# Multi-Tag Selection in Cognitive Ambient Backscatter Communications for Next-Generation IoT Networks

Authors: Mi Ji Kim; Junsu Kim; Su Min Kim
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

In this paper, we propose multi-tag selection schemes to improve achievable rate of a secondary ambient backscatter communication (ABC) system with multiple tags and a single power beacon in cognitive radio (CR) environments. Using the secondary power beacon, which plays a role as radio frequency (RF) source when there is no ambient RF source signals, with spectrum sensing capability, the secondary ABC system determines operation modes according to activity of the licensed primary system. When the primary system is active, a tag is randomly selected due to a lack of channel information, while when it is inactive, the best tag maximizing achievable rate is selected using the secondary power beacon. Moreover, we apply a successive interference cancellation (SIC) technique when the secondary power beacon is able to work. The performance of the proposed multi-tag selection schemes is mathematically analyzed in terms of bit error rate (BER) and achievable rate. Finally, the performance of the proposed schemes is evaluated through simulations in terms of BER and achievable rate. It is shown that our approach can significantly outperform a conventional ABC system in CR environments, especially under a low-active primary system regime.


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## Body

## 1. Introduction

As Internet of things (IoT) era is coming, the number of wireless devices constructing IoT networks is explosively increasing. This causes a serious shortage in spectrum resource which is necessarily required for wireless connectivity. In order to solve this problem, many researchers have been conducting studies to improve spectral efficiency for large-scale wireless communications.Recently, an ambient backscatter communication (ABC) system exploiting existing radio frequency (RF) signals such as TV, FM radio, and Wi-Fi was proposed [1]. It is a very promising IoT technology to solve the spectrum shortage problem as it does not require additional spectrum for communications [2]. Moreover, it enables wireless transmissions with very low power since ABC devices do not require an RF transceiver at transmitter side. Therefore, it is also promising to solve a battery problem of wireless IoT devices with combination of energy harvesting technologies [3–7].In the ABC system, a tag, a passive transmitter that is not equipped with an RF transceiver, can modulate and transmit wireless signals by adjusting antenna impedance. That is, if it adjusts the impedance to absorb or reflect the ambient RF signals, a bit “0” or “1” is modulated, respectively. More specifically, in reflecting state, the tag maximally reflects the ambient signals so that the received power level is high at the receiver, where it is regarded as bit “1.” On the contrary, in absorbing state, the tag absorbs the ambient signals as much as possible so that the received power level at the receiver is low, which leads to decide bit “0.”So far, there have been many studies on the ABC systems with various ambient RF signals such as FM radio [1], Wi-Fi [8–10], Bluetooth [11], ultra-wideband (UWB) [12], OFDM signals [13], and so on. For a variety of ambient signals, many researchers have been studying on signal modulation and coding [13, 14], semi-coherent [15] and non-coherent [16] detections, and performance analysis and approximation [17–19]. Thereafter, they are extended to multi-antenna systems [20, 21], cooperative communications [22, 23], and multi-tag environments [24–30].So far, there have been several studies on multi-tag ABC systems. In [24], a location-based tag-reader paring scheme was proposed to enhance bit error rate (BER) performance of the proposed ABC system. In [25], employing a multiple-input multiple-output (MIMO) reader, a least-squares-based channel estimation protocol and a low complexity algorithm were proposed in order to obtain the optimal transceiver designs to maximize backscattered throughput among multiple single-antenna tags. To exploit a multi-user diversity gain, several tag selection schemes have been proposed. In [19], a tag selection scheme was proposed to maximize BER at the receiver and its BER performance is mathematically analyzed. In [27, 28], tag selection schemes were proposed to improve secrecy outage and data rate in a wire-tap channel with a single eavesdropper. In [29, 30], artificial noise-aided tag scheduling schemes were proposed in order to maximize the secrecy rate. These studies mainly focus on performance improvements in the perspective of physical layer security in wire-tap channels.On the other hand, cognitive radio (CR) communication, which allows unlicensed systems to share and utilize the spectrum bands of the licensed primary system when it is idle, is another promising technology to solve the spectrum shortage problem [31, 32]. There have been many studies on resource allocation and management in CR networks [33]. Among them, medium access control (MAC) protocols are designed and proposed for multi-user environments in both centralized and distributed manners [34–37]. In CR networks, sensing the primary system and reporting the sensing results to a secondary fusion node are important issues. Accordingly, there are several studies on the performance improvements in primary sensing [38] and reporting [39]. Recently, there are also a few studies on ABC systems under CR environments [40–42]. In these studies, the ABC system plays a role as an unlicensed secondary system under CR restrictions, where the secondary system is able to access the primary channel when it is only allowed by the primary system.More specifically, in [40], an adaptive harvest-then-transmit protocol was proposed for an RF-powered cognitive radio network. In the proposed protocol, backscattering, harvesting, and transmitting modes are adaptively controlled to enhance transmission rate. In [41], error-floor-free detectors were proposed to tackle direct link interference using a multi-antenna receive beamforming technique in a cognitive ABC network which consists of a single tag and a single receiver as a secondary ABC system in a CR environment. Most recently, in [42], a novel spectrum sharing system was proposed to maximize data rate of secondary backscatter transmission subject to a minimum rate requirement of the primary system by jointly optimizing the time sharing and power allocation parameters. The previous work considers a new paradigm for IoT networks as cognitive backscatter communications where the secondary system exploits existing RF signals transmitted from the primary system. However, its performance can be limited by activity of the primary system since if there is no RF source signals, no backscatter information can be transmitted. Moreover, in previous work, only a single tag is considered although a basic feature of IoT networks is to require massive number of IoT devices in the network.In this paper, we consider a secondary ABC system with multiple tags and a single power beacon, which can opportunistically access wireless channel of the licensed primary system under CR requirements. In this concept, according to the activity of the primary system, we propose adaptive multi-tag selection schemes to improve the performance of the secondary ABC system in terms of bit error rate (BER) and achievable rate. Therefore, the proposed schemes can significantly improve the performance of the secondary ABC system, especially under a low-active primary system regime. The contributions of this paper are summarized as follows:(i)
Employing a power beacon in the secondary CR system, a novel multi-tag selection scheme is proposed in order to improve the achievable rate of the secondary system in overlay CR environments.(ii)
The performance of the proposed multi-tag selection scheme is mathematically analyzed in terms of BER and achievable rate of the secondary system.(iii)
Through extensive simulations, the performance of the proposed multi-tag selection scheme is evaluated. It is shown that the proposed scheme can obtain additional spectral efficiency by improving average BER and activity of the secondary system.The rest of this paper is organized as follows. In Section2, the system model considered is illustrated. The proposed multi-tag selection schemes are presented in Section 3, and their performance analysis is provided in Section 4. In Section 5, numerical results for performance evaluation are shown. Finally, we conclude this paper in Section 6.


