Multitone ASK Waveform Design for Simultaneous Wireless Information and Power Transfer

In the era of Internet of Things (IoT) networks, far-field wireless power transfer using radio frequency (RF) waves has attracted attention as a solution to remove the need for batteries at the sensors. However, RF communication signals can be used for energy as well as information for better resource management. Therefore, recently, simultaneous wireless information and power transfer (SWIPT) technology has gained significance for charging these low-power IoT devices wirelessly. In this paper, a novel N-tone multitone amplitude shift keying (ASK) transmission signal scheme is proposed by utilizing the non-linearity of integrated information-energy rectifier receiver architecture. The data rate is increased by transmitting $(N-1)$ symbols over a single N-tone Multitone ASK signal stream. Wireless power transfer (WPT) and wireless information transfer (WIT) performances of the proposed transmission scheme are analyzed, and a trade-off between WPT and WIT performances is discussed. WPT performance of the designed transmitted signal has been shown to improve with increasing the minimum level of the symbols approaching the maximum possible power efficiency of the rectifier. Logarithmically distributed symbols have been shown to improve WPT compared to linearly distributed symbols due to the non-linearity of the rectifier circuitry, whereas linearly distributed symbols result in better WIT performance. It is possible to attain a good WIT performance with a low transmitted signal power.

SECTION I. Introduction

Internet of Things (IoT) envisions a global wireless network where trillions of wireless sensors are connected via the Internet and generate data from a diverse range of applications in biomedical implants, vehicular communications, home automation, etc. Wireless standards such as 5G and beyond will underpin the growth in the ubiquitous deployment of IoT devices [1]. To make such deployments feasible, there is a need for sustainable batteryless energy sources. One promising technology aiming to provide both power and data transfer is Simultaneous Wireless Information and Power Transfer (SWIPT). SWIPT provides an energy-efficient green solution by exploiting the same communication signal for data transfer as well as Wireless Power Transfer (WPT) [2].

At the receiver, SWIPT operation can be achieved by two types of receiver architectures: separated information-energy receiver architecture with two separate paths for information detection and power extraction and integrated information-energy receiver architecture utilizing a rectifier circuitry for power transfer as well as information detection [3], [4], [5], [6]. In the separated information-energy receiver architecture, information demodulation is performed using conventional techniques with a local oscillator and mixer. High-frequency RF components consume a high amount of power. For example, the power consumption of a full ultra-low-power receiver is 3.8 mW, out of which the local oscillator consumes 28% of the total power consumption, and 9% is consumed by the mixer [7], [8], [9].

The latter integrated information-energy receiver architecture offers the advantage of removing the local oscillator for information detection from the receiver circuitry and reduces the overall power consumption for signal processing [10], [11], [12]. However, conventional communication signals cannot be used for information detection at the rectifier output. Therefore, new communication signals are required to be designed for such an integrated information-energy receiver architecture.

Initially, for an integrated information-energy receiver architecture, a simple energy modulation scheme using a single-tone waveform, transmitting information symbols by varying the energy levels of the waveform, is introduced [10]. In [12], a double half-wave rectifier is utilized to extend the voltage region for amplitude symbols. A biased amplitude-shift-keying (ASK) transmission scheme has been introduced where each symbol carries some minimum energy to attain a continuous minimum power transfer with the information transfer [13]. However, in all these transmission schemes for integrated information-energy receiver architecture, only a single-tone signal is utilized, and a complex case of OFDM, where multiple symbols over multiple tones are transmitted, is not considered.

From the WPT perspective, higher peak-to-average-power ratio (PAPR) waveforms such as multitone signals perform better than a single-tone waveform, delivering higher power conversion efficiency (PCE) at the rectifier output [14], [15], [16], [17], [18], [19], [20], [21]. Utilizing the PAPR of the multitone signal by varying the number of tones according to the transmitted information has been proposed in [22]. Further, a non-uniform spaced multitone waveform utilizing PAPR has also been shown to perform better in the case of low signal-to-noise ratio scenarios [23]. A multitone transmission method by transmitting information in the ratios of tones’ amplitudes has been introduced in [24], which helps make the communication signal immune to the transmission distance. However, information detection at the receiver is feasible for only two or three tones and becomes complicated and impractical for more than the 3-tone multitone signal.

A frequency-based information detection has been introduced in [25] to minimize the ripples at the rectifier output. Information is transferred by varying the frequency spacing between the tones of the multitone frequency-shift-keying (FSK) signal according to transmitted symbols. Another way of information detection for the multitone FSK has also been proposed by measuring the output PAPR levels [26]. A Multitone phase-shift-keying (PSK) waveform scheme utilizing the tones’ phases for information transmission with the higher transmission output data rate has been introduced in [27]. Ripples in the output voltage have been reduced by utilizing the phases for information symbols transmission. However, complex transmitters would be required to modify multiple-tone phases for information transmission. Also, phase-based information transmission is more susceptible to noisy and fading environments compared to amplitude-based modulations [28], [29], [30]. Therefore, it is necessary to develop amplitude-based transmission schemes for SWIPT integrated receiver architecture shown in Fig. 1.

FIGURE 1.

Integrated receiver rectifier for SWIPT.

