Simultaneous Harvest-and-Transmit Ambient Backscatter Communications under Rayleigh Fading

Ambient backscatter communications is an emerging paradigm and a key enabler for pervasive connectivity of low-powered wireless devices. It is primarily beneficial in the Internet of things (IoT) and the situations where computing and connectivity capabilities expand to sensors and miniature devices that exchange data on a low power budget. The premise of the ambient backscatter communication is to build a network of devices capable of operating in a battery-free manner by means of smart networking, radio frequency (RF) energy harvesting and power management at the granularity of individual bits and instructions. Due to this innovation in communication methods, it is essential to investigate the performance of these devices under practical constraints. To do so, this article formulates a model for wireless-powered ambient backscatter devices and derives a closed-form expression of outage probability under Rayleigh fading. Based on this expression, the article provides the power-splitting factor that balances the tradeoff between energy harvesting and achievable data rate. Our results also shed light on the complex interplay of a power-splitting factor, amount of harvested energy, and the achievable data rates.

of network challenges and data communication issues arise that require further exploration. Furthermore, limited theoretical knowledge of ambient backscatter communication demands new dimensions for performance evaluation of the network.
Motivated by the aforementioned observations, we perform the analysis of backscatter communication under Rayleigh fading. Specifically, our contribution is two-fold: • Derivation of closed-form expression of outage probability for wireless-powered devices operating under Rayleigh fading. • Derivation of the power-splitting factor that balances the tradeoff between energy harvesting and achievable data rate. The remainder of the paper is organized as follows. Section 2 discusses the related work on conventional backscatter and ambient backscatter communications. In Section 3, a detailed description of the system model is provided. Section 4 provides the performance analysis while Section 5 discusses the numerical results. Finally, Section 6 provides key findings and conclusions.

II. RELATED WORK
Backscatter communication has been considered from different aspects in wireless networks [15]. The authors of [16] employed backscatter communication to enable device-to-device communications. Besides this, several detection schemes for backscatter communication systems are proposed in [17], [18], [19]. A detector that does not require the channel state information (CSI) was constructed using a differential encoder in [18]. Specifically, they developed a model and derived optimal detection and minimum bit-error-rate (BER) thresholds. Moreover, the expressions for lower and upper bounds on BER were also derived that were corroborated through simulation results. A joint-energy detection scheme is proposed in [19] that requires only channel variances rather than specific CSI. The same authors provided a study of BER computation, optimal and suboptimal detection, and blind parameter acquisition. The non-coherent signal detection outperformed the conventional techniques in terms of detection accuracy and computation complexity. A successive interference cancellation (SIC) based detector and a maximum-likelihood (ML) detector with known CSI are presented in [17], to recover signals not only from readers but also from RF sources. In addition to this, the authors derived BER expressions for the ML detector. It was shown that the backscatter signal can significantly enhance the performance of the ML detector as compared to conventional single-input-multiple-output (SIMO) systems.
Capacity and outage performance analysis for ambient backscatter communication systems was studied in [20], [21], [22], [23]. The authors of [20] analyzed the channel capacity over orthogonal frequency division multiplexing (OFDM) signals. The ergodic capacity optimization problem at the reader with SIC was investigated by the authors of [21]. Specifically, the authors jointly considered the transmit source power and the reflection coefficient and improved the ergodic capacity. For ambient backscatter communication systems, the BER of an energy detector was derived and the BER-based outage probability was obtained in [22]. Zhao et al. in [23], the effective distribution of signal-to-noise ratio (SNR) was derived and the SNR-based outage probability was evaluated over real Gaussian channels.
More recently, the authors in [24] investigated a cognitive radio network having ambient backscatter communication. In particular, it was considered that a wireless-powered secondary user can either harvest energy or adopt ambient backscattering from a primary user on transmission. A time allocation problem was developed in order to maximize the throughput of the secondary user and to obtain the optimal time ratio between energy harvesting and ambient backscattering. Reference [25] introduced a hybrid backscatter communication scheme as an alternative access scheme for a wireless-powered transmitter. Specifically, when the ambient RF signals were not sufficient to support wireless-powered communications, the transmitter can choose between bistatic backscattering or ambient backscattering based on a dedicated carrier emitter. A throughput maximization problem was formulated to find the optimal time allocation for the hybrid backscatter communication operation. Both [24] and [25] studied a deterministic scenarios.