## 2. System Model

Figure1 shows a secondary ABC system in a CR environment where primary and secondary systems coexist. The licensed primary system consists of a single transmitter generating RF signals and a single receiver. The secondary system consists of a single power beacon that transmits additional RF signals, K tags, and a single receiver. The activity of the primary system, which is a ratio of busy and idle states, is denoted by ν∈0,1. In the secondary ABC system, there are two operation modes according to the primary activity. If the primary system is active, the secondary ABC system modulates backscatter bits using the RF signals sent from the primary transmitter, while if the primary system is idle, it modulates backscatter bits using the RF signals generated by the secondary power beacon.Figure 1
A cognitive ambient backscatter communication system with multiple tags and a single power beacon.By employing a new power beacon as a part of the secondary ABC system, the secondary tags are still able to modulate and transmit their information to the secondary receiver by using the RF signals from the secondary power beacon, even if the primary system is idle. To this end, the secondary power beacon is capable to sense the primary channel and it generates and transmits its own RF signals when the primary channel is decided as idle. Since the secondary power beacon is a part of the secondary system, the channel gains can be estimated at the secondary receiver using pilot signals, while it is impossible for the primary channel. Thus, we assume known channel information for the secondary power beacon and unknown channel information for the primary channel in this paper. It is worth noting that known channel information enables to apply for interference cancellation techniques.In this system model,hP, hTi, and hR denote the channel gains between the primary transmitter and the primary receiver, the i-th tag, and the secondary receiver, respectively, αTi and αR denote the channel gains between the secondary beacon and the i-th tag and the secondary receiver, respectively, and gRi denotes the channel gain between the i-th tag and the secondary receiver. We assume that all the channels suffer from i.i.d. block Rayleigh fading, i.e., hx∼cn0,σhx2, αx∼cn0,σαx2, gx∼cn0,σgx2, x∈R,Ti,Ri, and i∈1,2,…,K, as in [26].Figure2 shows the frame structure of the secondary ABC system. In the training period, a preamble signal is transmitted to determine bit decision threshold values, Φ0 and Φ1, which imply the average received power values at the receiver when Bn=0 and Bn=1. That is, we consider a binary phase shift keying (BPSK) modulation for the secondary ABC system. A data frame consists of sensing, channel estimation, tag selection, and data transmission periods. In the sensing period, the secondary power beacon senses the primary channel using an energy detector (in this paper, we assume perfect sensing at the secondary power beacon; therefore, the performance of the proposed multi-tag selection scheme evaluated in this paper corresponds to the upper bound). Based on this, the primary activity is determined as either busy or idle. The channel gains hx and αx are estimated in the channel estimation period [43]. In the tag selection period, a single tag to transmit is scheduled. The channel estimation and tag selection are performed at the secondary receiver, and it is imformed to tags during the tag selection period. Finally, data transmission and detection are performed in the data transmission period. Note that since the secondary ABC system operates based on sensing at the secondary beacon, the secondary ABC system does not require synchronization with the primary system. However, the synchronization among the secondary beacon, multiple tags, and the secondary receiver is possible based on the frame structure in Figure 2.Figure 2
Frame structure of the secondary ABC system.


## 3. Proposed Multi-Tag Selection Schemes

In this section, we propose multi-tag selection schemes to maximize achievable rate of the secondary ABC system considering the primary activity.


### 3.1. Tag Selection Schemes according to the Primary Activity

#### 3.1.1. Status of the Primary System Is Busy

When the primary system is busy, the received signal at the secondary ABC receiver for thei-th tag and the n-th sample is given by(1)yn=hRsn+ηgRihTisnBn+ωn=hRsn+ωn,ifBn=0,hR+ηgRihTisn+ωn,ifBn=1,where sn denotes the primary RF signal, η denotes the antenna efficiency factor, Bn denotes the secondary backscatter bit, and ωn denotes the additive white Gaussian noise (AWGN) with zero mean and unit variance, i.e., ωn∼cn0,σω2. For this case, the channel estimation is impossible since the primary signal sn is unknown at the secondary system. Thus, we randomly select a tag as follows:(2)i∗=Uniform1,…,K.


#### 3.1.2. Status of the Primary System Is Idle

When the primary system is idle, we operate the secondary power beacon to generate ambient RF signals artificially. Thus, the received signal at the secondary receiver for thei-th tag and the n-th sample is rewritten by(3)yn=αRxn+ηgRiαTixnBn+ωn=αRxn+ωn,ifBn=0,αR+ηgRiαTixn+ωn,ifBn=1,where xn denotes the RF signal transmitted by the secondary power beacon.Since the secondary power beacon is a part of the secondary system, the channel gains can be estimated for this case and we can employ a successive interference cancellation (SIC) technique at the secondary receiver. In the following, we present the proposed multi-tag selection schemes for both SIC-disabled and SIC-enabled cases.(i)
Tag selection without SIC: for this case, we apply a tag selection scheme maximizing BER proposed in [19]. Then, the selected tag is determined by(4)i∗=argmaxi∈1,…,KαR+ηαTigRi2−αR2.(ii)
Tag selection with SIC: for knownxn, we can eliminate the interference term from the secondary power beacon based on the channel estimation [44]. This is possible since the power beacon is a part of the secondary system. Additionally, we assume the perfect channel estimation in order to investigate the performance upper bound. Then, the received signal for the i-th tag can be rewritten by(5)zn=yn−α^Rxn=ηgRiαTixnBn+ωn=ωn,ifBn=0,ηgRiαTixn+ωn,ifBn=1,where α^R is the estimated channel gain and with the perfect estimation, α^R=αR. For this case, the best tag maximizing achievable rate is selected as follows:(6)i∗=argmaxi∈1,…,KηαTigRi2.


