Mobile Networks and Applications https://doi.org/10.1007/s11036-017-0980-0
Signal Ratio Detection and Approximate Performance Analysis for Ambient Backscatter Communication Systems with Multiple Receiving Antennas Shuo Ma1 · Gongpu Wang1 · Yanwen Wang2 · Zhuyan Zhao3 © Springer Science+Business Media, LLC, part of Springer Nature 2017
Abstract Recently, ambient backscatter attracts much attention since it can utilize ambient radio frequency signals to enable batteryfree devices to communicate with others. Most existing studies about ambient backscatter assume that the reader is equipped with one receiving antenna. In practice, the reader can utilize multiple antennas to overcome channel fading. In this paper, we investigate the problem of signal detection for ambient backscatter systems with multiple receiving antennas. Specifically, we formulate a new transmission model where the reader is equipped with at least two antennas and propose a ratio detector that exploits the ratio of the signal strength received at each antenna. It is shown that the closed-form expression of the optimal detection threshold for this detector is difficult to derive. Therefore, we derive a reasonable approximate expression for the optimal detection threshold. Moreover, we obtain the closed-form expression for approximate bit error rate (BER). Furthermore, we propose an antenna selection scheme if the reader is equipped with more than two antennas. The selection scheme is investigated through the BER performance. It is found that the largest gain in BER can be achieved when the antenna number increases from two to three, and that much less gain is obtained from enlarging the antenna number when the reader already has four antennas. Finally, simulation results are provided to corroborate our theoretical studies. Keywords Ambient backscatter · Ratio detection · Approximate threshold · BER · Multiple receiving antennas · Antenna selection scheme
1 Introduction With the rapid development of Internet and fast growing demand for Internet of Things (IoT), the fifth generation (5G) mobile communication technology which will increase the transmission rate by 10 to 100 times and support massive access to the Internet have been actively advanced. 5G will make it possible to interconnect all things. Obviously, 5G is closely related to IoT with the advantages of lower cost, less energy consumption, and stronger reliability. Due to the high flexibility, 5G is able to process diverse data produced
Gongpu Wang
[email protected] Shuo Ma
[email protected] 1
Beijing Jiaotong University, Beijing, China
2
ZTE Corporation, Xian, China
3
Nokia Bell Labs, Beijing, China
by IoT. In turn, IoT will provide efficient and optimized network configuration of 5G to satisfy the requirement of various terminals. One of the fundamental technologies involved in IoT is Radio Frequency Identification (RFID). A typical RFID system mainly consists of a reader and a tag. The tag reflects the signals generated by the reader to transmit its binary information. This is called backscatter, the key technology of RFID communication systems. To my best knowledge, it is a new communication pattern which is distinguished from traditional point-to-point or cooperative wireless communication styles. The origin of backscatter traces back to World War II where it was applied to distinguish the coming airplane as “friend or foe” through detecting its backscattered signals [1]. From 1990 to 2000, Electronic Toll Collection (ETC), a well-known and successful application of RFID system, was widely applied for drivers to pay the fees on roads or highways without stopping [2]. Since 2000, a series of RFID systems have been extensively utilized to facilitate our lives.
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One disadvantage of the conventional RFID systems is that they require special radio sources to trigger the tag. To avoid such requirement, ambient backscatter, a new type of backscatter was proposed in 2013 [3]. It utilizes ambient existed radio frequency (RF) resources, such as radio television signals, radio broadcast signals and Wireless Fidelity (Wi-Fi) signals [25], to supply the battery-free tags with both energy and signals [3, 4]. The essential communication principles of ambient backscatter can be described as follows [3]: (i) The tag conveys its two symbols “1” or “0” by switching the antennas impedance inside to backscatter the received wireless signals or not; (ii) The reader detects the two states in terms of the differences between the forms of received signals. Note that ambient backscatter can be applied not only in RFID systems but also in sensors and IoT. Ambient backscatter technology can gather energy from wireless signals around for battery-free devices such as sensors to perform communications as well as calculations [5]. It can therefore liberate sensors from batteries for power supply and avoid heavy human operations. Ambient backscatter will be a boost for IoT because it provides a new way of gathering energy which supports ubiquitous and constant communication. Future applications may exist in the following aspects: –
– –
Communication between smart cards. Smart cards can utilize ambient radio frequency to communicate with each other and exchange information such as accounting payment between credit cards. Tracking of material flow. The tags in material flow can be tracked wherever radio frequency resources cover. Wearable devices. Ambient backscatter can solve the problems of limited battery capacities and frequent recharging. As a result, it can offer better user experiences.
