Ambient backscatter communications (AmBC) has been considered as a cutting-edge technology for the Internet of Things (IoT) due to the ability to offer microwatt-level power consumption . As applications of AmBC become more data-intensive, such as wearable devices and security cameras/microphones , the expectation for higher data rates and greater reliability poses new challenges for AmBC. Inspired by Wi-Fi and cellular networks that use multiple-antenna techniques to improve uplink rate or reliability , multiple-antenna backscatter is a promising approach to meet the challenges.
Growing attempts have already been devoted to exploring the merits of multiple antennas in conventional backscatter communications (CoBC), e.g., radio frequency identification (RFID) [4, 5]. Despite the fact that much has been understood through these studies, hardly any of existing analytical models cannot be directly applied to AmBC. Specifically, CoBC needs a dedicated RF source to transmit known signals while ambient RF signals are unknown in AmBC. Furthermore, these studies make assumptions about time synchronization and non-coupling problem between antennas, which cannot be guaranteed in practical AmBC due to the small form factor and the minimalist design .
The goal of this paper is to study the AmBC-compatible multiple-antenna backscatter designs. We observe that spatial modulation (SM), which always keeps only one antenna active at any instant, potentially exempts the ambient backscatter tags from the inter-antenna synchronization and mutual coupling problems in the antenna array. In this paper, we present SM-backscatter, a practical multiple-antenna backscatter design by exploring the use of spatial modulation in AmBC. Benefits from both backscatter modulation and spatial modulation, SM-backscatter ensures ultra-low power consumption and high spectral efficiency. In addition, we consider the joint detection of the backscatter signal and RF source signal and obtain the optimal detector based on the maximum likelihood principle. To analyze the detection performance, we design a two-step algorithm to derive bounds on the bit error rate (BER) of the backscatter signal and the source signal, respectively.
The main contributions are summarized as follows.
We propose a practical multiple-antenna backscatter design for AmBC by exploring the use of spatial modulation. To the best of our knowledge, this is the first SM design for AmBC.
We obtain the optimal detector for the joint detection of the backscatter signal and the source signal. We also derive the upper bounds on the BER of both signals based on the optimal detector.
Simulation results indicate that our scheme significantly improves the throughput compared to the single-antenna case in AmBC.
The remainder of this paper is organized as follows. Section II depicts the theoretical model for AmBC with spatial modulation. In Section III, we derive the optimal detector and analyze the BER performance of the RF source signal and the backscatter signal. Next, simulation results are provided in Section IV. Section V presents the state of the art. Finally, Section VI concludes the paper.
Ii System Model
We consider an AmBC system consists of a single-antenna ambient RF source, an M-antenna reader, and an L-antenna backscatter tag, as shown in Fig. 1. The ambient RF source can be common RF signal transmitters in our living environment, such as Wi-Fi access points (APs), TV or frequency modulation (FM) radio towers. Due to the broadcast characteristics of the RF signal, both the reader and the backscatter tag can receive the RF signal. The backscatter tag can reflect the incoming excitation signal by changing the load impedance, i.e., reflection coefficient, between two impedances loads to transmit symbols. Specifically, the RF signal is harvested when the matching impedance is selected, while the RF signal is reflected if the mismatch impedance is selected. These two states represent bit “0” and bit “1”, respectively. The reader needs to detect the signals from both the RF source and the backscatter tag.
In this paper, we make the following assumptions: 1) the channel state information (CSI) is only available at the reader; 2) the time delay between the arriving of the RF source signal and the backscattered signal at the reader can be ignored; 3) there is no the thermal noise at the tag because the circuit only consists of passive components. These assumptions have been considered in , , .
Ii-a Channel Model
Denote , and as coefficients of the channel from the ambient RF source to the m-th antenna of the reader, from the source to the l-th antenna of the tag, and from the l-th antenna of the tag to the m
-th antenna of the reader, respectively. The channel vector of the direct links is. and are the forward channel vector and backward channel matrix, respectively, where . We assume that the channels are block flat fading and independent from each other.