### 3.2. Detection Mechanism

#### 3.2.1. Status of the Primary System Is Busy

When the primary system is busy, the decision thresholds, average received power levels during training period, for thei-th tag are determined by(7)Φ0,i=1N0∑n=1N0hR2Ps+σω2+2hRsnωn,(8)Φ1,i=1N0∑n=1N0μi2Ps+σω2+2μisnωn,where N0 is the number of transmitted samples for a single backscatter bit during the training period, Ps is the average transmit power of the RF source signal sn, σω2 is the noise variance, and μi≜hR+ηgRihTi. In the data transmission period, the selected i∗-th tag modulates and transmits a backscatter bit Bn, and then the received signal at the secondary receiver is written by(9)yn=hRsn+ηgRi∗hTi∗snBn+ωn.The average received power at the secondary receiver during data transmission period can be calculated as(10)ΦB=1NB∑n=1NByn2=hR2Ps+σω2+ΩB0,ifBn=0,μi∗2Ps+σω2+ΩB1,ifBn=1,where(11)ΩB0=2NB∑n=1NBℜhRsnωnH,(12)ΩB1=2NB∑n=1NBℜμi∗snωnH,where NB denotes the number of samples while transmitting a backscatter bit Bn, ℜ⋅ denotes the real part of a complex number, and ⋅H is the conjugate and transpose operation. Note that the cross-correlation terms in (7), (8), (11), and (12) can be negligible for sufficiently large N0 and NB since sn and ωn are statistically uncorrelated.Finally, the backscattered bitBn can be decoded at the secondary receiver with a comparison between the instantaneous average received power, ΦB, and the threshold values, Φ0 and Φ1, as follows [17]:(13)B^n=0,ifΦB−Φ0,i∗≤ΦB−Φ1,i∗,1,ifΦB−Φ0,i∗>ΦB−Φ1,i∗,=0,ifΦB≤ξ,1,ifΦB>ξ.where ξ=hR2+μi∗2/2Ps.


#### 3.2.2. Status of the Primary System Is Idle

If the primary system is idle, the secondary power beacon is able to be active. Without SIC, the decision thresholds for thei-th tag are predetermined by(14)Φ0,i=1N0∑n=1N0αR2Px+σω2+2αRxnωn,Φ1,i=1N0∑n=1N0εi2Px+σω2+2εixnωn,where Px is the average transmit power of the secondary beacon signal xn, σω2 is the noise variance, and εi≜αR+ηgRihTi. In the data transmission period, the received signal at the secondary receiver for the selected i∗-th tag is expressed as(15)yn=αRxn+ηgRi∗αTi∗xnBn+ωn.Then, the average received power at the secondary receiver during data transmission period is calculated by(16)ΦB==αR2Px+σω2+ΩB0′,ifBn=0,εi∗2Px+σω2+ΩB1′,ifBn=1,where(17)ΩB0′=2NB∑n=1NBℜαRxnωnH,ΩB1′=2NB∑n=1NBℜεi∗xnωnH.Finally, the backscattered bitBn can be decoded at the secondary receiver as follows:(18)B^n=0,ifΦB≤ξ′,1,ifΦB>ξ′,where ξ′=αR2+εi∗2/2Px.With SIC, the decision thresholds for thei-th tag can be simplified as(19)Φ0,i=1N0∑n=1N0ωn2,Φ1,i=1N0∑n=1N0ηgRiαTixn+ωn2.In the data transmission period, the received signal at the secondary receiver for the selectedi∗-th tag is expressed as(20)yn=ηgRi∗αTi∗xnBn+ωn.The average received power at the secondary receiver during data transmission period is rewritten by(21)ΦB=σω2,ifBn=0,ρi∗2Px+σω2+ΩB1′′,ifBn=1,where ρi≜ηgRiαTi and(22)ΩB1′′=2NB∑n=1NBℜρixnωnH.Finally, the backscattered bitBn can be decoded at the secondary receiver as follows:(23)B^n=0,ifΦB≤ξ′′,1,ifΦB>ξ′′,where ξ′′=ρi∗2/2Px.


## 3.1. Tag Selection Schemes according to the Primary Activity

### 3.1.1. Status of the Primary System Is Busy

When the primary system is busy, the received signal at the secondary ABC receiver for thei-th tag and the n-th sample is given by(1)yn=hRsn+ηgRihTisnBn+ωn=hRsn+ωn,ifBn=0,hR+ηgRihTisn+ωn,ifBn=1,where sn denotes the primary RF signal, η denotes the antenna efficiency factor, Bn denotes the secondary backscatter bit, and ωn denotes the additive white Gaussian noise (AWGN) with zero mean and unit variance, i.e., ωn∼cn0,σω2. For this case, the channel estimation is impossible since the primary signal sn is unknown at the secondary system. Thus, we randomly select a tag as follows:(2)i∗=Uniform1,…,K.


### 3.1.2. Status of the Primary System Is Idle

When the primary system is idle, we operate the secondary power beacon to generate ambient RF signals artificially. Thus, the received signal at the secondary receiver for thei-th tag and the n-th sample is rewritten by(3)yn=αRxn+ηgRiαTixnBn+ωn=αRxn+ωn,ifBn=0,αR+ηgRiαTixn+ωn,ifBn=1,where xn denotes the RF signal transmitted by the secondary power beacon.Since the secondary power beacon is a part of the secondary system, the channel gains can be estimated for this case and we can employ a successive interference cancellation (SIC) technique at the secondary receiver. In the following, we present the proposed multi-tag selection schemes for both SIC-disabled and SIC-enabled cases.(i)
Tag selection without SIC: for this case, we apply a tag selection scheme maximizing BER proposed in [19]. Then, the selected tag is determined by(4)i∗=argmaxi∈1,…,KαR+ηαTigRi2−αR2.(ii)
Tag selection with SIC: for knownxn, we can eliminate the interference term from the secondary power beacon based on the channel estimation [44]. This is possible since the power beacon is a part of the secondary system. Additionally, we assume the perfect channel estimation in order to investigate the performance upper bound. Then, the received signal for the i-th tag can be rewritten by(5)zn=yn−α^Rxn=ηgRiαTixnBn+ωn=ωn,ifBn=0,ηgRiαTixn+ωn,ifBn=1,where α^R is the estimated channel gain and with the perfect estimation, α^R=αR. For this case, the best tag maximizing achievable rate is selected as follows:(6)i∗=argmaxi∈1,…,KηαTigRi2.


## 3.1.1. Status of the Primary System Is Busy

When the primary system is busy, the received signal at the secondary ABC receiver for thei-th tag and the n-th sample is given by(1)yn=hRsn+ηgRihTisnBn+ωn=hRsn+ωn,ifBn=0,hR+ηgRihTisn+ωn,ifBn=1,where sn denotes the primary RF signal, η denotes the antenna efficiency factor, Bn denotes the secondary backscatter bit, and ωn denotes the additive white Gaussian noise (AWGN) with zero mean and unit variance, i.e., ωn∼cn0,σω2. For this case, the channel estimation is impossible since the primary signal sn is unknown at the secondary system. Thus, we randomly select a tag as follows:(2)i∗=Uniform1,…,K.