2 Related work Ambient backscatter has attracted much attention in academia ever since it was put forward in 2013 [3]. The authors in [6] have verified that sensors could keep working just motivated by existing wireless signals without batteries. The reference [3] first designed a prototype of ambient backscatter communication system and found its communication range as well as bit error rate (BER) performance through experiments. Differential detection based on average energy of received signals was also proposed in [3] for the reader to avoid channel estimation. However, this energy detector may result in error propagation, and meanwhile its transmission data rate is low. To address this two problems, the authors in [7]
introduced a multi-antenna cancelation design that could be operated on backscatter devices and enabled long range communications and concurrent transmissions utilizing a new coding scheme. They also performed detection utilizing the ratio of received signals to approximate that of wireless channel parameters roughly. A new backscatter communication system exploiting the fullduplex technology [8, 9] was presented in 2015 [10]. It enables high-throughput and long-range communication between low-power backscatter IoT sensors and WiFi APs where ambient WiFi signals are utilized as the excitation signals for the sensors [10]. In addition, the reference [11] demonstrated that the Wi-Fi and ZigBee signals could be created through Bluetooth signals, which was referred to as inter-backscatter technology. Physical circuits of new backscatter communication systems have been designed [3, 7, 10, 11] and the feasibilities have also been verified through experiments. The theoretical analysis about ambient backscatter was provided in [12–14]. The references [12, 14] systematically investigated BER performance of ambient backscatter systems with differential encoding and maximum likelihood (ML) detection. The authors in [13] designed an optimal energy detector for ambient backscatter system with single receiving antenna. In energy detection scheme, the transmitter would repeatedly transmit one bit to satisfy the detection requirement which results in low transmission rates. In comparison, multi-antenna technology can perform detection utilizing instant receiving signals, which is more feasible. Differential modulation and a suboptimal ML detector were proposed in the reference [15]. A detection algorithm based on statistical covariances was suggested in [16] and was shown to outperform the energy detector at low signal-to-noise ratio (SNR) regions. A maximum likelihood detector based on the joint probability density function of received signals is derived with unknown channel state information (CSI) [17]. Most existing theoretical studies of signal detection are focused on the scenarios where the reader is equipped with single receiving antenna. However, the system with single receiving antenna is limited in the transmission rate and vulnerable in poor channel conditions. Multiple antennas can provide larger transmission rates and more reliable communication [25]. Multi-antenna technology is efficient against fading and can increase the link reliability. The fadings of multiple receiving signals are independent, thus the possibility of fading in all channels is considerably reduced. In addition, multiple receiving antennas can significantly increase transmission rates. Various MIMO optimization problems with matrix variables could be simplified into ones with vector variables to decrease the complexity of computation [18].
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The prototype of multi-antenna devices in ambient backscatter system was proposed [7] and it turned out that RFID tags could communicate with each other at distances up to tens of meters and even separated by multiple walls in the experiments. The authors in reference [19] built up a system model with multiple antennas and proposed a blind detector, and it was shown that there exists error floors for this blind detector. In this paper, we re-investigate the detection problem for ambient backscatter communication systems with multiple receiving antennas at the reader. Different from the blind detector suggested in [17, 19], we utilize the ratio detector [7] and study its BER performance. It is found that the closed-form detection threshold is difficult to obtain due to the complexity of probability density function (PDF) of the ratio. Therefore, we derive an effective approximate detection threshold and the corresponding close-formed BER expression. In addition, we propose an antenna selection scheme when the reader is equipped with more than two antennas which efficiently lowers the BER. Finally, simulation results are provided to prove the suggested theories. The rest of this paper are organized as follows: Section 2 builds up a theoretical model for ambient backscatter communication system where the reader is equipped with multiple antennas. Section 3 proposes the ratio detector and derives the approximate closed-formed BER. In addition, an antenna selection scheme is suggested in Section 4. Finally, Section 5 provides the simulation results and Section 6 concludes the whole paper.
