Subcarrier-Wise Backscatter Communications Over Ambient OFDM for Low Power Iot Mahyar Nemati, Morteza Soltani, Jie Ding, and Jinho Choi

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Subcarrier-wise Backscatter Communications over Ambient OFDM for Low Power IoT Mahyar Nemati, Morteza Soltani, Jie Ding, and Jinho Choi

Abstract—Ambient backscatter communication (AmBC) over Fig. 1. A source broadcasts its RF signal to communicate orthogonal-frequency-division-multiplexing (OFDM) signals has with the legacy receiver. The tag also receives the RF signal recently been proposed as an appealing technique for low through the forward-link channel due to its relatively short power Internet-of-Things (IoT) applications. The special spectrum structure of OFDM signals provides a range of flexibility in distance from the source. Integrated circuit of the tag includes terms of bit-error-rate (BER) performance, data rate, and power passive components to harvest/capture enough power from consumption. In this paper, we study subcarrier-wise backscatter ambient RF signal to modulate and backscatter it towards communication over ambient OFDM signals. This new AmBC is the reader. The reader also receives the ambient RF signal to exploit the special spectrum structure of OFDM to transmit which is considered to be direct-link interference for signal data over its squeezed orthogonal subcarriers. We propose a basis transmission scheme and its two modifications to support detection. In addition, AmBC can cause an interference for a higher data rate with superior BER performance compared to a legacy receiver due to same spectrum utilization [3], [11]. existing methods. The basis scheme can transmit one bit per sub- It is also noteworthy that there are two other types of tags carrier using on-off keying (OOK) modulation in the frequency such as active and semi-passive tags [7]–[9] in conventional domain. In the first modification, interleaved subcarrier block backscattering systems (e.g., RFID systems, wireless sensor transmission model is employed to improve the BER performance of the system in frequency-selective channels. It results in a networks (WSN)); however, in this study, we only focus on trade-off between the size of the blocks and data rate. Thus, passive tags to comply with what has been mostly considered in the second modification, interleaved index modulation (IM) is in the literature thus far, and also to emphasize the suitability employed to mitigate the data rate decrementation of the former of the AmBC for low power IoT applications. Nevertheless, modification. It also stabilizes and controls the power of the it does not restrict our AmBC system model to only passive signal to result in interference reduction for a legacy receiver. Analytical and numerical evaluations provide a proof to see the tags. performance of the proposed method in terms of BER, data rate, In the literature, a number of approaches are studied for and interference. AmBC over different dominant RF signals transmitted from various sources such as TV/FM towers, cellular base sta- Index Terms—AmBC, data rate, interference, OFDM, power, tions, and even Wi-Fi access points (APs). AmBC was firstly subcarrier. I.INTRODUCTION set up over ambient digital TV (DTV) signals for a short- range (up to 8 m) D2D communication with a data rate Ambient backscatter communication (AmBC) [1] is a of 1 kbps [1]. Likewise, the AmBC system in [12] with promising technology for low power Internet-of-Things (IoT) the same principles achieved a higher data rate of 20 kbps applications, e.g., green IoT [2], which is also considered to be using Wi-Fi signals. Subsequently, a data rate of 1 Mbps a type of joint power-information transmission technologies. was obtained in [13] by using the principles of full-duplex AmBC technology enables small battery-less IoT devices (e.g., systems [11]. Afterwards, a noncoherent detection method passive tags) to harvest power from far-field radio-frequency using multiple antennas was proposed in [14] to remove the (RF) signals. Then, a new communication takes place over need of channel state information (CSI) for signal detection the same spectrum of the RF signals [3]. It makes AmBC in AmBC systems regardless of the signal type. Furthermore, arXiv:2007.08157v1 [eess.SP] 16 Jul 2020 a promising power- and spectrum-efficient technology for some experiments were carried out in [15] for AmBC over future IoT. In a nutshell, battery-less IoT devices or tags FM signals. It supported a low data transmission rate of modulate and backscatter the surrounding RF signals towards up to 500 bps for agricultural monitoring sensors. However, a receiver (i.e., reader) [1], [4]. Different from the conven- the front-end of these studies only allows data transmission tional backscatter communications, such as in RF identification in one single band which makes them difficult to work in (RFID) systems [5]–[9], AmBC does not require a dedicated different environments [16]. Also, none of the aforementioned source or reader for direct device-to-device (D2D) and even approaches evaluated or exploited the physical layer structure multi-hop communications [10], [11]. of the signals/waveforms for performance improvements. In general, an AmBC system includes a tag, a reader, Among different dominant RF signals/waveforms, an ambient RF source, and a legacy receiver as shown in orthogonal-frequency-division-multiplexing (OFDM) M. Nemati, J. Ding, and J. Choi are with the School of Information waveform has a special spectrum structure which can Technology, Deakin University, Geelong, VIC 3220, Australia (e-mail: ne- provide a range of flexibility in terms of bit-error-rate [email protected], [email protected], [email protected]) (BER) performance, data rate, and power consumption. M. Soltani is with the Department of Electrical and Computer En- gineering, University of Idaho, 83844 Moscow, Idaho, USA (e-mail: Moreover, it is a common modulation scheme in most of the [email protected]) modern communication systems (e.g., LTE/LTE-A, Wi-Fi, 2