## 3.1.2. Status of the Primary System Is Idle

When the primary system is idle, we operate the secondary power beacon to generate ambient RF signals artificially. Thus, the received signal at the secondary receiver for thei-th tag and the n-th sample is rewritten by(3)yn=αRxn+ηgRiαTixnBn+ωn=αRxn+ωn,ifBn=0,αR+ηgRiαTixn+ωn,ifBn=1,where xn denotes the RF signal transmitted by the secondary power beacon.Since the secondary power beacon is a part of the secondary system, the channel gains can be estimated for this case and we can employ a successive interference cancellation (SIC) technique at the secondary receiver. In the following, we present the proposed multi-tag selection schemes for both SIC-disabled and SIC-enabled cases.(i)
Tag selection without SIC: for this case, we apply a tag selection scheme maximizing BER proposed in [19]. Then, the selected tag is determined by(4)i∗=argmaxi∈1,…,KαR+ηαTigRi2−αR2.(ii)
Tag selection with SIC: for knownxn, we can eliminate the interference term from the secondary power beacon based on the channel estimation [44]. This is possible since the power beacon is a part of the secondary system. Additionally, we assume the perfect channel estimation in order to investigate the performance upper bound. Then, the received signal for the i-th tag can be rewritten by(5)zn=yn−α^Rxn=ηgRiαTixnBn+ωn=ωn,ifBn=0,ηgRiαTixn+ωn,ifBn=1,where α^R is the estimated channel gain and with the perfect estimation, α^R=αR. For this case, the best tag maximizing achievable rate is selected as follows:(6)i∗=argmaxi∈1,…,KηαTigRi2.


## 3.2. Detection Mechanism

### 3.2.1. Status of the Primary System Is Busy

When the primary system is busy, the decision thresholds, average received power levels during training period, for thei-th tag are determined by(7)Φ0,i=1N0∑n=1N0hR2Ps+σω2+2hRsnωn,(8)Φ1,i=1N0∑n=1N0μi2Ps+σω2+2μisnωn,where N0 is the number of transmitted samples for a single backscatter bit during the training period, Ps is the average transmit power of the RF source signal sn, σω2 is the noise variance, and μi≜hR+ηgRihTi. In the data transmission period, the selected i∗-th tag modulates and transmits a backscatter bit Bn, and then the received signal at the secondary receiver is written by(9)yn=hRsn+ηgRi∗hTi∗snBn+ωn.The average received power at the secondary receiver during data transmission period can be calculated as(10)ΦB=1NB∑n=1NByn2=hR2Ps+σω2+ΩB0,ifBn=0,μi∗2Ps+σω2+ΩB1,ifBn=1,where(11)ΩB0=2NB∑n=1NBℜhRsnωnH,(12)ΩB1=2NB∑n=1NBℜμi∗snωnH,where NB denotes the number of samples while transmitting a backscatter bit Bn, ℜ⋅ denotes the real part of a complex number, and ⋅H is the conjugate and transpose operation. Note that the cross-correlation terms in (7), (8), (11), and (12) can be negligible for sufficiently large N0 and NB since sn and ωn are statistically uncorrelated.Finally, the backscattered bitBn can be decoded at the secondary receiver with a comparison between the instantaneous average received power, ΦB, and the threshold values, Φ0 and Φ1, as follows [17]:(13)B^n=0,ifΦB−Φ0,i∗≤ΦB−Φ1,i∗,1,ifΦB−Φ0,i∗>ΦB−Φ1,i∗,=0,ifΦB≤ξ,1,ifΦB>ξ.where ξ=hR2+μi∗2/2Ps.


### 3.2.2. Status of the Primary System Is Idle

If the primary system is idle, the secondary power beacon is able to be active. Without SIC, the decision thresholds for thei-th tag are predetermined by(14)Φ0,i=1N0∑n=1N0αR2Px+σω2+2αRxnωn,Φ1,i=1N0∑n=1N0εi2Px+σω2+2εixnωn,where Px is the average transmit power of the secondary beacon signal xn, σω2 is the noise variance, and εi≜αR+ηgRihTi. In the data transmission period, the received signal at the secondary receiver for the selected i∗-th tag is expressed as(15)yn=αRxn+ηgRi∗αTi∗xnBn+ωn.Then, the average received power at the secondary receiver during data transmission period is calculated by(16)ΦB==αR2Px+σω2+ΩB0′,ifBn=0,εi∗2Px+σω2+ΩB1′,ifBn=1,where(17)ΩB0′=2NB∑n=1NBℜαRxnωnH,ΩB1′=2NB∑n=1NBℜεi∗xnωnH.Finally, the backscattered bitBn can be decoded at the secondary receiver as follows:(18)B^n=0,ifΦB≤ξ′,1,ifΦB>ξ′,where ξ′=αR2+εi∗2/2Px.With SIC, the decision thresholds for thei-th tag can be simplified as(19)Φ0,i=1N0∑n=1N0ωn2,Φ1,i=1N0∑n=1N0ηgRiαTixn+ωn2.In the data transmission period, the received signal at the secondary receiver for the selectedi∗-th tag is expressed as(20)yn=ηgRi∗αTi∗xnBn+ωn.The average received power at the secondary receiver during data transmission period is rewritten by(21)ΦB=σω2,ifBn=0,ρi∗2Px+σω2+ΩB1′′,ifBn=1,where ρi≜ηgRiαTi and(22)ΩB1′′=2NB∑n=1NBℜρixnωnH.Finally, the backscattered bitBn can be decoded at the secondary receiver as follows:(23)B^n=0,ifΦB≤ξ′′,1,ifΦB>ξ′′,where ξ′′=ρi∗2/2Px.


## 3.2.1. Status of the Primary System Is Busy

When the primary system is busy, the decision thresholds, average received power levels during training period, for thei-th tag are determined by(7)Φ0,i=1N0∑n=1N0hR2Ps+σω2+2hRsnωn,(8)Φ1,i=1N0∑n=1N0μi2Ps+σω2+2μisnωn,where N0 is the number of transmitted samples for a single backscatter bit during the training period, Ps is the average transmit power of the RF source signal sn, σω2 is the noise variance, and μi≜hR+ηgRihTi. In the data transmission period, the selected i∗-th tag modulates and transmits a backscatter bit Bn, and then the received signal at the secondary receiver is written by(9)yn=hRsn+ηgRi∗hTi∗snBn+ωn.The average received power at the secondary receiver during data transmission period can be calculated as(10)ΦB=1NB∑n=1NByn2=hR2Ps+σω2+ΩB0,ifBn=0,μi∗2Ps+σω2+ΩB1,ifBn=1,where(11)ΩB0=2NB∑n=1NBℜhRsnωnH,(12)ΩB1=2NB∑n=1NBℜμi∗snωnH,where NB denotes the number of samples while transmitting a backscatter bit Bn, ℜ⋅ denotes the real part of a complex number, and ⋅H is the conjugate and transpose operation. Note that the cross-correlation terms in (7), (8), (11), and (12) can be negligible for sufficiently large N0 and NB since sn and ωn are statistically uncorrelated.Finally, the backscattered bitBn can be decoded at the secondary receiver with a comparison between the instantaneous average received power, ΦB, and the threshold values, Φ0 and Φ1, as follows [17]:(13)B^n=0,ifΦB−Φ0,i∗≤ΦB−Φ1,i∗,1,ifΦB−Φ0,i∗>ΦB−Φ1,i∗,=0,ifΦB≤ξ,1,ifΦB>ξ.where ξ=hR2+μi∗2/2Ps.