The equivalent complete channel matrix of the system can be expressed as
where is the composite backscatter channel vector passing through the l-th antenna of the tag.
Unlike the dyadic backscatter channel in CoBC , we consider the channel of the direct links. Moreover, the forward and backward backscatter channel in AmBC are independent, but they have a link correlation in CoBC.
Ii-B Signal Model
We consider the spatial modulation on the backscatter tag. In SM-backscatter, only one antenna of the tag is active at a single time instant. The index of the active antenna is mapped as a spatial constellation point to transmit additional information when the conventional signal constellation point is transmitted. This process is called tridimensional constellation diagram, as shown in Fig. 2.
This design can entirely avoid the inter-antenna synchronization and mutual coupling problems in the antenna array. We consider a tag with four antennas as an example here to illustrate the process of SM-backscatter. The controller can select the active antenna and impedance to control the mapping process of the bit information. Specifically, “001” represents that the first antenna reflects the RF signal and transmits the bit “1” simultaneously. At time instant n, the original bits are modulated at the tag as
where represents the active antenna, and is one of the unit-energy modulated symbols from the backscatter tag, i.e., reflection coefficients.
At any instant, the number of transmitted bits for the ambient backscatter system that use constellation diagram of size and L transmit antennas is
Denote as the average transmit power of the RF signal, which is unknown to the reader. The signal received by the m-th antenna of the reader can be expressed as
where is one of the unit-energy modulated symbols from the RF source,
is the zero-mean additive white Gaussian (AWGN) noise with variance.
The received SNRs of the direct path and the composite backscatter path are , . The relative SNR between the composite backscatter path and the direct path is . Generally, we assume , . The equivalent signal model reads
Therefore, the received signal at the reader is
where is the equivalent complete channel matrix of the backscatter channels.
Iii Optimal Detector and Performance Analysis
In this section, we obtain the optimal detector based on maximum likelihood (ML) principle to minimize the bit error rate (BER) of both the RF source signal and the backscatter signal. In addition, we further analyze the BER performance of the SM-Backscatter system. The closed-form expressions are derived using the union bounding technique. For convenience, we assume that the tag and RF source adopt binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) modulation , , respectively. However, the analysis is compatible with other modulation schemes.
Iii-a Optimal Detector
Mathematically, the ML estimations ofand can be expressed as
where is the symbol transmitted by the -th backscatter antenna.
The proposed detector considers the joint detection of the backscatter signal (i.e., the antenna indexes and transmitted symbols) and the RF source signal. Therefore, the direct link interference from the RF source signal can be solved.
Iii-B Analytical BER of the Backscatter Signal
It is not straightforward to calculate the BER of SM-backscatter. There are two estimation processes involved, the estimation of the antenna index and the transmitted symbol. These processes are dependent in the calculation. We can detect the tag symbols correctly only if both estimates are correct. Denote the BER of the backscatter signal and the source signal as and , respectively. Due to and are mutually related in (8), we design a two-step algorithm to calculate and . We assume that all transmitted symbols are equiprobable.
Given , the estimation of is as follows:
Based on the optimal detector, we can derive the average BER of using the union bounding technique 
where is the number of bits in error between and , is the pairwise error probability (PEP),
where , , .
See Appendix A. ∎
Case 1: if , we have
The BER of is independent of the estimation of , but is related to the ambient source transmit power. Then, the BER of is given by
Mathematically, in this case, the BER of can be written as
Considering two cases together, can be expressed as
Iii-C Analytical BER of the RF Source Signal
Given , we detect the form as follows:
where , .
Case 1: if , we have
Mathematically, in this case, the BER of is derived as
Case 2: if , we define .
where and .
The BER of is
Mathematically, we can derive . Then, for the case 2, the BER of is
Considering two cases together, is given by
The corresponding average BERs can be expressed as and , respectively.
