048, much larger capacity gain about 6–22% over simple pairing scheme is shown for instantaneous feedback case, but similar gain about 4–10% is shown for outdated feedback case compared to when NW = 1024. While the gain difference between two feedback case is almost constant with 2–3% when NW = 1024, the difference increases as Z0P increases when NW = 2048. Simulation results with respect to varying impulsive noise rate parameter , which are omitted due to space limitations, show that as the impulsive noise increases, the achievable data rate decreases, but the relative capacity gain increases.

Y.-S. Sung et al. / Electric Power Systems Research 121 (2015) 200–206

Fig. 5. Capacity gain over simple pairing scheme with respect to Z0P when  = 4.

205

Fig. 6. Outage probability with respect to target data rate Rth when Z0P = −100 dBm/Hz and  = 4.

5. Conclusion We also evaluated the outage probability of the proposed scheme. The outage probability is defined as the probability that the instantaneous rate is less than the given threshold, Rth . It is worth mentioning that we can use the outage probability to measure the system reliability when Rth is considered as a target data rate. Fig. 6 compares the outage probabilities of the simple pairing and the proposed optimal pairing schemes when Z0P = −100 dBm/Hz and  = 4. It is observed that the proposed scheme provides enhanced outage performance. When NW = 1024 and Rth = 144 Mbps, the outage probabilities of the simple pairing scheme and the proposed scheme with outdated feedback are found to be about 0.67 and 0.10, respectively. This implies that the simple pairing scheme cannot achieve the target data rate of Rth = 144 Mbps with the probability of 67%, whereas the probability that the proposed scheme fails to achieve Rth = 144 Mbps is only 10%. Regardless of the number of subcarriers of wireless system, the difference between the target data rate which produces same outage probability for simple pairing and optimal pairing with outdated feedback cases is almost same with 10 Mbps. On the contrary, the difference between the target data rate which produces same outage probability for two feedback cases is much larger when NW = 2048.

In this paper, we have proposed an optimal subcarrier pairing scheme for powerline/wireless diversity OFDM systems using MRC. We have proved that the optimal subcarrier pairing is performed to sort the powerline subcarriers in ascending order of their SNRs and the wireless subcarriers in descending order of their SNRs. Further, the sorted subcarriers of both the powerline and wireless subcarriers are sequentially paired and the remaining powerline subcarriers with higher SNRs are used without pairing. We have observed from numerical results, that the proposed scheme achieves enhanced data rate with a gain of 5–22% compared to the simple pairing scheme, and the outage probability for specific target data rate is also lowered significantly. Throughout the paper, we focused on BB-PLC system for MV powerline networks. For remaining works, the effectiveness of the proposed scheme will be verified in more various PLC candidates in smart grid such as NB-PLC in MV network, BB-PLC in LV network, and NB-PLC in LV network. Acknowledgements This work was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government

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