Legacy receiver Ambient OFDM source using on-off keying (OOK) modulation to improve the data rate of the system significantly. • However, since low power IoT devices are mostly accompanied by low/medium data transmission rates (i.e., < 1 Mbps [25], [26]), in the first modification, referred to as 퐡푎 퐡푏 Modification-I, one bit is transmitted over an interleaved block of subcarriers; where repetition coding is used ℎ푐 for one bit in each block of subcarriers to improve the Reader Tag (훽) Backward-link BER performance of the system over frequency-selective 퐡풔 channels significantly. Dyadic-backscatter-link • Furthermore, instead of struggling to cancel the direct- Fig. 1: Illustration of AmBC system model. link interference at the reader for a better BER performance, like the existing methods in [19]–[24], we simply sacrifice a portion of subcarriers to boost the BER and even first commercial 5th generation (5G) of mobile performance of our approach profiting from repetition communication standard (3GPP Release 15) [17]). In [11], coding. [18]–[22], three different AmBC methods were proposed to • It is noteworthy that although the superior BER perfor- transmit only one bit over one OFDM symbol (duration). mance is obtained at the expense of data rate (because Authors in [11] showed that backscattering one bit over of using cluster of subcarriers for one bit transmission), one OFDM symbol provides a satisfactory data rate (∼ 1 Modification-I still supports a higher data rate than the Mbps using OFDM system based on IEEE 802.11a) for short existing methods. distances (1 − 3 m). A method in [18] used matched-filtering • Finally, in the second modification, referred to as at the tag to impose a certain property that improves the signal Modification-II, an interleaved index modulation (IM) detection performance at the reader. In [19]–[21], an AmBC is employed not only to compensate the decrease of data approach was evaluated which exploits the cyclic prefix rate of the Modification-I, but also control the power of (CP) of OFDM signals to address direct-link interference the signal resulting in interference reduction for a legacy cancellation when the duration of the CP, denoted by Tcp, receiver. is greater than maximum delay spread of the multipath The rest of the paper is organized as follows. In Section channels, denoted by τ, i.e., T τ. Hence, they require cp II, the system model of subcarrier-wise backscatter com- extra overhead to avoid failure in communications. In [22], a munication over ambient OFDM is described. This is the noncoherent detection strategy was investigated to solve the basis scheme for other two modifications. Section III pro- noncoherent maximum likelihood (ML) detection problem for vides signal detection and BER analysis of the basis scheme. a general Q-ary signal constellation which uses a suboptimal Then, Modification-I and Modification-II are proposed and energy detector. Furthermore, in [23], [24], an AmBC method described in Section IV. Simulation results and comparisons was investigated to send data over null (i.e., guard-band) are given in Section V. Finally, Section VI concludes the paper. subcarriers of an OFDM signal; however, it does not have a Notation: (.)T and b.c denote the transpose operation and closed-form expression for the bit detection threshold at the the floor operation, respectively. The 2-norm and absolute reader. Eventually, the main remarks of the aforementioned value of a and a are denoted by ||a|| and |a|, respectively. existing methods are summarized as follows. CN (a, R) represents the distribution of circularly symmetric • There is a severe spectrum inefficiency in the aforemen- complex Gaussian (CSCG) random vectors with mean vector a tioned AmBC methods since they either do not consider and covariance matrix R. C and R represent sets of complex the physical layer structure of the OFDM signals or send and real numbers, respectively. The Gaussian Q-function is 2 only one bit data over one OFDM symbol regardless of 1 R ∞ −z given by Q(x) = √ e 2 dz. the number of subcarriers. 2π x • Moreover, the communication fails in presence of a II.SYSTEM MODEL severe frequency-selective channel conditions. In other words, they mainly work in a very short-range and poor- In this section, we describe the system model of our scattering environment with a strong line-of-sight (LoS) subcarrier-wise backscatter communication over OFDM sig- environments. nals utilizing OOK modulation as shown in Fig. 1. This is • In addition, there is an ignorance of interference caused considered to be a basis scheme for the other two modifi- by AmBC for the legacy receivers due to same spectrum cations. We describe our AmBC method in three stages as utilization. follows. In this paper, we aim at filling these gaps by proposing a subcarrier-wise backscatter communication over ambient A. First Stage OFDM. In particular, we derive a basis transmission scheme At the first stage, at the source (e.g., Wi-Fi AP in Fig. 1), and its two modifications to improve the data rate with a an OFDM symbol with a total of N subcarriers is transmitted, satisfactory BER performance as follows. which is given by • In the basis scheme, it can transmit one bit per subcarrier x = U s, (1) 3

Matching At the tag, the desired data is a vector d = Rectifier Clock T Network [d1, d2, . . . , dNd ] , where dl (l = 1, ..., Nd) represents the data symbol. If OOK is employed, we can have dl ∈ {0, 1}. Memory clk Throughout the paper, we assume that dl is regarded as a bit 퐝 퐮 for convenience. Fig. 2 illustrates the tag’s RF-analog front- Filtering end which has a filter bank of passive notch filters. We con- 퐑 × 퐮 sider a matrix, denoted by R, that works as a filtering matrix (a) The tag’s RF-analog front-end. Power of the ambient RF th signal is transferred from the antenna to the rectifier through to pass or nullify the l cluster of subcarriers corresponding the matching network. The rectifier supplies the needed DC to dl = 1 and dl = 0, respectively. Passive analog notch filters power. Once the tag is powered up1, u is being filtered and can be employed for this task. transmitted. 1) Discussion on Feasibility of Filtering: In order to put the filtering matrix R into action, we need to have highly Memory 푑1 selective filters due to a narrow subcarrier spacing of ∆f Cluster 1 2 Δf typically in UHF band. Let ∆fl and fc denote the bandwidth 푑 1 2 and center frequency of the lth notch filter in the filter bank Cluster 2 퐮 Δf2 ∑ R, respectively (as shown in Fig. 2 (b)). It is ideal to have 푑푁 ⋮ ∆fl = ∆f. However, finding perfect high-order passive RF 푑 ⋮ Cluster 푁푑 filters with ∆fl = ∆f in UHF band, e.g., fc = 2.4 GHz Δf 푁푑 in IEEE 802.11, is challenging. We still do not find such an Passive Notch Filter Bank appropriate passive RF notch filter as of writing of this paper. (b) Passive notch filter bank is used to pass or halt different Nevertheless, this challenge is similar to the traditional and OFDM subcarriers with regard to d. well-known issue of frequency selecting/planning in cognitive Fig. 2: Tag receives the ambient OFDM signal and modulates its subcarriers radio transceivers where the scarce spectrum, e.g., UHF spec- th th with OOK modulation. l filter nullifies l cluster of subcarriers when dl = 0 trum, is utilized densely [31], [32]. Standard reflective and and passes it when d = 1. l absorptive filters are suitable for most of these applications; however, absorption filters are better choices in performance T where s = [s1, s2, . . . , sN ] is the vector of modulated data as they provide greater levels of attenuation and frequency symbols. We omit the guard-band subcarriers for simplicity of selectivity besides their non-reflective properties [31]–[38]. the notations to avoid any confusion since it does not affect The passive RF notch filters in [32]–[35] provide a stopband T −1 T N×N with range of ∆fl ≈ 0.5 − 4 MHz in UHF band. For instance, our system. In (1), U , [M FN ] where FN ∈ C is the discrete Fourier transform (DFT) matrix and M represents the passive notch filter in [33] provides a highly selective −1 narrow rejection with a narrow 10 dB rejection stopband of the last Ncp rows of the FN for CP [27]. ∆fl = 2.4 MHz over fc = 3.4 GHz. Moreover, the notch filters in [32], [34] can provide a higher frequency selectivity B. Second Stage with a fractional bandwidth of up to 0.02% in UHF band, x At the second stage, the OFDM symbol, i.e., , with length i.e., ∆fl ≈ 480 kHz over fc = 2.4 GHz. Recently, in [31], of Ns = N + Ncp, reaches to the tag and the reader as shown [39], RF notch fitters are proposed with even more tunable in Fig. 1. The received ambient OFDM symbol at the reader bandwidth from ∆fl = 0 MHz up to ∆fl = 96 MHz over is given by higher frequencies up to fc = 3.4 GHz. Besides, these RF ya = Ha x, (2) notch filters have steep roll-off responses in the transition band and at the tag is expressed as between the stopband and passband. However, considering the current OFDM standards, e.g., IEEE 810.11a, the stopband of u = Hb x, (3) the RF notch filters is still mostly much wider than one OFDM subcarrier spacing, e.g., ∆f = 312.5 kHz, i.e., ∆f > ∆f. where H and H are the N × N lower l a b s s Therefore, we utilize the feasibility of aforementioned RF triangular Toeplitz filtering matrices with the first notch filter concepts and consider that the stopband of notch column of h = [h , ··· , h , 0, ··· , 0]T and a a,o a,à filters in the filter bank covers a cluster of N subcarriers with h = [h , ··· , h , 0, ··· , 0]T , respectively. They f b b,o b,`b N subcarriers as its guardband shown in Fig. 3. So, the total correspond to the channel impulse responses of the direct-link g number of required subcarriers becomes and the forward-link channels from the source to the reader and the tag, respectively. Here, ` and ` represent the a b N = Nd(Nf ) + (Nd − 1)Ng. (4) channels orders and we assume L = max(à, `b) 6 Ncp, i.e., τ 6 Tcp. In (4), let consider N is fixed, then the total number of data symbols, i.e., Nd, is given by 1It is noteworthy that the harvested power is a nonlinear function of the input RF power [28], [29]. Moreover, when the input power is below the N + N N = g . (5) harvesting circuit power sensitivity threshold, the harvested power is zero d N + N [30]. In this study, we assume that the harvested power is enough to trigger f g the tag. Nevertheless, our proposed method is not limited to the passive tags and a secondary battery can be used like in semi-passive tags if needed. 2UHF: Ultra High Frequency 4