In this paper, a novel Multitone ASK transmission scheme for integrated information-energy receiver architecture is proposed. The signal is designed in such a way that the non-linearity of the rectifier is utilized for information detection. The information detection and power transfer are performed from the same rectified signal. Information is transmitted by varying the amplitudes of tones at the transmitter, and the information detection is performed by analyzing the magnitudes of the corresponding relevant baseband tones at the rectifier output. PCE and bit-error-rate (BER) are used to investigate WPT and wireless information transfer (WIT) performances, respectively. The effect of the chosen minimum energy level of the symbols, number of tones, and symbols’ amplitude distribution over signal PAPR, output PCE, and BER is analyzed.

The advantage of the proposed Multitone ASK transmission scheme is its information detection via exploiting the intermodulation process of the same rectifier circuitry, which eliminates the need for a local oscillator and reduces the overall power consumption of the SWIPT system. In this work, it is possible to transmit $(N-1)$ symbols over a N-tone multitone signal, providing a conventional OFDM-type communication for the integrated information-energy receiver architecture. Therefore, a higher data rate is achieved without increasing the bandwidth by using the same multitone signal earlier used for WPT solely. In this work, only the individual tones’ power level would be modified according to the transmitted data stream, resulting in a simple transmitter.

This paper is organized as follows. Section II introduces the theoretical model of designing a Multitone ASK signal and analyses the effect of different information streams versus varying average signal power with the non-linearity of the rectifier. Next, Section III discusses the effect of symbol levels’ distribution over PCE in terms of achievable signal PAPR. Then, the WPT and WIT performances of the SWIPT system with the Multitone ASK transmission scheme are analyzed in Section IV. In the end, a conclusion is drawn in Section V.

SECTION II. Signal Model

An integrated information-energy rectifier receiver is illustrated in Fig. 1 consisting of an input matching network, diodes rectifier, and a resistor-capacitance low-pass-filter (RC-LPF). Here, the same rectifier receiver is used for both WPT and WIT. Received Multitone ASK signal $x(t)$ centered around frequency $f_{c}=2.45$ GHz is passed through the rectifier receiver, resulting in a baseband signal $y(t)$ which is utilized not only for power transfer but also for decoding the transmitted information.

The transmitted Multitone ASK signal spectrum $X(f)$ and the corresponding rectified baseband output signal spectrum $Y(f)$ are shown in Fig. 2. The information is embedded in the amplitudes of tones of the N-tone multitone RF signal. Information is encoded in the multitone RF signal in such a way that the non-linearity of the rectifier is utilized to extract the information from the baseband signal $y(t)$ at the output. N-tones multitone signal after passing through the rectifier results in baseband signal consisting of various intermodulation (IM) frequency components of various orders as a result of mixing between various tones of the multitone signal. However, $2^{nd}$ order intermodulation frequency components (IM₂) dominates at the receiver output [31].

FIGURE 2.

Four-tone Multitone ASK RF signal spectrum $X(f)$ centered around frequency $f_{c}=2.45$ GHz and rectified baseband output spectrum $Y(f)$ consisting of intermodulations frequency tones (in MHz) carrying information (colored) and extra intermodulations components (black).

Here, information is transmitted as amplitudes of tones of multitone signal, and after rectification, information is decoded from the second-order intermodulation frequency components, IM₂s between consecutive tones. A reference N-tone multitone signal $r(t)$ with an average signal power of $P_{\mathrm {in}}$ is considered as\begin{equation*} r(t)= \mathrm {Re}{\left \{{{\sum _{n=1}^{N} \sqrt {\frac {2 P_{\mathrm {in}}}{N}}e^{j(2\pi f_{n}t)}}}\right \}}. \tag {1}\end{equation*} The transmitted Multitone ASK signal $x(t)$ is generated by embedding the information symbols over the reference signal $r(t)$ and can be considered as\begin{equation*} x(t)= \mathrm {Re}{\left \{{{\sum _{n=1}^{N} \sqrt {\frac {2 l_{s_{n-1}}P_{\mathrm {in}}}{N}}e^{j(2\pi f_{n}t)}}}\right \}} \tag {2}\end{equation*} where $l_{s_{n-1}}$ denotes the transmitted information level over the $n^{th}$ tone frequency $f_{n}$ . Here, $n^{th}$ tone of $r(t)$ are modified by the transmitted information symbol level $l_{s_{n-1}}$ . For an amplitude modulation order of L, $l_{s_{n-1}}$ is chosen from the available information symbol set ($\boldsymbol {S}$ ) consisting of L levels $l_{1}$ , $l_{2}$ , $\cdots $ , $l_{L}$ . Here, phases of the transmitted tones are considered zero.

At the rectifier output, the information is decoded from the amplitudes of the relevant baseband tones in the MHz frequency range, as shown in Fig. 2. The filtered baseband output consists of dc and the accumulation of several intermodulation frequency components. However, the filtered output $y(t)$ consists of only dc and even order $4^{th}$ order, $6^{th}$ order, $\cdots $ , etc., frequency components. All the odd-order intermodulation components $3^{rd}$ order, $5^{th}$ order, $\cdots $ , etc., are filtered out by LPF as all these IM frequency components lie in the RF frequency range. Among even order frequency components, IM₂ would be dominating compared to $4^{th}$ order, $6^{th}$ order, $\cdots $ , etc., frequency components [31].