III. EXPERIMENTAL SYSTEM MODEL DESIGN
Let us consider an IoT network that consists of N number of ambient backscatter devices. These ambient backscatter devices are considered to be powered by ambient RF source. This consideration is under the assumption that ambient RF sources (like Radio signals, TV signals and WiFi signals) are abundant in the environment. These backscatter devices use the harvested energy from the ambient RF signals and transmit their data to the gateway as shown in Figure 1.
A typical ambient backscatter device has three major operations, i.e., spectrum sensing, energy harvesting, and data exchange. Inspired by [6], we consider the circuit model of an ambient backscatter device is shown in Figure 2. Here, the main purpose of the spectrum sensor is to detect suitable ambient RF signals, whereas, the energy harvesting circuit enables the backscatter devices to operate a self-sustainable manner. This self-sustainability is essential for IoT networks as they are expected to operate with minimum human intervention. When the device is in operation mode, the spectrum sensing is performed in order to detect RF signal with large power. Afterward, the detected signal is employed for either backscatter communication or energy harvesting. The analog-to-digital converter (ADC) uses the harvested energy and convert it into direct current that is utilized by other modules including a microcontroller. The microcontroller performs multiple communication operation including processing the information and matching the impedance of antenna for better reception of RF signals. We consider that the amount of energy consumed by energy harvester is negligible [6] and satisfies the following condition In the above expression E h , E b , E s , E m denotes the harvested energy, energy consumed for backscatter communication, energy consumed for spectrum sensing and the energy consumed by micro-controller/ sensor for data gather and processing. Some of the key symbols used throughout this paper are provided in Table I  We now characterize the energies harvested and consumed during one time slot. We consider that compressive sensing is performed in each time slot. Thus, the time slot T is divided into phases, i.e., compressive sensing duration (denoted as α) and energy harvesting/ backscattering duration (denoted as (1 − α)). After compressive sensing, the received signal at the device is divided into two streams of power. The first part is used for energy harvesting while the other part is used for performing backscattering operation. This separation is performed with a factor ρ, where 0 < ρ ≤ 1. A graphical representation of an interplay of ρ and α is provided in Figure 3. Assuming that an i-th backscatter device detects an ambient RF, then the received signal at the device is given as where y i,1 is the received signal, s 1 denotes the normalized signal, P represents the transmit power, and P l,1 = d θ 1 is the path loss experienced by the backscatter device and θ is the path loss exponent. Furthermore, h i,1 represents the channel gain between the ambient RF source and backscatter device which is assumed to be Rayleigh faded, n i,1 is the zero mean additive white Gaussian noise (AWGN) with N 0 variance while β is the reflection coefficient of the backscatter devices. The harvested energy is then denoted as where Ω 1 = P N0 , ρ represents the fraction of power used for energy harvesting, η is the energy conversion efficiency that is considered to be same for all the backscatter devices as they employ same circuitry.
The amount of energy consumed by the compressive sensing module is a linear multiplication of the number of samples and sampling rate. More specifically, it can be represented as where M is the number of wideband signals that have been detected during the phase of spectrum sensing, f is the sampling rate, and e is the energy consumed for each sample. The amount of energy consumed the backscattering module can be represented in terms of circuit power as where P b is the amount of circuit power consumed during backscattering phase. For the sake of simplicity and without loss of generality, we consider that the power consumed by micro-controller is fixed. As a result of backscattering, the received message at the gateway can be written as where y i,2 is the received signal at the gateway, s i,2 denotes the normalized signal sent by the i-th backscattering device, P represents the transmit power, and P l,2 = d θ 2 is the path loss between backscatter device and the gateway. Furthermore, h i,2 represents the Rayleigh faded channel gain between the backscatter device and the gateway, n i,2 is the zero mean AWGN with zero mean and N 0 variance.

IV. PERFORMANCE ANALYSIS AND METHODOLOGY
In this section, we derive the communication outage and power shortage probabilities of the backscatter devices. Based on these probabilities, we aim to find the balancing value of the ρ.

A. Outage Performance
Using the Shannon capacity formula, the achievable sum rate at the gateway can be written as where R i is the achievable rate of i-th backscattering device which is given as where Ω 2 = P b N0 . The outage probability of achievable rate can occur due to the following two conditions 1) If the harvested energy is below the energy required for operations of backscatter device. 2) If the achievable rate is below the required rate at the gateway. Thus, using the total probability theorem, the outage probability can be written as where ϕ represents the threshold of required data rate and ψ = E b + E s + E m is the energy threshold for operation of the backscatter device. From the above equation, we note that if the harvested energy is below the threshold, then the backscatter device would not be able to transfer any data to the gateway. In this case, the probability that the rate falls below a required threshold would always be 1. Thus, we can write The probability that the harvested energy would fall below a specified threshold can be written as After some simplifications, it can be represented as In contrast, the probability of energy harvesting increasing beyond the threshold can be represented as whereγ 1 is the average channel gain between RF source and the backscattering device. Let us now consider the case when the harvested energy is greater than ψ. In this case, the probability that the achievable data rate falls below a pre-determined threshold can be written as After some straightforward simplifications, we obtain whereγ 2 is the average channel gain between backscattering device and the gateway. Substituting the Eqs (10), (12), (13), and (15) in (9), we obtain After solving 16, we have