## 3.2.2. Status of the Primary System Is Idle

If the primary system is idle, the secondary power beacon is able to be active. Without SIC, the decision thresholds for thei-th tag are predetermined by(14)Φ0,i=1N0∑n=1N0αR2Px+σω2+2αRxnωn,Φ1,i=1N0∑n=1N0εi2Px+σω2+2εixnωn,where Px is the average transmit power of the secondary beacon signal xn, σω2 is the noise variance, and εi≜αR+ηgRihTi. In the data transmission period, the received signal at the secondary receiver for the selected i∗-th tag is expressed as(15)yn=αRxn+ηgRi∗αTi∗xnBn+ωn.Then, the average received power at the secondary receiver during data transmission period is calculated by(16)ΦB==αR2Px+σω2+ΩB0′,ifBn=0,εi∗2Px+σω2+ΩB1′,ifBn=1,where(17)ΩB0′=2NB∑n=1NBℜαRxnωnH,ΩB1′=2NB∑n=1NBℜεi∗xnωnH.Finally, the backscattered bitBn can be decoded at the secondary receiver as follows:(18)B^n=0,ifΦB≤ξ′,1,ifΦB>ξ′,where ξ′=αR2+εi∗2/2Px.With SIC, the decision thresholds for thei-th tag can be simplified as(19)Φ0,i=1N0∑n=1N0ωn2,Φ1,i=1N0∑n=1N0ηgRiαTixn+ωn2.In the data transmission period, the received signal at the secondary receiver for the selectedi∗-th tag is expressed as(20)yn=ηgRi∗αTi∗xnBn+ωn.The average received power at the secondary receiver during data transmission period is rewritten by(21)ΦB=σω2,ifBn=0,ρi∗2Px+σω2+ΩB1′′,ifBn=1,where ρi≜ηgRiαTi and(22)ΩB1′′=2NB∑n=1NBℜρixnωnH.Finally, the backscattered bitBn can be decoded at the secondary receiver as follows:(23)B^n=0,ifΦB≤ξ′′,1,ifΦB>ξ′′,where ξ′′=ρi∗2/2Px.


## 4. Performance Analysis

In this section, we mathematically analyze the performance of the proposed multi-tag selection schemes in terms of BER and achievable rate. For analytical tractability, it is assumed that the channel between the selected tag and the secondary receiver,gR, is line of sight and regarded as a constant as in [19]. This is reasonable since the distance between a tag and the secondary receiver is usually close in ABC networks.


### 4.1. Average BER

In this paper, BER is defined as a probability that the transmitted and estimated backscatter bits are not the same at the receiver. Thus, the BER for a single slot is expressed as(24)Pb=PrB^n≠Bn=PrB^n=0|Bn=1PrBn=1+PrB^n=1|Bn=0PrBn=0,∀n.Note that bit “0” or “1” can be designed as equally probable in practice, and thereforePrBn=0=PrBn=1=0.5 without loss of generality.Hence, the average BER for a single frame which consists of multiple slots is given by(25)P¯b=EPb=EPrB^n≠Bn,∀n,=νP¯bbusy+1−νP¯bidle,where ν is the primary activity, P¯bbusy is the average BER when the primary system is busy, and P¯bidle is the average BER when the primary system is idle.In the following, we derive BER for a single slot and average BER when the primary system is either busy or idle. When it is idle, the secondary beacon is active in order to provide source RF signals. For this case, we also consider to employ the SIC technique in order to further improve the BER performance at the secondary receiver.


#### 4.1.1. Random Tag Selection When the Primary System Is Busy

Let us recallμi≜hR+ηgRihTi and Φ˜B≜ΦB−σω2. Similar to [19], for the selected i∗-th tag, if μi∗2>hR2, conditional bit error probabilities of the energy detection are derived as(26)PrB^n=0|Bn=1=PrΦ˜B<ξ|Bn=1=PrΩB1<−μi∗2−hR22Ps=Qμi∗2−hR2μi∗βs,PrB^n=1|Bn=0=PrΦ˜B>ξ|Bn=0=PrΩB0>−μi∗2−hR22Ps=Qμi∗2−hR2hRβs,where ξ=hR2+μi∗2/2Ps and βs=8σω2/NBPs.Ifμi∗2<hR2, they are rewritten, respectively, by(27)PrB^n=0|Bn=1=Q−μi∗2−hR2μi∗βs,PrB^n=1|Bn=0=Q−μi∗2−hR2hRβs.Substituting (32)–(35) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be derived as(28)Pbbusy=12Qμi∗2−hR2μi∗βs+Qμi∗2−hR2hRβs.Thus, average BER over all slots is obtained as(29)P¯bbusy=EPbbusy=12∫0∞QβsmfM1mdm+∫0∞QβsnfN1ndn,where M1=μi∗2−hR2/μi∗ and N1=μi∗2−hR2/hR.Unfortunately, since the channel gains are not known exactly, it is hard to find the exact PDFs ofM1 and N1. However, the average BER can be approximated as [19](30)P¯bbusy≈12∫0∞Qβ1z+Qβ2zfYi∗zdz,where βs,1=βs/C1σμi∗, βs,2=β/C2σhR, βs=8σω2/NBPs, and C1 and C2 are constants that are determined by the number of tags and channel variances. Here, since we select a tag randomly, assuming i.i.d. block Rayleigh fading, the PDF of Yi∗ is obtained by(31)fYi∗y=1σμi∗2+σhR2e−1/σμi∗2y+e−1/σhR2y,y>0,where Yi∗≜μi∗2−hR2.