For example, after passing a 3-tone Multitone ASK signal $x(t)$ from (2) through the rectifier receiver model depicted in Fig. 1, the obtained baseband rectifier output $y(t)$ can be represented as a combination of dc and the dominant IM₂s as\begin{align*} y(t)& = \mathrm {dc}+A_{1}\cos \left ({{2\pi (f_{2}-f_{1})t}}\right ) +A_{2}\cos \left ({{2\pi (f_{3}-f_{2})t}}\right ) \\ & \quad +A_{3}\cos \left ({{2\pi (f_{3}-f_{1})t}}\right ), \tag {3}\end{align*} where $A_{1}$ , $A_{2}$ , and $A_{3}$ represent the amplitudes of IM₂ at $(f_{2}-f_{1})$ , $(f_{3}-f_{2})$ , and $(f_{3}-f_{1})$ , respectively. Here, the baseband tones amplitudes are related to the corresponding intermodulating tones’ amplitudes of multitone RF signal. The baseband tone amplitude corresponds to the product of the intermodulating tones, i.e., $A_{1}\propto l_{s_{0}}l_{s_{1}}$ , $A_{2}\propto l_{s_{1}}l_{s_{2}}$ , and $A_{3}\propto l_{s_{1}}l_{s_{3}}$ as $A_{1}$ , $A_{2}$ , and $A_{3}$ are amplitudes of intermodulation frequency component between $f_{1}$ and $f_{2}$ , $f_{2}$ and $f_{3}$ , and $f_{1}$ and $f_{3}$ , respectively.

In this paper, $(N-1)$ information symbols are transmitted over a single N-tone multitone signal. The Multitone ASK signal is designed in such a way that the information is in amplitude levels of IM₂ between consecutive tones only, i.e., $(f_{2}-f_{1}),~(f_{3}-f_{2}), \cdots , (f_{N}-f_{N-1})$ tones amplitudes would carry the information as shown in Fig. 2. In Fig. 2, 4-tone signal is depicted where the first tone is kept constant, and the other three tones’ amplitudes are modified according to the transmitted information symbols from the available symbol set $\boldsymbol {S}$ . The baseband output signal spectrum $Y(f)$ contains various intermodulation frequency components. However, the three information symbols are decoded from the corresponding intermodulation frequency components, $(f_{2}-f_{1})$ , $(f_{3}-f_{2})$ , and $(f_{4}-f_{3})$ as depicted in colour in Fig. 2.

To make a simultaneous transmission of these $(N-1)$ information symbols possible over a single N-tone multitone signal, $f_{n}$ ’s are chosen in a particular way such that $(N-1)~\textrm {IM}_{2}$ s between consecutive frequencies do not overlap each other and also do not coincide with other non-consecutive IM₂s. This is done to obtain a unique $(N-1)$ desired baseband frequencies at the output. This results in asymmetrically spaced tones around the center frequency of 2.45 GHz instead of general equally spaced tones of a multitone signal. Here, these frequencies $f_{n}$ s are obtained using the algorithm used in [27].

For an N-tone Multitone ASK signal from (2), average power of the transmitted signal after embedding $(N-1)$ information symbols would be\begin{equation*} P_{\mathrm {avg}}= \frac {P_{\mathrm {in}}}{N}(l_{s_{0}}+l_{s_{1}}+l_{s_{2}}+\cdots +l_{s_{N-1}}), \tag {4}\end{equation*} and should satisfy\begin{equation*} \frac {P_{\mathrm {in}}}{N}(l_{s_{0}}+l_{s_{1}}+l_{s_{2}}+\cdots +l_{s_{N-1}})\leq P_{\mathrm {in}}. \tag {5}\end{equation*}

Assuming the first tone amplitude is constant equal to $P_{\mathrm {in}}/N$ , i.e., $l_{s_{0}}$ be equal to 1, (4) results into\begin{equation*} l_{s_{1}}+l_{s_{2}}+\cdots +l_{s_{N-1}}\leq N-1. \tag {6}\end{equation*} There exists a condition over the possible maximum information symbol level $l_{L}$ so that it is feasible to transmit all $(N-1)$ symbols to be the maximum $l_{L}$ simultaneously. Therefore, from (6), $l_{L}$ must satisfy\begin{align*} (N-1)l_{L} & \leq N-1, \tag {7}\\ l_{L} & \leq 1. \tag {8}\end{align*} As the information is being transmitted through the tones’ amplitudes, the average power of the transmitted multitone signal keeps changing with the transmitted information patterns. For a particular available average power $P_{\mathrm {in}}$ at the transmitter, the maximum average power of the transmitted signal after embedding information in multitone signal’s tones is $P_{\mathrm {avg,max}}=P_{\mathrm {in}}$ when all the transmitted information symbols are chosen to be the maximum levels $l_{L}=1$ . Similarly, the average power of the transmitted signal would be minimal when all the transmitted information levels are chosen to be the lowest information level $l_{1}$ ,\begin{equation*} P_{\mathrm {avg,min}}=(1+(N-1)l_{1})\frac {P_{\mathrm {in}}}{N}. \tag {9}\end{equation*} For the L information symbols, the average symbol power would be\begin{equation*} P_{\mathrm {sym\_avg}}=\frac {1}{L}\sum _{i=1}^{L} l_{i}. \tag {10}\end{equation*}

Let the information levels be linearly distributed between $l_{\min }$ and $l_{\max }$ for a modulation order L. Thus, the available L information symbol levels can be defined as\begin{equation*} l_{i}=l_{\min }+(i-1)\frac {l_{\max }-l_{\min }}{L-1},\hskip 0.5pc \forall \hskip 0.5pc i=1,2,\cdots ,L. \tag {11}\end{equation*} For example, for $L=4$ , $l_{\min }=0.1$ , and $l_{\max }=1$ , available symbol levels set $\boldsymbol {S}$ would be having information levels as 0.1, 0.4, 0.7, and 1.