Guardbound, can be asymmetric between the tag and the reader, and we ignore the propagation Δ푓 delay [20]. Δf푙 At the reader side, the CP portion is discarded and the remaining part, denoted by vector yd, goes through the DFT operation. … … … r = FN yd c −1 c c −1 = FN HaFN s + FN hc β R HbFN s + n˜, (9) Freq. where (.)c denotes the circularized matrix reflecting the effect 푙th Cluster of CP after CP removal at the receiver; and ñ is the back- 푁푔 subcarriers 푁푓 subcarriers ground noise in the frequency domain. c Fig. 3: Illustration of RF notch filter over OFDM subcarriers. The lth RF Since filtering matrix R acts as a frequency selective th notch filter with bandwidth of ∆fl is controlled by dl to pass or halt the l matrix to nullify or preserve the subcarriers in the frequency cluster of subcarriers. domain with respect to d, and also with respect to the Assumption 1, its response in the discrete time domain can notationally be defined as Rc F−1 [diag(d)] F . Thus, It is evident that a larger ∆fl is easier for filter bank implemen- , N N tation at the cost of data rate. It is also noteworthy that using from (9), we have a large number of passive RF components (e.g., different load Frequency response Frequency response of h I of h impedance states) is a routine technique to reach higher mod- a N b z }|c −1{ z }|−1{ z }|c −1{ ulation orders in the conventional AmBC models [16], [40]. r = FN HaFN s + hc β FN FN [diag(d)] FN HbFN s + n˜. Accordingly, in our model, various passive RF components (10) can be used for filtering different subcarrier frequencies. Note Therefore, the received vector in the frequency domain that thermal noise is neglected in the incident signal at the becomes tag because it does not have any active RF component, which ˜ ˜ is a common assumption for passive tags and is supported in r = Has + hc β Hb [diag(d)] s + ñ, (11)

[19]–[21], [23], [24] as well. However, the signal is attenuated where H˜ a and H˜ b are the N × N diagonal matrices with ˜ ˜ T by a factor of β inside the tag. There is extensive efforts in the hã = FN ha = [ha,0, ··· , ha,N ] and h˜b = FN hb = ˜ ˜ T literature (e.g., in [6], [16], [28], [30], [41]–[43] and references [hb,0, ··· , hb,N ] for their diagonal elements, respectively. therein) where similar passive tag structures with passive filters The numbers of active and inactive subcarriers in the are proposed. However, evaluating the electronic circuit of the backscattered signal, i.e., yb in (7), are not fixed as they depend tag in details is beyond the scope and space of this paper. on d which is a random data vector. To be more specific, the Assumption 1 (Highly Selective Notch Filter): In the analysis numbers of active and inactive subcarriers equal Q = ||d||0 given in the next parts, we assume to have near-perfect high- and K = N − Q, respectively. Let define two supports for d quality factor filters similar to the notch filters in [32], [34], as I1 , {l|[d]l = 1} and I0 , {l|[d]l = 0}. Then, the total [39] that are able to satisfy the condition of signal-to-noise-ratio (SNR) of the received signal in (11) is defined as the total received signal power, i.e., including both ∆fl 6 ∆f → Nf = 1,Ng = 0, (6) direct-link and bachscattered signals, at the reader over the in order to simplify the analysis and verify the feasibility of background noise power; and can be expressed as the preliminary idea. A similar assumption has been taken into P |h˜ |2 + P |h˜ + h βh˜ |2 account in [44]. a,l a,l c b,l l∈I0 l∈I1 Eb 2) Backscattered Signal: Eventually, the tag backscatters Γ = × , (12) N N the filtered signal to the reader. The backward-link channel 0 where E stands for bit energy. Moreover, from (11), the from the tag to the reader has a single path [12], [20], [23] b received signal through the lth subcarrier, denoted by r , is because the distance between the tag and the reader has to l ˜ be sufficiently close in backscatter communication; and its hs,l z }| { channel coefficient is denoted by hc as shown in Fig. 1. The ˜ ˜ rl = (ha,l + hcβhb,l dl)sl +n ˜l, l = 1,...,Ns, (13) received backscattered signal at the reader is given by ˜ where hs,l ∈ h˜s = hcβh˜b denotes the composite source- yb = hc β R u. (7) tag-reader channel coefficient as shown in Fig. 1 which C. Third Stage is usually referred to as the dyadic-backscatter-link in the literature [40], [45]. Consequently, the SNR of the received Finally, at the third stage, at the reader, the received signal signal over the lth subcarrier is given by with the background noise n ∼ CN (0,N0) is given by  ˜ 2 Eb|ha,l|  Γl = , y = ya + yb + n. (8)  N0 dl=0 (14) It is worth mentioning that the length of the OFDM symbol is ˜ ˜ 2  Eb|ha,l+hs,l|  Γl = . much longer than the propagation delay due to short distance  N0 dl=1 5

