I Introduction
Ambient backscatter [1], a newborn green technology for the Internet of Things (IoT), has attracted much attention from both academia and industry [2, 3, 4, 5, 6, 7]. Ambient backscatter utilizes the ambient radio frequency signals to enable the backscatter communications of low datarate devices such as tags or sensors, and can free them from batteries.
A typical ambient backscatter communication system includes three components: a radio frequency (RF) source, a tag (or a sensor), and a reader, as shown in Fig. 1. The communication process between the tag and the reader mainly contains two steps: first, the tag harvests energy from the signals of the RF source; second, the tag modulates its binary information onto the received RF signals and then backscatters them to the reader.
Almost all existing studies [1, 2, 3, 4, 5, 6, 7] about ambient backscatter communication are based on the assumption of flatfading channels. However, the frequencyselective channels often exist in many practical scenarios. For ambient backscatter communication systems, frequencyselective channels may result in multiple copies of backscattered signals at the reader, together with multiple source signals. Accordingly, it is one challenging problem for the reader to decode and recover the tag signals.
In this paper, we investigate the ambient backscatter communication systems over frequencyselective channels and propose a transceiver design to cope with the signal detection challenge at the reader. Our design smartly utilizes the cyclic prefix (CP) of orthogonal frequencydivision multiplexing (OFDM) source symbols, which can facilitate signal detection at the reader via cancelling the signal interference. Moreover, different from the transceiver design in [4], our design leads to no interference to the legacy receivers. A chisquare based detector is then proposed and the corresponding optimal detection threshold is derived. Simulation results show that our transceiver design for the frequencyselective channels is efficient and achieves low bit error rate (BER) due to interference cancellation.
The rest of this paper is organized as follows: Section II formulates the model of the ambient backscatter communication system over frequencyselective channels. Section III proposes the transceiver design and Section IV derives the chisquare based detector together with the optimal detection threshold. Section V provides the simulation results and finally Section VI summarizes this paper.
Ii System Model
Consider an ambient backscatter communication system over frequencyselective channels in Fig. 1. The multipath channels between the RF source and reader, the RF source and tag, the reader and tag are denoted by , , , respectively. Both the reader and the legacy receiver receive signals from the RF source and the tag over frequencyselective channels.
Suppose the signal transmitted by the RF source is
with the zeromean and the variance of
and . Due to the multipath channels , the signal arriving at the tag antenna can be given as(1) 
The tag next modulates its own binary signal onto the received signal to communicate with the reader via backscattering or not. Specifically, the tag changes its antenna impedance to reflect to the reader so as to indicate ; and when indicating , the tag switches the impedance to a certain value so that no signal can be reflected. Assume that and are equiprobable.
Finally, the received signal at the reader can be expressed as
(2) 
where represents the complex attenuation inside the tag, denotes the additive white Gaussian noise (AWGN) and we assume .
Remark 1
The reader aims to recover the tag signal from the received signal . Nevertheless, since the binary signal hides in the received signal , it is inefficient to utilize the methods in traditional pointtopoint and relay communication systems to realize the recovery of . In addition, the frequencyselective channels worsen this dilemma due to multiple copies of the source signals that appear in the received signals . Consequently, a transceiver design together with a signal detector are required to achieve accurate recovery of , which will be introduced in our later Section III and Section IV, respectively.
Iii Interferencefree Transceiver Design
In this section, we describe an interferencefree transceiver design, whose implementation mainly consists of three crucial aspects: the tag signal design, the signal interference cancelling method, and the discrete Fourier transformation (DFT) operation.
Iiia Tag Signal Design
With the assumption that the RF source emits OFDM symbols, the structures of the RF source signal , the tag signal , and the received signal at the tag, are presented in Fig. 2.^{1}^{1}1Since the OFDM technique is ubiquitous in current wireless systems such as LTE and WiFi, it is reasonable to consider the RF source emitting OFDM symbols. We set and as the lengths of the CP and the effective part of the OFDM symbol, respectively. The parameter is defined as .
Obviously, both and have repeating sequences, even if the signal experiences the multipath channels . Besides, we divide one OFDM symbol period into four phases for the designed tag signal . In Phase 1, Phase 3, and Phase 4, no received signal will be reflected, i.e., . In this case, the signals arriving at the reader directly come from the RF source. However, in Phase 2, the tag modulates its binary data onto the signal from to while no signal is backscattered to the reader in the rest of the Phase 2. By exploiting the signals arriving at the reader in Phase 2 and Phase 4, we can cancel the signal interference, which will be presented in the next subsection.
Remark 2
It can be checked from Fig. 2 that the signal structure of merely effects the samples in the CP of the OFDM symbol. Since the CP will be removed at the legacy receiver, this transceiver design at the tag will lead to no interference to the legacy receivers.
IiiB Signal Interference Cancelling Method
Denote the received signals at the reader in Phase 2 and Phase 4 as and , respectively. We can obtain
(3)  
(4) 
where and are both AWGN. Assume that and .
Apparently, the term in (3) and (4) carries no tag binary information and thus is the interference for the tag signal recovery at the reader, which should be cancelled so as to enhance detection accuracy.
Signal interference cancelling is implemented via subtracting from , thus the received signals can be written as
(5) 
where and .
Assuming and , we rewrite (5) in matrix as
(6) 
IiiC DFT Operation
Define
(8)  
(9)  
(10) 
Denote F as the DFT matrix with the th element . Let us consider a Toeplitz matrix T, which possesses the first row of and the first column of .