For an N-tone multitone signal carrying $(N-1)$ information symbols with a modulation order L, $L^{N-1}$ different patterns of the transmitted symbols are possible, which is also similar to different possible patterns of $(N-1)\log _{2}L$ bits over the N-tone multitone signal, and can also be represented by $2^{(N-1)\log _{2}L}$ different information bits patterns. Different information patterns over the multitone signal may still result in the same average signal power of the transmitted stream. For example, from (4), the multitone signal average power for a 4-tone signal with $[{0.1~0.4~0.7}]$ information stream is similar to a signal having $[{0.4~0.7~0.1}]$ information stream. Therefore, out of these $L^{N-1}$ different multitone streams information patterns, the total possible different transmitted power levels would be $\binom {N+L-2}{N-1}$ . The mean of these different average powers of the transmitted multitone streams, ${P_{\mathrm {avg}}|}_{\mathrm {mean}}$ as a result of different information symbol combinations and from (4) can be represented as\begin{align*} {P_{\mathrm {avg}}|}_{\mathrm {mean}}=\frac {P_{\mathrm {in}}}{N}+\frac {1}{\binom {N+L-2}{N-1}}\sum _{j=1}^{\binom {N+L-2}{N-1}}\left ({{\sum _{i=1}^{N-1} l_{s_{j,i}}\frac {P_{\mathrm {in}}}{N}}}\right ) \tag {12}\end{align*} where $l_{s_{j,i}}$ represents $i^{\mathrm {th}}$ symbol $l_{s_{i}}$ in the $j^{\mathrm {th}}$ possible combination of transmitted power levels. These $\binom {N+L-2}{N-1}$ different combinations of information sequence over a single multitone stream can further be reduced depending upon L and the amplitude distribution between $l_{\min }$ and $l_{\max }$ due to further overlapping among the average signal power.

For linearly distributed information symbol levels, the average signal power of a single N-tone signal can be rewritten from (4) and (11) as\begin{align*} P_{\mathrm {avg}} & = \frac {P_{\mathrm {in}}}{N} \left [{{1+(N-1)l_{\min }+\left \{{{\sum _{n=1}^{N-1}i_{n}-(N-1)}}\right \}}}\right . \\ & \quad \times \left .{{ \frac {l_{\max }-l_{\min }}{L-1}}}\right ], \hskip 1pc i_{n} \in \{1, 2, \cdots , L\}. \tag {13}\end{align*} For a 3-tone signal, the average signal power $P_{\mathrm {avg}}$ of the transmitted signal from (4) and (13) is $P_{\mathrm {avg}}=\left ({{1+l_{s_{1}}+l_{s_{2}}}}\right)P_{\mathrm {in}}/N$ with first tone power to be constant as $P_{\mathrm {in}}/N$ and $l_{s_{0}}$ to be 1, and can also be represented as\begin{align*} {P_{\mathrm {avg}}|}_{N=3}& =\frac {P_{\mathrm {in}}}{N}\left ({{1+2l_{\min }+\left ({{i+j-2}}\right )\frac {l_{\max }-l_{\min }}{L-1}}}\right ), \\ & \qquad \qquad \quad i,j \in \{1, 2, \cdots , L\}. \tag {14}\end{align*} In (14), $(i+j)$ for $i,j \in \{1, 2, \cdots , L\}$ results in $(2L-1)$ different mutually exclusive values. Table 1 represents the $L^{(N-1)}=16$ different patterns of transmitted information symbols $l_{s_{1}}$ and $l_{s_{2}}$ for $N=3$ , $L=4$ , $l_{\min }=0.1$ , and $l_{\max }=1$ . However, it can be seen that for these 16 different patterns, the factor $(l_{s_{1}}+l_{s_{2}})$ affecting average signal power $P_{\mathrm {avg}}$ results in a set of only seven different values $\left \{{{0.2, 0.5, 0.8, 1.1, 1.4, 1.7, 2}}\right \}$ from (14), for information embedded multitone stream. Table 2 represents a few of 64 possible combinations for $N=4$ with $L=4$ , $l_{\min }=0.1$ , and $l_{\max }=1$ . Here in Table 1 and Table 2, transmitted symbol sequences are arranged in such a way that symbol sequence patterns resulting in the same average power of the transmitted multitone stream are being put together. The resulting same average signal power for different symbol patterns is highlighted by grouping these in red. By generalizing for an N-tone multitone signal, there exist $(N-1)L-(N-2)$ different transmitted average signal powers for the different patterns of $(N-1)$ transmitted symbols $l_{s_{1}},~l_{s_{2}},\cdots ,l_{s_{N-1}}$ with the factor of $(l_{s_{1}}+l_{s_{2}}+\cdots +l_{s_{N-1}})$ from (4), lying between $[(N-1)l_{\min },~(N-1)l_{\max }]$ .