3 System model Consider an ambient backscatter communication system that consists of three components: a reader, a tag and a RF source (Fig. 1). The RF source can be a broadcasting center or a Wi-Fi gateway. The tag can be the sensor that collects environmental parameters such as temperature or humidity. Different from conventional RFID systems, the tag communicates with the reader through backscattering the signals produced by the RF source. Assume that the tag receives signal s(n) from the RF source and the binary information to be transmitted by the tag is B(n). The tag will transmit B(n) to the reader by backscattering s(n) or not. Specifically, if the tag symbols B(n) = 1, the tag will backscatter the received signal s(n) and if the tag symbols B(n) = 0, it will alter its antenna impedance so that little energy is reflected [3, 12]. The reader is equipped with K antennas. Denote the channels between the RF source antenna and the kth antenna of the reader as hk , and the channels between the kth antenna of the reader and that of the tag as fk , where
k ∈ [1, K]. Denote the channel between the tag and the RF source as g. The channels hk , fk , and g are assumed as slow-fading and complex zero-mean Gaussian distributed. That is, hk ∼ CN (0, Nhk ), fk ∼ CN (0, Nfk ), and g ∼ CN (0, Ng ), where Nhk , Nfk , k = 1, 2, · · · , K and Ng represent the corresponding channel variances. Suppose that the complex attenuation of the signal s(n) inside the tag is η. We can obtain the received signal rk (n) at the k-th antenna of the reader as hk s(n) + wk (n), B(n) = 0 (1) rk (n) = hk s(n) + ηgfk s(n) + wk (n), B(n) = 1 where wk (n) denotes the zero-mean additive white Gaussian noise (AWGN). We assume that the channels are perfectly estimated [20–23]1 and known to the reader [12]. The reader aims at detecting B(n) = 0 or B(n) = 1 from the received signals rk (n). Clearly, the received signals rk (n) have different PDFs for the case B(n) = 1 and the case B(n) = 0.
4 Signal detection In this section, we will first consider the case where the reader has two antennas. We investigate the ratio detector and analyze its BER performance. Next we study the case where the reader has more than two antennas, and propose an antenna selection scheme.
4.1 Ratio detector When the reader is equipped with two antennas, it will receive signals r1 (n) and r2 (n) at the same time. The ratio detection algorithm can be described as follows. The reader first calculates the amplitude ratio γ (n) of the two received signals r2 (n) . (2) γ (n) = r1 (n) The specific expressions of γ (n) in two different backscatter states are ⎧ 2 (n) ⎨ γ0 (n) = hh21 s(n)+w s(n)+w1 (n) , B(n) = 0 γ (n) = (3) h s(n)+ηf g2 s(n)+w2 (n) 2 ⎩ γ1 (n) = h1 s(n)+ηf g1 s(n)+w1 (n) , B(n) = 1 Define μi = hi + ηgfi ,
i = 1, 2
(4)
as the composite channel between the reader and the tag when B(n) = 1. Obviously, the reader will detect the signal B(n) through exploiting some differences between γ1 (n) and γ0 (n). 1 which
is difficult but achievable
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1.6
theory
Pk
1.4
0 1
simulation
1
simulation
0 1
1.2
p
1 0.8 th
0.6
Pk
0
0.4 0.2
Fig. 1 System model with multiple receiving antennas 0
Assume that s(n) ∼ CN (0, Ps ), wi (n) ∼ CN (0, Nw ) and therefore we can find hi s(n) + wi (n) ∼ CN (0, σi2 ) and μi s(n) + wi (n) ∼ CN (0, εi2 ), where σi2 = |hi |2 Ps + Nw and εi2 = |μi |2 Ps + Nw , i = 1, 2. Note that γ0 (n) and γ1 (n) are both the ratios of two Rayleigh random variables. According to [24, (7.58)], their PDFs can be found as pγ0 (γ ) = pγ1 (γ ) =
2σ12 σ22 (1 − ρ02 )γ (σ12 γ 2 + σ22 ) 3