D. Data Transmission Rate Analysis for the received power and the test statistic are derived. Let While the existing methods in [11], [18]–[21] send one bit β = 1 for notational simplicity. Then, at the reader, the over one OFDM symbol period, our proposed method can conditional distribution of rl on sl and dl is given by N > 1 transmit up to d bits over one OFDM symbol period. For 1 1 ˜ ˜ 2 f(rl | dl, sl) = √ exp − |rl − (ha,l + hs,ldl)sl| . example, consider an OFDM system based on IEEE 802.11a πN0 N0 speciﬁcations (i.e., OFDM symbol duration of T = 4 µsec, (15) DFT size of 64, ∆f = 312.5 KHz, and N = 52 used Considering that dl is equally likely (i.e., Pr(dl = 0) = 1 subcarriers), then, the existing methods can support a data rate Pr(dl = 1) = 2 ), the maximum likelihood (ML) detection 1 of up to η = 4 µsec = 250 kbps; while our proposed method is equivalent to the maximum posteriori probability (MAP) Nd detection [48], which is as follows can support a data rate of η = 4 µsec . If we assume ∆fl varies between 0.5 − 4 MHz based on the current ﬁlters in [32]– H0 [34], [39], i.e., N ≈ 1 to 12 subcarriers, then, N ≈ 52 to > f d f(rl | dl = 0, sl) < f(rl | dl = 1, sl), (16) 4 subcarriers and we can expect a variable data rate from 1 H1 MHz up to 13 MHz. Such a data rate performance is up to N d where H , i ∈ {0, 1}, represents that d = i. Here, s ∈ S times better than the existing AmBC systems in the literature. i l l is unknown and equally likely√ (e.g., binary phase shift keying (BPSK)), where S = {± Eb}. Thus, the likelihood function III.SIGNAL DETECTIONAND BER ANALYSIS of dl for given rl becomes 3 We consider the reader is able to detect the pilots from X the source. Then, the reader can estimate the both the direct- f(rl | dl) = f(rl | sl, dl) Pr(sl). (17) link and dyadic-backscatter-link CSIs. In other words, they sl∈S can be estimated by letting the source send pilots reaching The ML detection becomes ˜ the reader through the direct-link ha and dyadic-backscatter- H0 1 ˜ 2 1 ˜ ˜ 2 ˜ X − |rl−ha,lsl| > X − |rl−(ha,l+hs,l)sl| link hs channels. Since there are two different paths, two N0 N0 e < e . (18) estimations are required. First, the tag initiates a zero data sl∈S H1 sl∈S vector, i.e., ||d|| = 0, and from (11), the reader receives 0 Note that this method is also applicable to other modulated r = H˜ x + n where x is the pilot OFDM symbol. a p p symbols with only one level of power, i.e., E . The ML Subsequently, reader estimates h˜ . Second, the tag initiates b a detection in (18), after some manipulations given in (19) and ∀l → d = 1, i.e., ||d|| = N , and from (11), the reader l 0 d (20) at the bottom of this page, becomes receives r = H˜ a + H˜ s xp + n and h˜s is estimated this √ 4 ˜ ˜ ˜ time . Therefore, h and h are assumed to be estimated 2ha,l Ebrl a s cosh H0 ˜ ˜ ˜2 ! N0 > (2ha,lhs,l + hs,l)Eb by minimum mean square error (MMSE) channel estimation √ ˜ ˜ < exp − . technique [27], [47] at the reader, which is similar to the cosh 2(ha,l+hs,l) Ebrl N0 N0 H1 assumption in [6] for coherent signal detection. (21) Assumption 2 (Near-Perfect CSI Estimation): We assume At a high SNR, since √ near-perfect CSI estimation at the reader, i.e., the direct-link ˜ 2ha,l Ebrl √ h˜ and dyadic-backscatter-link h˜ channels are estimated and cosh ˜ ! a s N0 2hs,l Eb|rl| √ known to the reader. ˜ ˜ ≈ exp − , (22) cosh 2(ha,l+hs,l) Ebrl N0 N0

A. Signal Detection the optimal decision threshold, denoted by δl, becomes √ In order to detect the signal, an energy detector over the (|h˜ | + |h˜ + h˜ |) E δ = a,l a,l s,l b . (23) subcarriers is proposed. It is noteworthy that the proposed l 2 detection method does not require direct-link interference Eventually, the test statistic can be given as cancellation. In the following, an optimal decision threshold  H1 ˜ ˜ ˜ 3Similar to the ﬁxed pilot pattern in LTE standard for slow fading channel  |rl| ≷ δl when |ha,l| < |ha,l + hs,l| (24a)  H estimation, the downlink pilots are unique complex numbers dependent on 0 H the source and subcarriers [46].  1 ˜ ˜ ˜ 4  |rl| δl when |ha,l| > |ha,l + hs,l| (24b) H˜ s is N × N diagonal matrix with h˜s for its diagonal elements.  ≶ H0

√ √ H0 √ √ 1 ˜ 2 1 ˜ 2 1 ˜ ˜ 2 1 ˜ ˜ 2 − |rl−ha,l Eb| − |rl+ha,l Eb| > − |rl−(ha,l+hs,l) Eb| − |rl+(ha,l+hs,l) Eb| e N0 + e N0 e N0 + e N0 , (19) < √ H 2r h˜ E 1 √ 2 cosh l a,l b 1 ˜ ˜ N 2 cosh 2rl(ha,l+hs,l) Eb 0 N0 z √ }| √ { H0 z √ }| √ { 1 ˜2 1 ˜ 1 ˜ 1 ˜ ˜ 2 1 ˜ ˜ 1 ˜ ˜ − h Eb + 2rlha,l Eb − 2rlha,l Eb > − (ha,l+hs,l) Eb + 2rl(ha,l+hs,l) Eb − 2rl(ha,l+hs,l) Eb e N0 a,l e N0 + e N0 e N0 e N0 + e N0 . (20) < H1 6

Fig. 4: The likelihood functions of the proposed method and BER regions for Pe|0 and Pe|1 in AWGN channels.