TABLE 1 Different Patterns of $(N-1)$ Transmitted Symbols for Multitone ASK With $N=3$ , $L=4$ , and $l_{\min }=0.1$

TABLE 2 Different patterns of $(N-1)$ Transmitted Symbols for Multitone ASK With $N=4$ , $L=4$ , and $l_{\min }=0.1$

From (3), it can be seen that relevant baseband intermodulation tones amplitudes at $\Delta f_{n}$ are proportional to the product of transmitted symbols at $n^{th}$ and $(n+1)^{th}$ tone. For example, amplitudes of relevant baseband intermodulation tones at $\Delta f_{1}$ and $\Delta f_{2}$ are proportional to $l_{s_{0}}l_{s_{1}}$ and $l_{s_{1}}l_{s_{2}}$ , respectively. Table 1 highlights relevant information carrying products $l_{s_{0}}l_{s_{1}}$ for $\Delta f_{1}$ and $l_{s_{1}}l_{s_{2}}$ for $\Delta f_{2}$ for $N=3$ with 16 possible different transmitted symbols patterns. Table 2 highlights relevant information carrying products $l_{s_{0}}l_{s_{1}}$ for $\Delta f_{1}$ , $l_{s_{1}}l_{s_{2}}$ for $\Delta f_{2}$ , $l_{s_{2}}l_{s_{3}}$ for $\Delta f_{3}$ for $N=4$ with a few of 64 possible different transmitted symbols patterns. It can be seen that the signals with the same average transmitted signal power but having a different sequence of symbol streams result in different variations in output baseband amplitudes. The reason for this is the non-linearity of the rectifier circuitry, where the baseband output tones magnitudes are a result of intermodulations among tones.

Due to the non-linearity of the rectifier, all baseband tones do not reflect the changes according to the varying signal average power $P_{\mathrm {avg}}$ while changing the symbol stream. For example, Fig. 3 shows the magnitude behavior of the first baseband output tone ($\Delta f_{1}$ ) at 1 MHz for varying information symbols pattern for a 3-tone Multitone ASK centred around 2.45 GHz with $L=2$ and $l_{\min }=0.1$ . Multitone ASK signal frequencies are selected using the Algorithm 1 of [27]. As the modulation order L is 2, the transmitted symbols can be either 0.1 or 1, and four different symbol patterns are possible over a 3-tone Multitone ASK signal. These different patterns are divided between two cases of symbol streams, $[0.1~l_{s_{2}}]$ and $[1~l_{s_{2}}]$ . The symbol $l_{s_{2}}$ transmitted over the third tone $f_{3}$ can switch between 0.1 and 1. It can be seen that although the transmitted signal average power, $P_{\mathrm {avg}}$ increases with the changing symbol $l_{s_{2}}$ from 0.1 to 1, the magnitude of the first baseband tone reduces.

FIGURE 3.

Magnitude variation of first baseband tone ($\Delta f_{1}=1$ MHz) for Multitone ASK centred around 2.45 GHz with $N=3$ , $L=2$ , and $l_{\min }=0.1$ for different information symbol patterns over multitone streams by varying symbol $l_{s_{2}}$ .

Fig. 4 and Fig. 5 illustrate the magnitude behavior of the relevant two baseband tones carrying information at $\Delta f_{1}=1$ MHz and $\Delta f_{2}=2$ MHz, respectively, for a 3-tone Multitone ASK signal with a modulation order of $L=4$ and $l_{\min }=0.1$ . Here, the 16 possible symbol patterns are divided among four cases. For example, the blue curve $[0.1~l_{s_{2}}]$ represents the multitone streams with a constant transmitted symbol $l_{s_{1}}$ as 0.1 over $f_{2}$ and varying the transmitted symbol level $l_{s_{2}}$ over $f_{3}$ among 0.1, 0.4, 0.7, and 1. Similarly, other cases are simulated where $l_{s_{1}}$ are considered constant as $[{0.4}]$ , $[{0.7}]$ , and [1] and only $l_{s_{2}}$ is varied. From Fig. 4, it can be seen that the magnitude of baseband tone at 1 MHz ($\Delta f_{1}$ ) reduces for the multitone streams when the symbol $l_{s_{2}}$ over the third transmitted tone $f_{3}$ increases in the order of 0.1, 0.4, 0.7, and 1 despite the increase in transmitted signal average power from (4).

FIGURE 4.

Magnitude variation of first baseband tone ($\Delta f_{1}=1$ MHz) for Multitone ASK centred around 2.45 GHz with $N=3$ , $L=4$ , and $l_{\min }=0.1$ for different information symbol patterns over multitone streams by varying symbol $l_{s_{2}}$ .

FIGURE 5.

Magnitude variation of second baseband tone ($\Delta f_{2}=2$ MHz) for Multitone ASK centred around 2.45 GHz with $N=3$ , $L=4$ , and $l_{\min }=0.1$ for different information symbol patterns over multitone streams by varying symbol $l_{s_{2}}$ .

However, the magnitude of the baseband tone $\Delta f_{2}$ at 2 MHz increases with the increasing symbol level of $l_{s_{2}}$ as seen in Fig. 5 for all cases of transmitted multitone streams. It shows that the different baseband tones undergo different variations when the overall average power of the transmitted signal changes while the transmitted symbols change. Therefore, a comparison of the obtained magnitude levels of the baseband tones at the rectifier output for the different transmitted symbol streams having different transmitted average power is not feasible due to the non-linearity of the rectifier. The baseband tones at the output reflect the changes in the symbol amplitudes only when the transmitted symbols result in the multitone streams having the same average signal power, $P_{\mathrm {avg}}$ .