[(σ12 γ 2 + σ22 )2 − 4ρ02 σ12 σ22 γ 2 ] 2 2ε12 ε22 (1 − ρ12 )γ (ε12 γ 2 + ε22 ) 3
[(ε12 γ 2 + ε22 )2 − 4ρ12 ε12 ε22 γ 2 ] 2
,
,
(5) (6)
respectively, where ρ0 and ρ1 are the correlation coefficients of r2 (n) and r1 (n). The coefficient ρ0 can be calculated as follows, E[r (n)r H (n)] 1 2 , (7) ρ0 = σ1 σ2 B(n)=0
E[r1 (n)r2H (n)]B(n)=0 = E[(h1 s(n) + w1 (n))(h2 s(n) + w2 (n))H ] Finally,we can obtain h hH P 1 2 s ρ0 = . σ1 σ2
1
2
3
4
5
6
Fig. 2 PDF of theory and simulation when SNR = 10dB
Next we aim at obtaining the optimal detection threshold. We choose the maximum a posteriori (MAP) detector. According to the Bayes formula, the posterior probability can be written as P {B(n) = i|γ (n)} P {B(n) = i}p{γ (n)|B(n) = i} , i = 0, 1 (11) = p{γ (n)} where p{γ (n)} denotes the PDF of the received signal γ (n). Noting that p{γ (n)} is always positive and is independent with the tag signal B(n). Assume that B(n) = 0 and B(n) = 1 are equiprobable. The MAP detection can be further simplified to the maximum likelihood (ML) detector, and the likelihood function is p{γ (n)|B(n) = i} = pγi (γ ),
i = 0, 1
(12)
where pγi (γ ) is Eq. 5 when i = 0 or Eq. 6 when i = 1 . Thus our ML detection rule is 1, if pγ1 (γ ) > pγ0 (γ ), ˆ (13) B(n) = 0, if pγ0 (γ ) > pγ1 (γ ).
where
H H = E[h1 s(n)hH 2 s (n)] = h1 h2 Ps .
0
(8)
(9)
That is when we obtain a value of γ (n), we substitute it ˆ to Eqs. 5 and 6, respectively. And then determine B(n) after comparing the values of Eqs. 5 and 6.
4.2 Detection threshold
Similarly, we can obtain ρ1 , the correlation coefficients of r2 (n) and r1 (n) when B(n) = 1, as follows, E[r (n)r H (n)] μ μH P 1 1 2 s 1 (10) = ρ1 = . ε1 ε2 ε1 ε2
It can be readily checked that the optimal detection threshold γth is the intersection of two PDF functions shown in Fig. 2. Therefore, γth is one solution to . (14) pγ (γ ) = pγ (γ )
The theoretical and simulation PDF results of γ0 (n) and γ1 (n) are shown in Fig. 2 when the SNR is 10dB. Clearly, our theoretical PDFs are consistent with our simulation results.
Unfortunately, the solution to the Eq. 14 can hardly be derived. To address this problem, we choose to obtain an approximate threshold. Our general idea is: we take the
B(n)=1
0
1
γ =γth
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mean of two peak values of PDFs as the detection threshold γˆth , instead. The peak values of pγ0 and pγ1 can be calculated by setting the first-order derivative to zero. The values of peak Pk0 and Pk1 can be found as 24bi4 pi −16bi2 A+144bi4 pi2 +E 2 −144bi2 pi2 A ,(15) Pki = 24ai bi3 pi D where 16bi2 B C + 4bi2 pi + + , 27 27 27B √ 3 B = 2592 3F + 4096bi6 + 132192bi6 pi2 − H ,
C = 32bi4 324pi3 + 81pi2 − 54pi + 8 , A=
(17)
H = 590976bi6 pi3 − 1679616bi6 pi4 + 41472bi6 pi ,
(22)
(19)
(21)
and a0 = σ12 , b0 = σ22 , p0 = ρ02 , a1 = ε12 , b1 = ε22 , p1 = ρ12 . Hence our approximate detection threshold γˆth is (23)
Although the approximate detection threshold γˆth has a closed-form solution, it is still complicated. Next we aim to find a simplified expression for γˆth in high SNR. We consider the case of large transmission power, i.e., Ps >> Nw . In such case, the correlation coefficients ρ0 and ρ1 will approximate 1. h1 hH 2 Ps (24) lim ρ0 ≈
= 1, |h1 |2 Ps |h2 |2 Ps Ps →+∞ μ1 μH P s 2 lim ρ1 ≈
= 1. |μ1 |2 Ps |μ2 |2 Ps Ps →+∞
Pˆk0 + Pˆk1 = 2
σ2 σ1
+ 2
ε2 ε1
.
(29)
where ε1 , ε2 , σ2 , σ1 are all positive numbers. We assume that σ1 ε2 < σ2 ε1 , i.e., Pˆk0 > Pˆk1 . Our ML ratio detector can be further expressed as ˆ B(n) =
0, 1,
γ > γ˜th (or at high SNR γ > γ˜th ), γ < γ˜th (or at high SNR γ < γ˜th ).