Consequently, we reconstruct the signal vector z based on DFT as, i.e., DFT outputs
(11) 
where
(12)  
(13)  
(14)  
(15) 
Iv Chisquare Based Signal Detection at the Reader
In this section, the chisquare based detector together with the optimal detection threshold are derived via the maximum likelihood (ML) principle. The corresponding BER expression is also obtained to evaluate the detection performance.
Iva Chisquare Based Detector
Due to the lower datarate of the tag signal than that of the signal , we suppose the signal remains equivalent within samples of
. Let us construct the test statistic for detecting
as(19) 
where , and is expanded as
(20) 
It can be readily checked that
(21) 
where
(22)  
(23)  
(24) 
Let and represent and , respectively. Apparently, under , the test statistic follows the noncentral chisquare distribution with degrees of freedom and noncentrality parameter [9], i.e., , where is the detection signaltonoise ratio (SNR) that can be calculated as
(25) 
While under , follows the chisquare distribution with degrees of freedom, which is denoted as .
Therefore, the probability density function (PDF) of
under is obtained as(26) 
where
(27) 
and as the Gamma function [10].
Similarly, under , the PDF of is
(28) 
where
(29) 
and is the order modified Bessel function of the first kind [10]
(30) 
Consequently, the chisquare based detector can be made through the ML principle as
(31) 
where is the probability density function (PDF) of given . We can also reformulate the ML detection rule (31) as
(32) 
One example of the PDFs of under two conditions and is presented in Fig. 3.
IvB Optimal Detection Threshold
The optimal detection threshold of this ML detector can be derived by setting that the PDF under equals to that under
(33) 
Define
(34) 
Substituting (27) and (29) into (33) will produce
(35) 
which can be further simplified as
(36) 
After exerting some mathematical manipulations in (36), one obtains
(37) 
Therefore, the detection rule can be summarized as
(38) 
IvC BER Performance
Define and as the probability of false alarm and the probability of missing detection, separately.
V Simulation Results
In this section, numerical results are provided to assess the performance of proposed chisquare based detector. All the channels follow Gaussian distributions with the zeromean and unitvariance. The number of channel taps
, and are assumed to be in following simulations. We set the attenuation , the noise power and the length of CP as , and , separately. We also exert Monte Carlo trials for every experiment to examine BER performance of the chisquare based detector.Fig. 4 plots the BER curves versus SNR for the chisquare based detector with the optimal detection threshold. We set the number of averaging samples as and , respectively. As seen, the BER performance could be enhanced with enlarging SNR or .
Fig. 5 depicts the BER curves versus the number of averaging samples with different SNR for our detector. We choose SNR as 13 dB and 16 dB, separately. It is found that the BER performance is improved with increasing . Besides, due to the exploitation of the approximation (40) for analytical BER, there is a small gap between the simulation and analytical results in Fig. 5.
Vi Conclusion
This paper focused on the data transmission of the ambient backscatter communication systems over frequencyselective channels. A novel interferencefree transceiver design, which exploits the CP structure of OFDM symbols to cancel the signal interference, was proposed to facilitate interference cancellation and signal detection in such scenario. Moreover, this transceiver design led to no interference to the legacy receivers since the CP will be removed at the legacy receiver. Furthermore, a chisquare based detector was derived, as well as the optimal detection threshold. Finally, the BER performance of the chisquare based detector was evaluated via Monte Carlo simulations. It was shown that the proposed transceiver design is efficient and the chisquare based detector demonstrates satisfying BER performance.
References
 [1] V. Liu, A. Parks, V. Talla, S. Gollakota, D. Wetherall, and J. R. Smith, “Ambient backscatter: wireless communication out of thin air,” in Proc. ACM SIGCOMM, Hong Kong, China, 2013, pp. 113.
 [2] G. Wang, F. Gao, R. Fan, and C. Tellambura, “Ambient backscatter communication systems: detection and performance analysis,” IEEE Trans. Commun., vol. 64, no. 11, pp. 110, Aug. 2016.
 [3] J. Qian, F. Gao, G. Wang, S. Jin, and H. Zhu, “Noncoherent detections for ambient backscatter system,” IEEE Trans. Wireless Commun., vol. 16, no. 3, pp. 14121422, Mar. 2017.
 [4] G. Yang, Y. C. Liang, R. Zhang, and Y. Pei, “Modulation in the air: backscatter communication over ambient OFDM carrier,” IEEE Trans. Commun., vol. 66, no. 3, pp. 12191233, Mar. 2018.

[5]
S. Ma, G. Wang, R. Fan, and C. Tellambura, “Blind channel estimation for ambient backscatter communication systems,”
IEEE Commun. Lett., vol. 22, no. 6, pp. 12961299, Jun. 2018.  [6] Z. Ma, T. Zeng, G. Wang, and F. Gao, “Signal detection for ambient backscatter system with multiple receiving antennas,” in Proc. IEEE 14th Can. Workshop Inf. Theory (CWIT), St. John s, NF, Canada, Jul. 2015, pp. 14.
 [7] D. Li, W. Peng, and Y. Liang, “Hybrid ambient backscatter communication systems with harvestthentransmit protocols,” IEEE Access, vol. 6, pp. 4528845298, 2018.

[8]
A. Papoulis and S. U. Pillai,
Probability, Random Variables and Stochastic Processes
. 4th ed. New York, NY, USA: McGrawHill, 2002, ch. 7, pp. 278279. 
[9]
D. Horgan and C. C. Murphy, ”On the convergence of the chi square and noncentral chi square distributions to the normal distribution,”
IEEE Commun. Lett., vol. 17, no. 12, pp. 22332236, Dec. 2013.  [10] I. M. Ryzhik, A. Jeffrey, and D. Zwillinger, Table of Integrals, Series and Products. San Diego, CA, USA: Academic, 2007.
Comments
There are no comments yet.