Iv Numerical Results
In this section, simulation results of the SM-backscatter system are presented to evaluate the performance of the proposed detection scheme and verify the correctness of our analytical expressions. All results consider the Rayleigh fading channel, with complete channel information at the reader. We set , and the variance of varies with . Gray mapping is considered when appropriate (i.e., for QPSK and BPSK). The figures illustrate the average BER versus , which is the average SNR of the direct path per receive antenna. Totally Monte Carlo runs are performed for average.
Figs. 4 and 6 show the BER of the backscatter signal versus SNR. In Fig. 4, is fixed to 4. The results show that the BER is related to the strength of the backscatter signal. Increasing significantly impacts the BER values. At the BER of , the case shows about a 5 dB gain with respect to . Fig. 6 shows the BER performance of the backscatter signal for different antenna numbers on the tag with . The results shows that single antenna alone cause a 1.5 dB and 3 dB gain for and , respectively. In both figures, the upper bounds are plotted for the comparison with the simultaion results. They can accurately illustrate the impacts of the relative SNR and the change of antenna number on the BER, which corroborate the correctness of (III-B).
Figs. 4 and 6 plot the BER of the source signal versus SNR. Specifically, Fig. 4 shows that the strength of the backscatter signal has a little effect on the BER performance of the source signal. When , there only has a 0.7 dB loss than that . Fig. 6 depicts the impact of the antenna number on the BER of the source single. At the BER of , , and show up to a 0.7 dB, 1.3 dB and 1.8 dB gain loss with respect to the conventional case, i.e., signal-antenna backscatter. The bounds in two figures are tight to the simulation results which verifies (26). Besides, comparing Figs. 6 and 6, we can see that the BER performance of the source signal is better than the SM-backscatter signal because the backscatter signal received by the reader suffers from double cascaded channel fading.
The four figures from Figs. 4 to 6 suggest that when the number of SM-backscatter antennas is less than eight, the backscatter signal has little effect on traditional RF communication. This result indicates that SM-backscatter is compatible with existing systems.
In Fig. 7, we compare the throughput gain of SM-backscatter versus single-antenna backscatter for various antenna numbers. As the SNR increases, the throughput of , and is close to 4, 3 and two times higher than the single-antenna backscatter system, respectively. The results prove that SM-backscatter can bring throughput gain. Fig. 6 and 6 show that an increase in the number of antennas leads to an increase in the BER of the system, which also indicates that SM-backscatter has a trade-off between increasing the number of antennas and guaranteeing detection performance.
V Related work
Of the existing studies in AmBC, the majority has focused solely on multiple antennas at the reader, while ignoring the tags. To address the direct link interference from ambient RF source, multiple-antenna readers are proposed in [8, 11] for the joint detection of the legacy and backscatter systems. Previous works on the multiple-antenna backscatter applied to AmBC systems are sparse. Though the achievable rate has been studied in AmBC with multiple-antenna tags , this work does not consider the effect of time synchronization and mutual coupling problems between antennas. A blind detector for the reader to detect the backscatter signal is proposed in . This work solely focuses on the detection mechanism for the reader to detect the backscatter signal and does not improve the data rate. Departure from these studies, our work considers both the feasibility of real-world implementation and the high spectral efficiency in AmBC with multiple-antenna tags.
In this work, we investigate the AmBC-compatible multiple-antenna backscatter designs to meet the higher commutation performance requirement. We propose a practical multiple-antenna backscatter design for AmBC, SM-backscatter, which can avoid inter-antenna synchronization and coupling problems caused by multiple antennas while ensuring high spectral efficiency and ultra-low power consumption. In addition, we provide a fundamental study on SM-backscatter, including system model, optimal detector and BER bound computations. Simulation results indicate that our scheme significantly improves the throughput compared to traditional single-antenna backscatter case. We hope that our investigations on AmBC-compatible multiple-antenna backscatter designs can provide some implications for future AmBC systems.
Appendix A Proof of PEP
According to , the can be expressed as
where is a Gaussian random variance with zero mean and variance .
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