(30)
(18)
(20)
Pk0 + Pk1 . 2
γ˜th =
(16)
D = 24pi2 − 20pi + 3, 1 C 2 E = , B + 108bi2 pi + 16bi2 + 81 B F = −bi2 pi3 D 2 (96pi2 − 11pi + 32),
γˆth =
Finally in the case of large SNR, we can define another simplified approximate detection threshold as
(25)
Accordingly, when Ps is large, we can have the following approximation 2σ12 σ22 1 − ρ02 γ σ12 γ 2 + σ22 , (26) pγ0 (γ ) ≈ 2 3 σ1 γ 2 − σ22 2ε12 ε22 1 − ρ12 γ ε12 γ 2 + ε22 pγ1 (γ ) ≈ . (27) 2 3 ε1 γ 2 − ε22 We can therefore utilize the above PDFs to find the approximate peak values, σ2 ε2 and Pˆk1 = . (28) Pˆk0 = σ1 ε1
4.3 BER performance analysis We can obtain the instantaneous BER, ˆ = 1|B(n) = 0} Pe = P {B(n) = 0}P {B(n) ˆ +P {B(n) = 1}P {B(n) = 0|B(n) = 1} 1 1 = P {γ < γ˜th |B(n) = 0} + P {γ > γ˜th |B(n) = 1} 2 2 γ˜th 1 2σ12 σ22 1 − ρ02 γ σ12 γ 2 + σ22 = 3 dγ 2 2 2 2 0 2 2 2 2 2 2 σ1 γ + σ2 − 4ρ0 σ1 σ2 γ +∞ 1 2ε12 ε22 1 − ρ12 γ ε12 γ 2 + ε22 + 3 dγ . (31) 2 2 2 2 2 γ˜th ε1 γ + ε22 − 4ρ12 ε12 ε22 γ 2 After calculating the integral in Eq. 31, we can obtain the final BER, 1 1 Pe = + 2 4 1 − 4
2 − 4Pˆk20
2 2 + 4Pˆk20 − 16ρ02 Pˆk20 2
2 − 4Pˆk21 ,
2 2 2 2 2 2 ˆ ˆ + 4Pk1 − 16ρ1 Pk1
(32)
where = Pˆk0 + Pˆk1 .
4.4 Antenna selection scheme We consider that the reader is equipped with multiple antennas and will select two of the antennas in detection. If the number of receiving antenna at the reader is K, then there will be K2 kinds of combination of two antennas when utilizing the ratio detector (29) described in the previous section.
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In order to improve the detection performance and decrease the BER, here we present an antenna selection algorithm which will choose two antennas to achieve better performance. Let us start with BER shown in Eq. 33.
Pe =
1 1 − 2 4 1 + 1 − 4 1 +
1 2 Pˆk 16 1−ρ02 1+ ˆ 0
Pˆk 3+ ˆ 1 Pk 0
2
Pk 1 Pˆk 1− ˆ 0 Pk 1
1 16
1−ρ12
3+
Pˆk 0 Pˆk 1
Pˆk 1+ ˆ 0 Pk 1
2
1−
2
Pˆk 0 Pˆk 1
2
.
(33)
2
As can be observed from above equation (33), the BER will be smaller when proper values of Pˆk0 and Pˆk1 are chosen. Noting that ρ0 and ρ1 are approximately equal for the same SNR. Accordingly, there exist two important variables in the expression of the BER: θ = Pˆk1 /Pˆk0 , ζ = Pˆk0 /Pˆk1 .
(34) (35)
It can be readily found that 1. The assumption σ1 ε2 < σ2 ε1 indicates that ζ changes from one to infinity and θ changes from zero to one. The variable ζ exerts a larger impact on the BER than the variable θ . 2. The only term containing θ is (3 + Pˆk1 /Pˆk0 )2 and it ranges from 9 to 16. In comparison, ζ is included in five terms and its range is much larger, so its impact on BER is far more than θ . 3. The BER will be lower if the variable ζ increases. Although increasing ζ results in decreasing θ , its impact is ignorable. Therefore, due to the inter-limitation of θ and ζ , we mainly consider the change of ζ when minimize BER. In other words, we will get a lower BER if we choose the maximal value of ζ among all K2 numbers. Subsequently, our antenna selection scheme can be described as follows. First, we compute the peak value of PDF on each receiving antenna according to Eq. 28. Next, we choose the two antennas which have the greatest value of ζ . The detailed steps of ratio detection with proposed antenna selection scheme are provided in Algorithm 1 where the notation y ij represents the value of ζ calculated with the ith and the jth antenna.