We note that in general, the phase information of the channel Fig. 5: Probability distribution functions of |r| when d = 0 and d = 1. γ = 5 σ2 = 2 σ2 = 2 σ2 = 2 gains along with their amplitudes is in fact relevant to the dB, a , b , c . detection. This is because with the fading assumption, the channel gains h˜ and h˜ could be added constructively or a,l s,l where γ Eb . Likewise, when bit 1 is transmitted the error destructively and therefore both (24a) or (24b) are likely to , N0 probability is shown in blue shadowed part of Fig. 4 and can happen. However, we only need to know whether the sum be obtained as of these gains are constructive or destructive and to this end, r1 r49 an accurate knowledge of channel phases are not required. In P = 1 − Q − γ − Q γ . (28) other words, only an estimate of the channel phase information e|1 2 2 would sufﬁce to determine whether the sum is constructive or Finally, the BER in an AWGN channel is given by destructive. r r r In the following subsections, the BER performance of the 1 1 25 1 49 Pe−AWGN = Q γ + Q γ − Q γ proposed scheme in additive white Gaussian noise (AWGN) 2 2 2 2 2 channels and frequency-selective channels is studied. r1 ≈ Q γ . (29) 2

B. BER Analysis in AWGN Channels Next, the BER performance of the proposed model in frequency-selective channels is studied. In this subsection, we omit the subcarrier index l for convenience and assume β = 1. Furthermore, assume that C. BER Analysis in Frequency-Selective Fading Channels the forward-link and direct-link channels can be modeled as In this subsection, we consider the case that the source is AWGN channels thanks to short distances between the source, not sufﬁciently close to the reader and the tag. As a result, the reader and the tag [49]. Equation (13) in AWGN channels the forward-link and direct-link channels can be modeled is rewritten as as frequency-selective fading channels. Suppose d = 0 is r = (1 + d)s +n. ˜ (25) transmitted. From (13), we have

˜ In such a scenario, the reader can see four different subcarrier r = has +n. ˜ (30) amplitudes from the received signal. Fig. 4 shows the likeli- d=0 hood functions of possible amplitudes of each subcarrier in Likewise, if d = 1 is transmitted, the received signal is the frequency domain, where the shaded areas represent error ˜ ˜ probabilities. Therefore, the error probability when bit 0 is r = (ha + hs)s +n. ˜ (31) transmitted is shown in yellow shadowed part of Fig. 4 and is d=1 given by Throughout the paper, for Rayleigh fading, we consider ˜ 2 ˜ 2 ˜ 2 ha ∼ CN (0, σa), hb ∼ CN (0, σb ) , hc ∼ CN (0, σc ) Pe|0 = which are common assumptions in the literature, e.g., [50], √ √ ˜ ˜ Z −δ (x+ E )2 Z ∞ (x+ E )2 [51]. Suppose that hb and hc are independent, then we have 1 − b − b N0 N0 ˜ 2 2 2 √ e dx + e dx hs ∼ CN (0, β σb σc ). We consider ha and hs are also 2 πN0 −∞ δ ˜ ˜ 2 2 2 2 √ √ independent. Since (ha + hs) ∼ CN (0, σa + β σb σc ), we Z −δ (x− E )2 Z ∞ (x− E )2 − b − b have + e N0 dx + e N0 dx . (26) −∞ δ ( 2 r d=0 ∼ CN (0,Ebσa + N0), 2 2 2 2 (32) Substituting δ from (23) into (26)√ with respect to the AWGN r d=1 ∼ CN (0,Eb(σa + β σb σc ) + N0). channel coefﬁcients, i.e., δ = 3 Eb , we have 2 The absolute values of r in (32) have Rayleigh distributions r r [50], [51]. The probability distribution functions (PDFs) of 1 25 them are shown in Fig. 5, where A |h˜ | and B |h˜ + h˜ | Pe|0 = Q γ + Q γ , (27) , a , a s 2 2 for notational simplicity. 7

q 2 2 4 Eb µ 1 µ 1 µ Let µ , α + 2 and κ + 2 − 2 . , N0 , 2 2σ , 2 4σ 4α After extensive analysis given in Appendix B and proﬁting from Hypergeometric function, i.e., 2F1(a, b; c; d) in [52], a closed-form expression of (38) is given as5

1 3 µ2 2F1 0, 2 ; 2 ; µ2+ 1 1 µ 2σ2 µ Pe|basis = − √ × q + √ + 2 8 µ2 1 8 2ακ2σ2 + 2 (a) The likelihood functions if A < B 2 4σ 1 3 µ4 µ3 2F1 0, 2 ; 2 ; µ2+4α2κ2 √ × + 2 2 2 q 4 16 2α κ σ µ 2 4α2 + κ 2 (α− µ )2 µ2 1 3 2α 2F1 0, ; ; 2 µ α − 2α 2 2 (α− µ )2+κ2 √ × 2α . (39) 2 2 r 4 2ακ σ 2 2 µ 2 α − 2α + κ