B. Balancing communication outage and power shortage
In this section, we aim to find the values of ρ that balances the tradeoff between communication outage and power shortage. In particular, we note that different values of ρ have a different impact on communication outage and power shortage. From (3), we can observe that the amount of energy harvested is the increasing function of ρ. In other words, as the value of ρ increases, the amount of harvested energy also increases, whereas, it decreases with a decrease in the value of ρ. In contrast, the achievable rate of any i-th backscattering device is a decreasing function of ρ. Since the achievable rate is dependent on the received SNR, therefore, increasing the value of ρ results in increasing the SNR while a reduction in ρ causes an increase in the values of SNR which in turn increases the achievable rate.
From the above arguments, we can observe that the balancing value of ρ can be found by solving the energy harvesting and SNR expressions simultaneously. Thus, we can write After cross multiplication and taking least common multiple, we obtain the ρ * as From the above expression, we can observe that ρ * is inversely proportional to the Ω 1 . Moreover, if P l,1 = P l,2 , then the balancing value of ρ * is halved. We also note that the value of ρ * increases with an increase in α indicating the direct relationship between ρ * and α.

V. RESULTS AND DISCUSSIONS
In this section, we provide results and relevant discussion on the above-mentioned analysis. Unless mentioned otherwise, following parameters have been used for generating simulation and analytical results: η = 0.5, B = 1M Hz, β = 0.5, d 1 = d 2 =5m, ϕ =2kbps, θ = 2, and ρ = 0.3. Figure 4 illustrates the outage probability as a function of increasing values of SNR. It can be seen that the outage probability decreases with an increase in the SNR. However, the impact of α on P out is different for different values of SNR. Specifically, we observe that an increase in the α results in an increase in the outage probability. It is because with an increase in α provides more time for compressive sensing and less time for energy harvesting and backscattering. On the other hand, an increase in ρ causes an increase in outage probability. This result is caused by allocating more fraction of received power for energy harvesting and less for performing backscatter communications. In addition, the simulation results closely follow the analytical curves which indicates the validity of our theoretical model. Figure 5 (a) shows the achievable rate as a function of increased SNR. As anticipated by the analytical expression, the increase in SNR improves the achievable rate. However, an increase in α decreases the achievable rate. In fact, the impact of α becomes more prominent at higher values of SNR showing a rapid rise in the curves. Where Figure 5 (a) is plotted for d 1 = d 2 = 5m, the curves of Figure 5 (b) are plotted against d 1 = d 2 = 10m. This increase in distance has a critical impact on the achievable rate. In particular, for the same values of SNR and α (e.g., SNR=0 dB and α=0.1), the achievable rate drops from 20 kbps to 5 kbps when the distance is increased. Figure 6 plots the harvested energy against increasing values of d 1 . Indeed, this results highlight the significance of distance between the RF source and the backscatter device. It can be seen that an increase in d 1 results in decreasing the harvested    We have plotted different curves of achievable rate and harvested energy against the increasing values of ρ. It can be observed that an increase in ρ causes an increase in the amount of harvested energy while simultaneously reducing the achievable rate. Since the value of α influences both rate and harvested energy, the lower values of α decreases the converging point of the curves of rate and energy curves. Similar trends can be shown in 7 (b), however, the converging point of the curves now shift towards the right-hand side while reducing both the harvested energy and rate. This trend can be attributed to the increase in d 1 and d 2 . This shift in balancing point shows that a higher value of ρ is required with an increase in distance. This also indicates that energy harvesting becomes a critical factor when the distance is increased between ambient RF source and the device and that between device and gateway.

VI. CONCLUSION
Ambient backscatter communications provide virtually endless opportunities to connect wireless devices. We anticipate that wearable devices, connected homes, industrial internet, and miniature embeddable are some of the areas where ambient backscatter communications would be adapted to provide pervasive connectivity. Thus, to better analyze the utility of these lowpowered devices, this article has provided a comprehensive analysis of ambient backscattering model from the perspective of achievable data rates and the amount of harvested energy. In addition to deriving closed-form expressions of outage probability and balancing power-splitting factor, we have shown that the distance between ambient RF source and the device plays a critical role in determining the life-cycle of devices and the outage probability at the gateway. In fact, we have demonstrated that an increase in distance shifts the balancing power-splitting point to the right-hand side. Besides this, we have observed that when the distance is increased from 5m to 10m against fixed values of SNR and α, the achievable rate at gateway drops from 20 kbps to 5 kbps. These results can act as a fundamental building block for designing and large-scale deployment of ambient backscatter devices in the future.