#### 4.1.2. Tag Selection without SIC When the Primary System Is Idle

Hereafter, we derive average BER without employing the SIC technique when the primary system is inactive.Let us recallεi≜αR+ηgRiαTi and Φ˜B≜ΦB−σω2. Similar to the BER derivation when the primary system is busy, for the selected i∗-th tag, if εi∗2>αR2, conditional bit error probabilities of the energy detection are derived as(32)PrB^n=0|Bn=1=Qεi∗2−αR2εi∗βx,(33)PrB^n=1|Bn=0=Qεi∗2−αR2αRβx,where ξ′=αR2+εi∗2/2Px and βx=8σω2/NBPx.Ifεi∗2<αR2, they are rewritten, respectively, by(34)PrB^n=0|Bn=1=Q−εi∗2−αR2εi∗βx,(35)PrB^n=1|Bn=0=Q−εi∗2−αR2αRβx.Substituting (32)–(35) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be derived as(36)Pbidle=12Qεi∗2−αR2εi∗βx+Qεi∗2−αR2αRβx.Thus, average BER over all slots is obtained as(37)P¯bidle=EPbidle=12∫0∞QβxmfM2mdm+∫0∞QβxnfN2ndn,where M2=εi∗2−αR2/εi∗ and N2=εi∗2−αR2/αR.Since it is hard to find the exact PDFs ofM2 and N2, using Theorem 1 in [19], the average BER can be approximated as(38)P¯bidle≈12∫0∞Qβx,1z+Qβx,2zfZi∗zdz,where Zi∗≜εi∗2−αR2, βx,1=βx/D1σεi∗, βx,2=βx/D2σαR, βx=8σω2/NBPs, and D1 and D2 are constants that are determined by the number of tags and channel variances. For this case, since the best tag i∗ is selected according to (6), the PDF of Zi∗ is obtained by [19](39)fZi∗z=Kσεi∗2+σαR2e−1/σεi∗2z+e−1/σR2z⋅1−σεi∗2σεi∗2+σαR2e−1/σεi∗2z−σαR2σεi∗2+σαR2e−1/σαR2zK−1,z>0,where K denotes the number of tags.


#### 4.1.3. Tag Selection with SIC When the Primary System Is Idle

When SIC is employed, since the interference from the RF source is eliminated, the analysis can be simplified. Similar to the case without SIC, we first defineρi≜ηgRiαTi and Φ˜B≜ΦB−σω2. Since ρi2>0, the BER for a single slot can be obtained as(40)PrB^n=0|Bn=1=PrΦ˜B<ξ′′|Bn=1=PrΩB1′′<−ρi∗22Px=Qρi∗β,(41)PrB^n=1|Bn=0=PrΦ˜B>ξ′′|Bn=0=PrΩB0′′>−ρi∗22Px=0,where βx=8σω2/NBPx.Substituting (40) and (41) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be simplified as(42)Pbidle=12Qρi∗βx.Finally, the average BER for all slots is obtained as(43)P¯bidle=EPbidle=12∫0∞Qρi∗βxfρi∗zdz,where(44)fρi∗z=1σρi∗2e−1/σρi∗2z1−e−1/σρi∗2zK−1,z>0,and σρi∗2=η2σαTi∗2σgRi∗2 and K is the number of tags.


### 4.2. Average Achievable Rate

Based on the obtained BERs, average achievable rate of the secondary ABC system is expressed as(45)R¯Bx=RsNB1−P¯bxNtot,x∈busy,idle,where Rs is the source data rate of the primary signal sn, NB is the number of backscattered bits, and Ntot is the total number of transmitted bits. P¯bx are obtained in (30), (38), and (43).Finally, the average achievable rate of the proposed secondary ABC systems is expressed as(46)R¯B=νR¯Bbusy+1−νR¯Bidle,where ν is the primary activity.


## 4.1. Average BER

In this paper, BER is defined as a probability that the transmitted and estimated backscatter bits are not the same at the receiver. Thus, the BER for a single slot is expressed as(24)Pb=PrB^n≠Bn=PrB^n=0|Bn=1PrBn=1+PrB^n=1|Bn=0PrBn=0,∀n.Note that bit “0” or “1” can be designed as equally probable in practice, and thereforePrBn=0=PrBn=1=0.5 without loss of generality.Hence, the average BER for a single frame which consists of multiple slots is given by(25)P¯b=EPb=EPrB^n≠Bn,∀n,=νP¯bbusy+1−νP¯bidle,where ν is the primary activity, P¯bbusy is the average BER when the primary system is busy, and P¯bidle is the average BER when the primary system is idle.In the following, we derive BER for a single slot and average BER when the primary system is either busy or idle. When it is idle, the secondary beacon is active in order to provide source RF signals. For this case, we also consider to employ the SIC technique in order to further improve the BER performance at the secondary receiver.


### 4.1.1. Random Tag Selection When the Primary System Is Busy

Let us recallμi≜hR+ηgRihTi and Φ˜B≜ΦB−σω2. Similar to [19], for the selected i∗-th tag, if μi∗2>hR2, conditional bit error probabilities of the energy detection are derived as(26)PrB^n=0|Bn=1=PrΦ˜B<ξ|Bn=1=PrΩB1<−μi∗2−hR22Ps=Qμi∗2−hR2μi∗βs,PrB^n=1|Bn=0=PrΦ˜B>ξ|Bn=0=PrΩB0>−μi∗2−hR22Ps=Qμi∗2−hR2hRβs,where ξ=hR2+μi∗2/2Ps and βs=8σω2/NBPs.Ifμi∗2<hR2, they are rewritten, respectively, by(27)PrB^n=0|Bn=1=Q−μi∗2−hR2μi∗βs,PrB^n=1|Bn=0=Q−μi∗2−hR2hRβs.Substituting (32)–(35) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be derived as(28)Pbbusy=12Qμi∗2−hR2μi∗βs+Qμi∗2−hR2hRβs.Thus, average BER over all slots is obtained as(29)P¯bbusy=EPbbusy=12∫0∞QβsmfM1mdm+∫0∞QβsnfN1ndn,where M1=μi∗2−hR2/μi∗ and N1=μi∗2−hR2/hR.Unfortunately, since the channel gains are not known exactly, it is hard to find the exact PDFs ofM1 and N1. However, the average BER can be approximated as [19](30)P¯bbusy≈12∫0∞Qβ1z+Qβ2zfYi∗zdz,where βs,1=βs/C1σμi∗, βs,2=β/C2σhR, βs=8σω2/NBPs, and C1 and C2 are constants that are determined by the number of tags and channel variances. Here, since we select a tag randomly, assuming i.i.d. block Rayleigh fading, the PDF of Yi∗ is obtained by(31)fYi∗y=1σμi∗2+σhR2e−1/σμi∗2y+e−1/σhR2y,y>0,where Yi∗≜μi∗2−hR2.