IV. DESCRIPTIONOF MODIFICATIONS (b) The likelihood functions if A > B In this section, we present two schemes by modifying the Fig. 6: The likelihood functions and BER regions for Pe|0 and Pe|1 for two basis scheme in Section II, which improve the BER and different possible scenarios in frequency-selective channels. mitigate the interference imposed on original ambient OFDM signal compared to the basis scheme at the cost of data rate, As a result, the test statistic is re-written for two different respectively. possible scenarios in frequency-selective channels as A. Modification-I  H1  |r| δ if A < B  ≷ , Fig. 6 (a) Since low power IoT devices are mostly accompanied by  H0 , (33) low/medium data transmission rate (i.e., < 1 Mbps [25], [26]), H  1 instead of transmitting one bit over each subcarrier in the basis  |r| ≶ δ if A > B , Fig. 6 (b) H0 scheme, one bit can be sent over a block of subcarriers. It √ A+B improves the BER performance of the system specifically in where δ = 2 Eb is derived from (23). Suppose that A < B as shown in Fig. 6 (a), then, after frequency-selective channels. Furthermore, when N is large analysis given in Appendix A, the following probabilities are enough and the number of paths is limited, i.e., N L, given. the channel coefficients of the adjacent subcarriers are being largely correlated [53]. Therefore, in order to further improve ( p γ Pr(|r| > δ d = 0, A < B, B) ≈ Q (B − A) 2 the BER performance, an interleaved block transmission can p γ . Pr(|r| < δ d = 1, A < B, B) ≈ Q (B − A) 2 be employed, which increases the diversity gain. From (6), (34) consider G blocks of L subcarriers among a total of N Consequently, we have subcarriers of the OFDM spectrum. Then, with block filtering r matrix, denoted by R , (7) can be re-expressed as γ b Pe(|r| A < B, B) = Q (B − A) . (35) 2 yb = hc β Rb u. (40) Likewise, when A > B, Then, G bits are sent over G blocks of L subcarriers using ( p γ repetition coding (i.e., L is an odd number). G = b N c is the P (|r| < δ d = 0, A > B, B) ≈ Q (A − B) 2 L . total number of blocks/bits over the frequency spectrum, i.e., P (|r| > δ d = 1, A > B, B) ≈ Q (A − B)p γ 2 N = G. At the reader, the received signal over the gth block (36) d of subcarriers, similar to (13), can be expressed as Then, similar to (35), we have ˜ r Hs,g γ z }| { Pe(|r| A > B, B) = Q (A − B) . (37) 2 rg = (H˜ a,g +hcβH˜ b,g dg)sg +ñg, g = 0,...,G−1. (41) Suppose that A and B are Rayleigh random variables with Majority logic decoding [48], along with the simple energy x x2 the PDF of f(x) = Ω exp(− 2Ω ), where Ω is the average detector given in Subsection III-A, is used for the signal power. Then, the error probability of the basis scheme can be detection at the reader. Consequently, from (39), the error obtained from (35) and (37) as probability of the Modification-I can be obtained by Z ∞ Z B L P = Pe(|r| A < B, B)f(A) dA f(B) dB+ X L e|basis P = P ` (1 − P )L−`. (42) 0 0 e|Mod-I ` e|basis e|basis Z ∞ Z ∞ L+1 `= 2 Pe(|r| A > B, B)f(A) dA f(B) dB. (38) 0 B 5See Appendix B for details. 8

backscatter communication. To this end, we can consider IM 3030 6 technique [55] in Modification-II. As a result, a fixed number Modification-IModification-I Modification-I Modification-IIModification-II Modification-II of Q = GM active subcarriers are being backscattered. Fig. 2525 5 7 (a) shows that IM backscattered signal in Modification-II has much lower power than the backscattered signal in the

2020 4 Modiﬁcation-I when M = 2 leading to lower interference ) [Mbps] ) ) [Mbps] ) level for legacy receiver. On the other hand, Fig. 7 (b) shows 1515 3 that better data rate performance is achieved as well. In particular, we assume an IM model where only the

1010 2 indices of active subcarriers are used to send information.

Signal Power [mW] Power Signal

Signal Power [mW] Power Signal Data rate ( rate Data Data rate ( rate Data th T Let the g IM block, denoted by bg = [bg,0, ··· , bg,L−1] , 5 1 5 1 contain M active subcarriers and K inactive subcarriers, i.e., ||bg||0 = M. For convenience, let Ig denote the support of 00 0 1010 2020 3030 4040 5050 0 20 4040 bg, i.e., Ig = {l|[bg]l = 1}. Therefore, the total number of UsedUsed Subcarriers Subcarriers (N)(N) Used Subcarriers (N)(N) bits transmitted per OFDM symbol duration is given by (a) (b) L Fig. 7: Evaluation of signal power and data rate with respect to the number Nb = G × blog2 c. (43) of used subcarriers in Modification-I and Modification-II when G = 4, M L = 13, M = 2, Eb = 1 mW and T = 4 µsec. Note that Nb in IM block transmission is equal to or greater than G in Modification-I and is less than N in basis scheme. th B. Performance Analysis of the Modification-I From (41), the g IM block can be rewritten as

In the Modification-I, the data transmission rate decreases H˜ s,g by a factor of ρ = G , while a better BER performance z }| { N r = (H˜ +h βH˜ b )s +ñ , g = 0,...,G−1. is achieved. In other words, utilization of repetition coding g a,g c b,g g g g (44) in a block with L subcarriers can correct up to L−1 errors 2 For the ML detection, we have in each block. For examples, considering an OFDM system based on IEEE 802.11a specifications, authors in [11] state ˆ 2 ˜ ˜ 2 that 1 Mbps is a satisfactory data rate for such low data rate bg = argmin ||rg|| − ||Ha,g + Hs,gbg|| Eb . (45) bg applications; accordingly, our proposed method can achieve the same data rate when G = 4 and L = 13, but with Since the analysis of ML detection of such OFDM-IM blocks 13 times higher diversity gain. Also, repetition coding and is well studied in [50], [53], [55]–[57], we do not include majority logic decoding are simple processes with a low details here. implementation complexity among linear block codes [54]. Moreover, the complexity of Rb is the same as R in (7). Additionally, it can still support a higher data transmission rate D. Performance Analysis of the Modification-II by using smaller blocks compared to the existing methods in Since backscattered signal uses the same spectrum as the [11], [19]–[24]. In other words, since each block of subcarriers legacy system, it can cause an interference over the legacy can transmit one bit data, smaller blocks lead to a higher system. The average backscattered signal power in the basis number of blocks, i.e., G, when the total number of subcarriers scheme and Modification-I is given by is fixed. It leads to a higher data rate compared to the larger 2 P ˜ 2 blocks. β Eb |hb,l| Backscattered Signal Power = l∈I1 , (46) N C. Modification-II where I1 denotes the support for indices of active subcarriers. 1 Both of the basis scheme and Modification-I have random Considering Pr(dl = 1) = Pr(dl = 0) = 2 , we have an N number of active and inactive subcarriers in the backscattered average of E {||I1||0} = 2 active subcarriers. On the other signal depending on d. Therefore, the power of the signal hand, in Modification-II, the total number of active subcar- changes randomly. Assuming dl ∈ {0, 1} is equally likely, riers is fixed and ||I1||0 = Q, i.e., Q = GM. Therefore, in 1 i.e., Pr(dl = 1) = Pr(dl = 0) = 2 , there are an average general, from (46), the signal power in Modification-II is fixed N of 2 active subcarriers being backscattered which become while two former schemes might have variable signal power in interfering subcarriers for a legacy receiver. Note that both the consecutive backscattered symbols with respect to the forward- ˜ OFDM signal transmitted by the source and the backscattered link channel coefficients in hb. Moreover, Modification-II signal by the tag occur at the same frequency. Therefore, to leads to a lower interference level for the legacy system when N control the power of the backscattered signal and keep the Q < 2 leading to a lower number of active subcarriers interference level for the legacy receiver low, it would be compared to the two former schemes. Furthermore, from (43), desirable to use a fraction of N subcarriers, say M( N) Modification-II supports higher data rate compared to the active subcarriers and K(= N − M) null subcarriers for the Modification-I when M > 1. 9