SECTION III. Amplitude Levels Distribution and PAPR

In the proposed Multitone ASK transmission scheme, the information is being transmitted through the varying amplitudes of tones. The reference multitone signal $r(t)$ is changed to Multitone ASK signal $x(t)$ by varying the amplitudes as in (2) to make the SWIPT transfer feasible. The average power $P_{\mathrm {in}}$ of the reference signal $r(t)$ is reduced to average signal power $P_{\mathrm {avg}}$ for $x(t)$ . $P_{\mathrm {avg}}$ depends upon the magnitudes of the transmitted information symbols from (4). Therefore, it is important to analyze the effect of tones’s varying amplitudes on the WIT and WPT performances of the SWIPT system. PAPR is one such merit in analyzing the signal’s WPT performance. From the WPT perspective, a multitone without the information would result in the highest PAPR. However, varying tones’ amplitudes provide the benefit of WIT in addition to WPT.

PAPR for a signal $x(t)$ can be represented by\begin{equation*} \textrm {PAPR}=\frac {P_{\mathrm {peak}}}{P_{\mathrm {avg}}}=\frac {\max \{|x(t)|^{2}\}}{\frac {1}{T}\int _{-T/2}^{T/2}x^{2}(t)dt}, \tag {15}\end{equation*} where T denotes the time-period of waveform $x(t)$ . The peak power of the Multitone ASK signal in (2) can be represented as\begin{equation*} P_{\mathrm {peak}}=\frac {2P_{\mathrm {in}}}{N}\left |{{\sqrt {l_{s_{0}}}+\sqrt {l_{s_{1}}}+\sqrt {l_{s_{2}}}+\cdots +\sqrt {l_{s_{N-1}}}}}\right |^{2}. \tag {16}\end{equation*}

From (15), (16), and (4), PAPR of a Multitone ASK signal can be represented in terms of transmitted information symbols levels $l_{s_{i}}$ s as\begin{equation*} \textrm {PAPR}=\frac {2\left |{{\sum _{i=1}^{N} \sqrt {l_{s_{i-1}}}}}\right |^{2}}{\sum _{i=1}^{N} l_{s_{i-1}}}. \tag {17}\end{equation*} By keeping the first tone’s power level constant, i.e., $l_{s_{0}}=1$ , the PAPR of a Multitone ASK signal would be\begin{equation*} \textrm {PAPR}=\frac {2\left |{{1+\sqrt {l_{s_{1}}}+\sqrt {l_{s_{2}}}+\cdots +\sqrt {l_{s_{N-1}}}}}\right |^{2}}{1+l_{s_{1}}+l_{s_{2}}+\cdots +l_{s_{N-1}}}. \tag {18}\end{equation*}

For all symbols having equal probability of transmission, the mean PAPR across multitone streams, ${\textrm {PAPR}|}_{\mathrm {mean}}$ , having transmission of different combinations of information symbols can be represented by\begin{equation*} {\textrm {PAPR}|}_{\mathrm {mean}}=\frac {2\left |{{1+(N-1)\frac {1}{L}\sum _{i=1}^{L} \sqrt {l_{i}}}}\right |^{2}}{1+(N-1)\frac {1}{L}\sum _{i=1}^{L} l_{i}}. \tag {19}\end{equation*} From (19), it can be seen that a maximum PAPR of $2N$ can be achieved when all the transmitted symbols are chosen as the highest available information level,\begin{equation*} {\textrm {PAPR}|}_{\max }={\textrm {PAPR}|}_{l_{i}=1}=2N. \tag {20}\end{equation*}

Similarly, signal PAPR would be lowest when the transmitted symbols are chosen as the lowest available information level, $l_{\min }$ ,\begin{equation*} {\textrm {PAPR}|}_{\min }=\frac {2|1+(N-1)\sqrt {l_{\min }}|^{2}}{1+(N-1)l_{\min }}. \tag {21}\end{equation*}

Symbol levels are distributed between $l_{\min }$ and $l_{\max }=1$ . Therefore, it is important to analyze the effect of the chosen $l_{\min }$ over the WPT and WIT performance. For linearly distributed information symbols defined in (11), (19) can be approximated as\begin{equation*} \textrm {PAPR}=\frac {\left |{{1+\frac {2(N-1)(L-1)}{3L(1-l_{\min })}\left ({{1+\left ({{\frac {L-l_{\min }}{L-1}}}\right )^{3/2}}}\right )}}\right |^{2}}{1+(N-1)\left ({{\frac {1+l_{\min }}{2}}}\right )}. \tag {22}\end{equation*}

Fig. 6 illustrates the analytical mean PAPR variation of 100 streams of 6-tone Multitone ASK signal with increasing $l_{\min }$ by (22) for multiple modulation orders. It can be seen that as the minimum assigned level to a symbol is increased, PAPR increases, and after a certain level, PAPR converges to the maximum attained value of $2N$ , similar to the case of a signal having all tones of equal power with the average signal power of $P_{\mathrm {in}}$ [22], [32]. Further, simulated PAPR variation of 6-tone Multitone ASK with $l_{\min }$ for 100 multitone streams is shown in Fig. 7. Fig. 7 illustrates that as $l_{\min }$ is increased PAPR is also increased, which indicates that the WPT performance of the signal is also improved. However, from a WIT perspective, this would minimize the difference between the received symbols’ magnitude over the output baseband tones worsening the WIT performance.