5 Simulation results In this section, we provide numerical results of the proposed algorithms and verify the feasibilities of our approximations. Suppose the peak error is the difference between the approximate peak (28) and the accurate peak. Define D0 =
|Pˆk0 − Pk0 | Pk0
and D1 =
|Pˆk1 − Pk1 | , Pk1
(36)
as error proportions, i.e., the ratios of peak errors and the accurate peak values. Figure 3 plots the error proportions over SNR. The approximate threshold γˆth and our proposed threshold γ˜th are also provided in Fig. 4. It can be seen from Figs. 3 and 4 that our proposed threshold is close to the approximate one at high SNR. Figure 5 plots the BER curves when the detection thresholds are set as γth , γˆth , and γ˜th , respectively. It can be seen from Fig. 5 that the BER curves are close to each other and the detection BER with γth is slightly below
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0.7 D D
0 1
0.5
0
Error proportion D , D
1
0.6
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
30
35
SNR
Fig. 3 Error proportion of approximate peak value
Fig. 6 Theoretical BER compared with simulation BER 100
2 1.8 1.6
10-1
1.2
BER
value of threshold
1.4
1 0.8
10-2
0.6
two antennas three antennas four antennas six antennas ten antennas
0.4 proposed threshold approximate threshold
0.2 0
10-3
0
5
10
15 20 SNR(dB)
25
30
Fig. 4 Approximate threshold compared with proposed threshold
35
0
5
10
15
20
25
30
35
30
35
SNR
Fig. 7 BER of different numbers of receiving antenna 2.4 max ratio with two antennas max ratio with three antennas max distance with two antennas max distance with three antennas
2.2
value of threshold
2
1.8
1.6
1.4
1.2
1
Fig. 5 BER with different detection thresholds
0
5
10
15 20 SNR(dB)
25
Fig. 8 Thresholds of selection with max ratio and max distance between Pˆk0 and Pˆk1
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studied the ratio detection algorithm that calculated the amplitude ratio of the received signals from different antennas. We showed that optimal detection threshold was almost impossible to obtain and found a reasonable approximation instead. Furthermore, we derived the closedform expression of the approximate BER. In addition, an antenna selection scheme was proposed to improve the system performance. Finally, simulation results were provided to corroborate our proposed studies. Acknowledgements This study is supported by the National Natural Science Foundation of China (No. 61571037), by the Fundamental Research Funds for the Central Universities (No.2016JBZ006 and No.2017YJS040), and by Technology & Innovation/Research/Radio system Beijing, Nokia Company. Fig. 9 BER performance of selection with max ratio and max distance between Pˆk0 and Pˆk1 with three receiving antennas
the others, which indicates that our proposed threshold is effective. In addition, we also plot the theoretical BER and the simulation BER in Fig. 6. These two lines coincide. When the reader has more than two receiving antennas, we select two of the antennas with our proposed selection scheme. The BER curves in the case of different receiving antennas are depicted in Fig. 7. It can be found that enlarging the number of receiving antennas will reduce the BER and enhance reliability of ambient backscatter communication systems. More importantly, it can be seen that the largest gain in BER can be obtained when the antenna number increased from two to three, and that much less gain is obtained from enlarging the antenna number when the reader already has four antennas. This finding indicates that equipping with three receiving antennas is a good configuration for the reader. The antenna selection criterion proposed in this paper is the maximal ratio of Pˆk0 and Pˆk1 . We consider another selection standard which is the maximal distance between Pˆk0 and Pˆk1 . The value of different thresholds are shown in Fig. 8 and the corresponding BER curves in Fig. 9. It can be seen that our proposed antenna selection scheme of selecting the maximum ratio outperforms the other one of choosing the largest distance.
6 Conclusion Ambient backscatter is a new-born wireless communication technology. At the time of writing, there are still many open problems in this area. In this paper, we investigated ratio detector and antenna selection for ambient backscatter communication systems with multiple receiving antennas. Specifically, we built up the theoretical model and
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