100 0 Existing method in [19] 10 Existing method in [24] Basis scheme simulation -1 Basis scheme analysis 10 -1 Mod-II, L=4, M=1 10 Mod-I simulation, L=5 Mod-I analysis, L=5 10-2 Existing method in [19]

BER Basis scheme simulation 10-2 BER ~8dB 10-3 Basis scheme analysis Existing method in [24] Mod-II, L=3, M=1 10-3 -4 Mod-I simulation, L=3 10 Mod-I analysis, L=3 Mod-I simulation, L=5 -5 Mod-I analysis, L=5 -4 10 10 0 5 10 15 20 25 30 0 5 10 15 20 25 SNR [dB] SNR [dB]

Fig. 8: BER performance in a short-range communication with strong LoS Fig. 9: BER performance in a frequency-selective channel (τ = Tcp). link when τ=0.

compared to the existing method in [19], we consider two V. NUMERICAL RESULTS different values of τ = 0 and τ = Tcp in our simulations. On In this section, we provide simulation results to evaluate the other hand, the BER performance of the existing method the performance of the proposed schemes. We consider an in [24] depends on the number of null subcarriers in an OFDM OFDM system model based on IEEE 802.11a specifications. symbol. Although the robustness of the existing model in [24] The parameters used in simulations are given in Table I, unless to the maximum channel delay spread is higher than that otherwise specified. in [19], its performance degrades when the number of null subcarriers is low. TABLE I: System numerical parameters. Fig. 8 compares the BER performance of the proposed System parameters Corresponding value AmBC schemes and the existing methods in [19] and [24] in DFT size 64 a short-range and poor-scattering environment such as those Number of used subcarriers 52 considered in [12], [49], [58]. In fact, the maximum delay DFT sampling frequency 20 MHz Subcarrier spacing 312.5 kHz spread is less than the sampling period due to a short-distance Cyclic prefix, Tcp 0.8 µsec scenario, i.e., τ = 0 [58]. Thus, the paths are considered Total OFDM symbol duration, Ts 4 µsec to be one resolvable path with strong LoS, e.g., AWGN channel. It is shown that the proposed schemes outperform the existing methods in [19] and [24] (e.g., about 8 dB SNR gain at BER= 10−2 for the basis scheme). Moreover, A. BER Performance Comparison Modification-II and Modification-I have respectively better For the first evaluation, we compare the BER performance BER performances than the basis scheme. of our proposed schemes with that of the existing methods On the other hand, Fig. 9 depicts their BER evaluations over in [19] and [24] which are the baseline methods for other a frequency-selective channel. A Rayleigh fading multipath existing methods in [20], [21], [23]. The BER performance of channel with τ = Tcp is considered for this simulation. As the existing method in [19, Eq.(54)] is a nonlinear function of shown in Fig. 9, the existing method in [19] has a poor γ. The input of the function in a high SNR is as follows: performance when Ncp − L becomes zero. However, our proposed schemes significantly improve the BER performance v q 2 u 2 2 ln(γ) of the system. The existing model in [24] performs better u(Ncp − L) γ − γ 1 + + 2 ln(γ) t Ncp−L ψ ≈ . (47) than the existing model in [19] and the basis scheme. But γ4 it is also shown that by increasing the size of the blocks in Modification-I, a better BER performance can be achieved As SNR increases, ψ approaches p(N − L) + 2 ln(γ). cp in our proposed method. Therefore, the BER decreases slowly. It is evident that its BER probability depends on the portion of CP not affected by the multipath channel, i.e., Ncp − L. Thus, the performance of the existing method in [19] becomes worse if the maximum B. Data Rate and Power Evaluation channel delay spread, i.e., τ, increases. Moreover, it requests In this subsection, we evaluate the performance of the an extra overhead since it needs longer CP than the maximum proposed method in terms of data rate while observing their channel delay spread. In order to show the robustness of transmitted signal power. Fig. 10 shows the data rate of the our proposed method to the maximum channel delay spread proposed basis scheme and its modifications with respect to 10 the number of used subcarriers. It is evident that the data rate 14 increases when the number of used subcarriers increases. In Basis scheme N the basis scheme, the data rate is η = . In Modification- Mod-I, L=3 Ts I, the data rate is η = G = b N c 1 and decreases as L 12 Mod-I, L=5 Ts L Ts increases. Finally, the data rate in Modification-II, from (43), Mod-I, L=10 10 Mod-II, L=3, M=1 is η = Nb . Furthermore, as shown in Fig. 11, the average Ts Mod-II, L=5, M=2 signal power for the basis scheme and Modification-I are 8 Mod-II, L=10, M=4 the same. Additionally, Modification-II supports higher data rate compared to Modification-I while enjoying lower signal 6 power.