FIGURE 6.

Analytical PAPR for Multitone ASK centred around 2.45 GHz with $N=6$ and linearly distributed amplitudes with variation in $l_{\min }$ .

FIGURE 7.

Simulated PAPR for Multitone ASK centred around 2.45 GHz with $N=6$ and linearly distributed amplitudes with variation in $l_{\min }$ for 100 multitone streams.

Also, it can be seen from Fig. 6 and Fig. 7 that as the modulation order L is increased, PAPR increases which implies that having a larger modulation order benefits the WPT performance. However, with the larger modulation order, L, it would be difficult to distinguish the different symbol levels. Therefore, there exists a trade-off for $l_{\min }$ selection as well as L selection for designing a Multitone ASK signal from WPT and WIT perspective for SWIPT operation.

Due to the presence of non-linearity in the rectifier, it is important to analyze the effect of non-linearly distributed amplitudes between $l_{\min }$ and $l_{\max }$ on the WPT and WIT performances. Let ${gf}_{\exp }$ be the growth factor for exponentially distributed amplitude levels for modulation order L which can be represented as\begin{equation*} gf_{\exp }=(l_{\max }/l_{\min })^{1/(L-1)}. \tag {23}\end{equation*} Therefore, exponentially distributed amplitude levels $l_{i}|_{\exp }$ can be defined as\begin{equation*} {l_{i}|}_{\exp }=l_{\min }{gf}_{\exp }^{(i-1)}, \hskip 1 pc \forall \hskip 1 pc {i=1,2,\ldots , L}. \tag {24}\end{equation*}

Similarly, for a logarithmically growth factor ${gf}_{\log }$ , logarithmically distributed amplitude levels ${l_{i}|}_{\log }$ can be defined as\begin{align*} {l_{i}|}_{\log }& =\log _{{gf}_{\log }}\left ({{{gf}_{\log }^{l_{\min }}+\left ({{i-1}}\right )\left ({{\frac {{gf}_{\log }^{l_{\max }}-{gf}_{\log }^{l_{\min }}}{L-1}}}\right )}}\right ), \\ & \qquad \quad \forall \hskip 1 pc {i=1,2,\ldots , L}. \tag {25}\end{align*}

Linearly distributed, exponentially distributed, and logarithmically distributed symbol levels between $l_{\min }=0.1$ and $l_{\max }=1$ for $L=4$ are shown in Fig. 8. PAPR for exponential and logarithmically distributed amplitude levels, $\textrm {PAPR}_{\exp }$ and $\textrm {PAPR}_{\log }$ are shown in Fig. 9 and Fig. 10, respectively. It can be observed that exponentially distributed amplitude levels result in the lowest PAPR whereas logarithmically distributed amplitude levels result in the highest PAPR for a particular $l_{\min }$ .\begin{equation*} \textrm {PAPR}_{\exp } \lt \textrm {PAPR}_{\mathrm {linear}} \lt \textrm {PAPR}_{\log } \tag {26}\end{equation*} The reason for this is the resulting average Multitone ASK signal average power which is higher for the logarithmic distributed levels compared to linearly distributed levels whereas exponential distributed symbol levels result in the Multitone ASK signals with a lower average power. A comparison of 6-tone Multitone ASK signal PAPR for different distributions of information symbol levels with $L=4$ are shown in Fig. 11. It can be seen that logarithmic amplitude level distribution is beneficial compared to linearly distributed amplitudes from WPT perspective.

FIGURE 8.

Linearly distributed, exponentially distributed, and logarithmically distributed symbols with $gf=10$ for $l_{\min }=0.1$ and $L=4$ .

FIGURE 9.

PAPR for Multitone ASK centred around 2.45 GHz with $N=6$ and exponentially distributed amplitudes with variation in $l_{\min }$ for 100 multitone streams.

FIGURE 10.

PAPR for 6-tone Multitone ASK centred around 2.45 GHz with logarithmic amplitudes ($gf=10$ ) with variation in $l_{\min }$ for 100 multitone streams.

FIGURE 11.

PAPR for 6-tone Multitone ASK centered around 2.45 GHz with linearly distributed, exponentially distributed, and logarithmically distributed levels ($gf=10$ ) with variation in $l_{\min }$ and $L=4$ for 100 multitone streams.

However, WIT performance would be worse for logarithmically distributed levels compared to linearly distributed levels. This can be observed from the analysis of the magnitude of the obtained baseband output tones at the rectifier output when transmitted symbols levels are logarithmically distributed in Fig. 12, Fig. 13, and Fig. 14. Fig. 12 illustrates the behavior of output baseband tone $\Delta f_{1}$ for the 3-tone Multitone ASK signal for $L=2$ and $l_{\min }=0.1$ . As $L=2$ , there are only two possible symbols 0.1 and 1 which is similar to the case of linear distribution in Fig. 3. Therefore, for the modulation order L of 2, symbol distribution does not provide any advantage and the only way to increase the WPT performance is to increase $l_{\min }$ .

FIGURE 12.

Magnitude variation of first baseband tone ($\Delta f_{1}=1$ MHz) for Multitone ASK centred around 2.45 GHz with $N=3$ , $L=2$ , and $l_{\min }=0.1$ for different patterns of logarithmically distributed information symbol over multitone streams by varying symbol $l_{s_{2}}$ .