### 4.1.2. Tag Selection without SIC When the Primary System Is Idle

Hereafter, we derive average BER without employing the SIC technique when the primary system is inactive.Let us recallεi≜αR+ηgRiαTi and Φ˜B≜ΦB−σω2. Similar to the BER derivation when the primary system is busy, for the selected i∗-th tag, if εi∗2>αR2, conditional bit error probabilities of the energy detection are derived as(32)PrB^n=0|Bn=1=Qεi∗2−αR2εi∗βx,(33)PrB^n=1|Bn=0=Qεi∗2−αR2αRβx,where ξ′=αR2+εi∗2/2Px and βx=8σω2/NBPx.Ifεi∗2<αR2, they are rewritten, respectively, by(34)PrB^n=0|Bn=1=Q−εi∗2−αR2εi∗βx,(35)PrB^n=1|Bn=0=Q−εi∗2−αR2αRβx.Substituting (32)–(35) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be derived as(36)Pbidle=12Qεi∗2−αR2εi∗βx+Qεi∗2−αR2αRβx.Thus, average BER over all slots is obtained as(37)P¯bidle=EPbidle=12∫0∞QβxmfM2mdm+∫0∞QβxnfN2ndn,where M2=εi∗2−αR2/εi∗ and N2=εi∗2−αR2/αR.Since it is hard to find the exact PDFs ofM2 and N2, using Theorem 1 in [19], the average BER can be approximated as(38)P¯bidle≈12∫0∞Qβx,1z+Qβx,2zfZi∗zdz,where Zi∗≜εi∗2−αR2, βx,1=βx/D1σεi∗, βx,2=βx/D2σαR, βx=8σω2/NBPs, and D1 and D2 are constants that are determined by the number of tags and channel variances. For this case, since the best tag i∗ is selected according to (6), the PDF of Zi∗ is obtained by [19](39)fZi∗z=Kσεi∗2+σαR2e−1/σεi∗2z+e−1/σR2z⋅1−σεi∗2σεi∗2+σαR2e−1/σεi∗2z−σαR2σεi∗2+σαR2e−1/σαR2zK−1,z>0,where K denotes the number of tags.


### 4.1.3. Tag Selection with SIC When the Primary System Is Idle

When SIC is employed, since the interference from the RF source is eliminated, the analysis can be simplified. Similar to the case without SIC, we first defineρi≜ηgRiαTi and Φ˜B≜ΦB−σω2. Since ρi2>0, the BER for a single slot can be obtained as(40)PrB^n=0|Bn=1=PrΦ˜B<ξ′′|Bn=1=PrΩB1′′<−ρi∗22Px=Qρi∗β,(41)PrB^n=1|Bn=0=PrΦ˜B>ξ′′|Bn=0=PrΩB0′′>−ρi∗22Px=0,where βx=8σω2/NBPx.Substituting (40) and (41) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be simplified as(42)Pbidle=12Qρi∗βx.Finally, the average BER for all slots is obtained as(43)P¯bidle=EPbidle=12∫0∞Qρi∗βxfρi∗zdz,where(44)fρi∗z=1σρi∗2e−1/σρi∗2z1−e−1/σρi∗2zK−1,z>0,and σρi∗2=η2σαTi∗2σgRi∗2 and K is the number of tags.


## 4.1.1. Random Tag Selection When the Primary System Is Busy

Let us recallμi≜hR+ηgRihTi and Φ˜B≜ΦB−σω2. Similar to [19], for the selected i∗-th tag, if μi∗2>hR2, conditional bit error probabilities of the energy detection are derived as(26)PrB^n=0|Bn=1=PrΦ˜B<ξ|Bn=1=PrΩB1<−μi∗2−hR22Ps=Qμi∗2−hR2μi∗βs,PrB^n=1|Bn=0=PrΦ˜B>ξ|Bn=0=PrΩB0>−μi∗2−hR22Ps=Qμi∗2−hR2hRβs,where ξ=hR2+μi∗2/2Ps and βs=8σω2/NBPs.Ifμi∗2<hR2, they are rewritten, respectively, by(27)PrB^n=0|Bn=1=Q−μi∗2−hR2μi∗βs,PrB^n=1|Bn=0=Q−μi∗2−hR2hRβs.Substituting (32)–(35) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be derived as(28)Pbbusy=12Qμi∗2−hR2μi∗βs+Qμi∗2−hR2hRβs.Thus, average BER over all slots is obtained as(29)P¯bbusy=EPbbusy=12∫0∞QβsmfM1mdm+∫0∞QβsnfN1ndn,where M1=μi∗2−hR2/μi∗ and N1=μi∗2−hR2/hR.Unfortunately, since the channel gains are not known exactly, it is hard to find the exact PDFs ofM1 and N1. However, the average BER can be approximated as [19](30)P¯bbusy≈12∫0∞Qβ1z+Qβ2zfYi∗zdz,where βs,1=βs/C1σμi∗, βs,2=β/C2σhR, βs=8σω2/NBPs, and C1 and C2 are constants that are determined by the number of tags and channel variances. Here, since we select a tag randomly, assuming i.i.d. block Rayleigh fading, the PDF of Yi∗ is obtained by(31)fYi∗y=1σμi∗2+σhR2e−1/σμi∗2y+e−1/σhR2y,y>0,where Yi∗≜μi∗2−hR2.


## 4.1.2. Tag Selection without SIC When the Primary System Is Idle

Hereafter, we derive average BER without employing the SIC technique when the primary system is inactive.Let us recallεi≜αR+ηgRiαTi and Φ˜B≜ΦB−σω2. Similar to the BER derivation when the primary system is busy, for the selected i∗-th tag, if εi∗2>αR2, conditional bit error probabilities of the energy detection are derived as(32)PrB^n=0|Bn=1=Qεi∗2−αR2εi∗βx,(33)PrB^n=1|Bn=0=Qεi∗2−αR2αRβx,where ξ′=αR2+εi∗2/2Px and βx=8σω2/NBPx.Ifεi∗2<αR2, they are rewritten, respectively, by(34)PrB^n=0|Bn=1=Q−εi∗2−αR2εi∗βx,(35)PrB^n=1|Bn=0=Q−εi∗2−αR2αRβx.Substituting (32)–(35) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be derived as(36)Pbidle=12Qεi∗2−αR2εi∗βx+Qεi∗2−αR2αRβx.Thus, average BER over all slots is obtained as(37)P¯bidle=EPbidle=12∫0∞QβxmfM2mdm+∫0∞QβxnfN2ndn,where M2=εi∗2−αR2/εi∗ and N2=εi∗2−αR2/αR.Since it is hard to find the exact PDFs ofM2 and N2, using Theorem 1 in [19], the average BER can be approximated as(38)P¯bidle≈12∫0∞Qβx,1z+Qβx,2zfZi∗zdz,where Zi∗≜εi∗2−αR2, βx,1=βx/D1σεi∗, βx,2=βx/D2σαR, βx=8σω2/NBPs, and D1 and D2 are constants that are determined by the number of tags and channel variances. For this case, since the best tag i∗ is selected according to (6), the PDF of Zi∗ is obtained by [19](39)fZi∗z=Kσεi∗2+σαR2e−1/σεi∗2z+e−1/σR2z⋅1−σεi∗2σεi∗2+σαR2e−1/σεi∗2z−σαR2σεi∗2+σαR2e−1/σαR2zK−1,z>0,where K denotes the number of tags.