The power of the backscattered signal can cause an interfer- Data rate [Mbps] 4 ence over the ambient OFDM signal for the legacy receiver. Hence, we define the bit-rate-to-interference (BRI) ratio as 2 the data rate, i.e., η, over the interference produced by active subcarriers. Let λ denote the BRI ratio and Eb is set to 1 mW. 0 In the basis scheme, considering η = N transmitted bits over 10 20 30 40 50 Ts N 6 Number of used subcarriers an average of 2 active subcarriers , the BRI is given by Fig. 10: Data rate evaluation of the proposed schemes. N Ts λbasis = N = 500 Mb/s/W. (48) 2 Eb Basis scheme The green columns in Fig. 12 (a) show the fixed BRI for the 25 Mod-I, L=3 basis scheme. For Modification-I where each bit is transmitted Mod-I, L=5 by a block of subcarriers, we have Mod-I, L=10 20 Mod-II, L=3, M=1 G Mod-II, L=5, M=2 T 500 λ = s = Mb/s/W. (49) Mod-II, L=10, M=4 Mod-I GL L 2 Eb 15 Fig. 12 (b) shows that by increasing the size of blocks, i.e., L, the BRI decreases. Moreover, for Modification-II where IM is 10 employed for backscatter communication, from (43), we have

Average Power [mW] G L 5 blog2 c Ts M λ = Mod-II GME b 0 L 10 20 30 40 50 blog c × 250 2 M Number of used subcarriers = Mb/s/W. (50) M Fig. 11: Signal power evaluation of the proposed schemes, Eb = 1 mW. Fig. 12 (c) shows that the highest BRI of the Modification-II is when L increases and M decreases. VII.ACKNOWLEDGEMENT This work was supported by Australian Research Coun- VI.CONCLUSIONS cil (ARC) Discovery 2020 Funding, under grant number In this paper, we studied subcarrier-wise backscatter com- DP200100391. munication over ambient OFDM in the frequency domain and proposed a basis scheme and its two modifications. In the APPENDIX A basis scheme, OOK modulation for each subcarrier has been In order to find Pr(|r| > δ d = 0, A < B, B), we have to used to transmit one bit per subcarrier. Considering interleaved solve the following integral with respect to Fig. 6 (a) block transmission, it was shown that Modification-I improves the BER performance of the system significantly. Finally, in Pr(|r| >δ d = 0, A < B, B) = √ √ Z −δ (x+A E )2 Z ∞ (x+A E )2 Modification-II, IM was employed to control the power of the 1 − b − b √ e N0 dx + e N0 dx signal so that the interference imposed on the original OFDM 2 πN0 −∞ δ √ √ −δ (x−A E )2 ∞ (x−A E )2 signal can be reduced. Moreover, a closed-form optimal de- Z − b Z − b + e N0 dx + e N0 dx . (51) cision threshold has been derived for the amplitude of the −∞ δ received subcarrier to detect the data at the reader. Analytical Therefore, we have expressions for the BER probability was also derived for both

AWGN and Rayleigh fading channels which coincide with the Pr(|r| > δ d = 0, A < B, B) = simulation results. rγ rγ Q (B − A) + Q (3A + B) . (52) 6 1 2 2 dl is equally likely, i.e., Pr(dl = 0) = Pr(dl = 1) = 2 . 11

(a) The BRI ratio in the basis scheme. (b) The BRI ratio in Modification-I. (c) The BRI ratio in Modification-II. Fig. 12: BRI ratio evaluation of the proposed basis scheme and its modifications. The BRI in the basis scheme is independent of M and L. The BRI in Modification-I depends on L. The BRI in Modification-II depends on both of M and L.

Likewise we have, In order to calculate the first expression of (55), i.e., f1(µ), by taking a partial integration, we have Pr(|r| < δ d = 1, A < B, B) = v r r u z }| { γ γ Z ∞ Z B z }| { d A2 Q (B − A) − Q (3B + A) . (53) f (µ) = Q [(B − A)µ] − exp − dA 2 2 1 2 0 0 dA 2σ B B2 x2 + 7 × exp − dB, (56) Since, Q(x) 6 exp(− 2 ) and A, B ∈ R , as SNR 2σ2 4σ2 p γ p γ increases, we can see Q (B − A) 2 Q (3A + B) 2 p γ p γ and consequently and Q (B − A) 2 Q (3B + A) 2 in (52) and (53), Q (3A + B)p γ respectively. In other words, the effect of 2 Z ∞ " B Z B # 2 p γ B B and Q (3B + A) on BER probability in (52) and (53) f1(µ) = uv − vdu exp − dB. (57) 2 2σ2 4σ2 is negligible and we ignore them in (34) in Section III-C. The 0 0 0 similar analysis is considered for (36) in Section III-C. µ2 1 We set α , 2 + 2σ2 , then, we have Z ∞ 1 B2 µ µ2 APPENDIX B √ 2 f1(µ) = Q(Bµ) − exp − 2 + exp − B 0 2 2σ 2π 2 In order to find the closed-form expression of (38), we first  2 2 2 2 p γ set σ = σ = σ , σ = 1, µ = , and β = 1 to simplify Z B  B B2 a b c 2 × exp −α2A2 + µ2BA dA exp − dB. the notation and analysis. Thus, we have  2 2 0  2σ 4σ | {z } g(B) ( 2 ha ∼ CN (0, σ ) (58) 2 . (54) ha + hs ∼ CN (0, 2σ ) Expression of g(B) in (58) is given by Therefore, we can assume that A and B are Rayleigh random √ π µ4 µ2 µ2 variables with average power of σ2 and 2σ2, respectively [50], g(B) = exp B2 erf B + erf (α − )B , 2α 4α2 2α 2α [51]. Consequently, the error probability of the basis scheme (59) in (38) is given by x 2 √1 R −t where erf(x) = π −x e dt. By substituting (59) into (58) Pe|basis = we have f1(µ) z }| { Z ∞ 2 ∞ B 2 2 B B Z Z A A B B f1(µ) = Q [Bµ] exp − dB− Q [(B − A)µ] exp − exp − dA dB + 2σ2 4σ2 σ2 2σ2 2σ2 4σ2 0 0 0 1 Z ∞ B2 B2 f (µ) exp − B exp − dB+ 2 2 2 2 z }| { 4σ 0 2σ 4σ Z ∞ Z ∞ 2 2 A A B B µ Z ∞ µ2 1 µ4 µ2 Q [(A − B)µ] exp − exp − dA dB . √ B exp −B2 + − erf B dB+ 2 2 2 2 2 2 2 0 B σ 2σ 2σ 4σ 4 2ασ 0 2 4σ 4α 2α (55) µ Z ∞ µ2 1 µ4 µ2 √ B exp −B2 + − erf (α − )B dB. 2 2 2 4 2ασ 0 2 4σ 4α 2α 7 + (60) R = {x|x > 0, x ∈ R} 12

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