## 4.1.3. Tag Selection with SIC When the Primary System Is Idle

When SIC is employed, since the interference from the RF source is eliminated, the analysis can be simplified. Similar to the case without SIC, we first defineρi≜ηgRiαTi and Φ˜B≜ΦB−σω2. Since ρi2>0, the BER for a single slot can be obtained as(40)PrB^n=0|Bn=1=PrΦ˜B<ξ′′|Bn=1=PrΩB1′′<−ρi∗22Px=Qρi∗β,(41)PrB^n=1|Bn=0=PrΦ˜B>ξ′′|Bn=0=PrΩB0′′>−ρi∗22Px=0,where βx=8σω2/NBPx.Substituting (40) and (41) into (24) and assuming PrBn=1=PrBn=0=0.5, BER for a single slot can be simplified as(42)Pbidle=12Qρi∗βx.Finally, the average BER for all slots is obtained as(43)P¯bidle=EPbidle=12∫0∞Qρi∗βxfρi∗zdz,where(44)fρi∗z=1σρi∗2e−1/σρi∗2z1−e−1/σρi∗2zK−1,z>0,and σρi∗2=η2σαTi∗2σgRi∗2 and K is the number of tags.


## 4.2. Average Achievable Rate

Based on the obtained BERs, average achievable rate of the secondary ABC system is expressed as(45)R¯Bx=RsNB1−P¯bxNtot,x∈busy,idle,where Rs is the source data rate of the primary signal sn, NB is the number of backscattered bits, and Ntot is the total number of transmitted bits. P¯bx are obtained in (30), (38), and (43).Finally, the average achievable rate of the proposed secondary ABC systems is expressed as(46)R¯B=νR¯Bbusy+1−νR¯Bidle,where ν is the primary activity.


## 5. Numerical Results

In this section, we evaluate the performance of the proposed multi-tag selection schemes in terms of BER and average achievable rate of the secondary ABC system through simulations. Throughout the simulations, we set unit i.i.d. channel gains for all the links, i.e.,σhx2=σαx2=σRx2=1, i∈1,2,…,K.Figures3 and 4 show the BER and the average achievable rate of the secondary ABC system for varying primary activity when the number of tags K=8 and SNR=15 dB. When the primary system is always busy, i.e., ν=1, all the schemes obtain the same BER and achievable rate. However, as shown in Figure 4, as the primary activity decreases, the achievable rate of the conventional scheme significantly degrades due to absence of ambient RF source signals, while those of the proposed multi-tag selection schemes are kept or even improved with SIC. Especially, for the proposed multi-tag selection scheme with SIC, the BER is further improved as the primary activity is decreased, while the BERs of both the proposed multi-tag selection scheme without SIC and the conventional scheme are almost maintained as the primary activity is getting low as shown in Figure 3. As a result, the proposed cognitive ABC system with multi-tag selection schemes can provide significantly improved achievable rate even under limited spectrum resource.Figure 3
Average BER of the secondary ABC system for varying primary activity (K=8 and SNR=15 dB).Figure 4
Average achievable rate of the secondary ABC system for varying primary activity (K=8 and SNR=15 dB).Figures5 and 6 show the BER and the average achievable rate of the secondary ABC system for varying SNR when ν=0.1. In Figure 5, it is shown that the BERs of the proposed multi-tag selection schemes with and without SIC are reduced, as the number of tags increases due to a selection diversity gain, while that of the conventional scheme is invariant. In addition, the proposed multi-tag selection scheme with SIC significantly outperforms that without SIC in high SNR regime. On the other hand, as shown in Figure 6, the achievable rate of the conventional scheme is very small with low primary activity, regardless of SNR and the number of tags. On the contrary, the proposed multi-tag selection schemes provide sufficient achievable rates in the whole range of SNRs. Furthermore, they can obtain a selection diversity gain, and thus their achievable rates increase as the number of tags increases, regardless of the primary activity. Additionally, the proposed multi-tag selection scheme with SIC always outperforms that without SIC thanks to the improved BER performance.Figure 5
Average BER of the secondary ABC system for varying SNRν=0.1.Figure 6
Average achievable rate of the secondary ABC system for varying SNRν=0.1.Figures7 and 8 show the BER and the average achievable rate of the secondary ABC system for varying the number of tags when ν=0.3 and SNR=15 dB. In the figures, it is shown that the BERs and the achievable rates of the proposed multi-tag selection schemes are almost converged to the best performance when the number of tags is more than five. This implies that only a small number of tags are enough to achieve sufficiently good performance. On the contrary, the BER of the conventional scheme is not affected by the number of tags and its average rate is significantly low, compared to those of the proposed multi-tag selection schemes with and without SIC. This is because in the conventional scheme, the secondary ABC system cannot operate during idle period of the primary system due to absence of the ambient RF source signal. However, in the proposed multi-tag selection-based cognitive ABC system, a power beacon with spectrum sensing capability for the primary channel can provide the ambient RF source signal to the tags, although the primary system is silent.Figure 7
Average BER of the secondary ABC system for varying number of tags (ν=0.3 and SNR=15 dB).Figure 8
Average achievable rate of the secondary ABC system for varying number of tags (ν=0.3 and SNR=15 dB).


## 6. Conclusion

In this paper, we proposed multi-tag selection schemes to improve the achievable rate of a secondary ABC system under CR environments. The performance of the proposed schemes was mathematically derived and evaluated through simulations. It is shown that the proposed multi-tag selection scheme without SIC can significantly improve the performance, compared to the conventional scheme, thanks to additional secondary power beacon and selection diversity gain. By applying SIC, it is further enhanced with reduced BER performance obtained from an interference cancellation technique. Further work will allow the power beacon to control the transmit power level and optimize it under given power constraint in order to design an energy-efficient secondary ABC system. In addition, incorporation of energy harvesting or conservation strategies for the secondary power beacon can be also considered. Furthermore, the impact of imperfect sensing at the secondary power beacon and machine learning-based detecting approaches for imperfect channel information conditions can be another research topic.



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*Source: 8885240-2022-01-31.xml*