FIGURE 13.

Magnitude variation of first baseband tone ($\Delta f_{1}=1$ MHz) for Multitone ASK centred around 2.45 GHz with $N=3$ , $L=4$ , and $l_{\min }=0.1$ for different patterns of logarithmically distributed information symbol over multitone streams by varying symbol $l_{s_{2}}$ .

FIGURE 14.

Magnitude variation of second baseband tone ($\Delta f_{2}=2$ MHz) for Multitone ASK centred around 2.45 GHz with $N=3$ , $L=2$ , and $l_{\min }=0.1$ for different patterns of logarithmically distributed information symbol over multitone streams by varying symbol $l_{s_{2}}$ .

Fig. 13 and Fig. 14 shows the magnitudes of $\Delta f_{1}$ and $\Delta f_{2}$ , respectively, for the 3-tone Multitone ASK signal for $L=4$ and $l_{\min }=0.1$ . It can be seen that the magnitude of output baseband tones gets compressed when higher symbol levels are transmitted, compared to the linear distribution case of Fig. 4 and Fig. 5. This results in lower WIT performance compared to the case of symbols’ linear distribution. Therefore, there exists a trade-off between WIT performance and WPT performance for the selection of the transmitted symbol distribution.

SWIPT system with desired WIT and WPT performances can be designed by an appropriate selection of minimum symbol level $l_{\min }$ and symbol distribution. If WIT performance is of more importance, lower $l_{\min }$ can be chosen while optimizing the symbol distribution for the required WPT performance. On the other hand, if WPT performance is of more importance, higher $l_{\min }$ can be chosen to the maximum WPT performance of the receiver.

SECTION IV. Performance Analysis of Multitone ASK

This section investigates the SWIPT performance of the designed Multitone ASK transmission scheme. To do this, the WPT and WIT performances are investigated using PCE and BER performance metrics. WPT and WIT performances of the designed Multitone ASK signal are evaluated on an information-energy rectifier-receiver model. The rectifier-receiver model consists of the input matching network with stubs and an input capacitance, a voltage doubler with two Skyworks SMS7630-079LF Schottky diodes, and an RC-LPF with an output capacitance and output load $R_{\mathrm {load}}$ . The model, implemented in Keysight ADS, corresponds to the physical design reported in [27], in which this rectifier model has been verified with measurements. In this paper, all Multitone ASK results are obtained by interfacing MATLAB with this Keysight ADS rectifier receiver model to have simulation results close to measurements.

Multitone ASK tone frequencies are selected as discussed in [27]. For example, tone frequencies for a multitone signal centered around 2.45 GHz results in 2.446 GHz, 2.447 GHz, 2.449 GHz, and 2.453 GHz for $N=4$ and greatest-common-divisor $\textrm {GCD}=1$ MHz from [27]. Figure 15 illustrates the 4-tone Multitone ASK waveform $x(t)$ centered around 2.45 GHz having all tones power equal and maximum for a data transfer of $[{1~0~1~0~1~0}]$ at $P_{\mathrm {in}}=0$ dBm. The symbol encoding is performed by gray coding for a minimal bit error [33]. Therefore, tones carry the information symbols $l_{s_{1}}$ , $l_{s_{2}}$ , and $l_{s_{3}}$ as the maximum $[{1~1~1}]$ . In such a case, Multitone ASK carries a maximum transmitted average signal power of $P_{\mathrm {in}}$ . Multitone ASK waveform with transmitted symbols of maximum level $l_{\max }$ result in Fig. 15 regardless of the symbol distribution.

FIGURE 15.

4-tone Multitone ASK waveform $x(t)$ centred around 2.45 GHz having all tones power equal and maximum for a data transfer of $[{1~0~1~0~1~0}]$ .

Fig. 16 illustrates the 4-tone Multitone ASK waveform when six information bits $[{0~0~0~0~0~0}]$ are transferred over the multitone stream with $l_{\min }=0.1$ and $L=4$ . As the transmitted symbols for this case are $[{0.1~0.1~0.1}]$ , i.e., three transmitted symbols are lowest amplitude level $l_{1}=0.1$ , the transmitted average signal power $P_{\mathrm {avg}}$ is the lowest, which is also represented in (9) by $P_{\mathrm {avg,min}}$ . Fig 17 shows the Multitone ASK for the same $[{0~0~0~0~0~0}]$ information stream with the increased minimum symbol level $l_{\min }=0.5$ . As can be seen, it carries a higher average signal power in comparison to Fig. 16, which would be helpful from WPT perspective.

FIGURE 16.

4-tone Multitone ASK waveform $x(t)$ centred around 2.45 GHz for $l_{\min }=0.1$ and $L=4$ for a data transfer of $[{0~0~0~0~0~0}]$ .

FIGURE 17.

4-tone Multitone ASK waveform $x(t)$ centred around 2.45 GHz for $l_{\min }=0.5$ and $L=4$ for a data transfer of $[{0~0~0~0~0~0}]$ .

Further, transmitted 4-tone Multitone ASK waveform $x(t)$ for a data transfer of $[{0~0~1~1~0~1}]$ is shown in Fig. 18 with the corresponding $l_{s_{i}}$ s as $[{0.1~0.7~0.4}]$ with $L=4$ , $l_{\min }=0.1$ , and $P_{\mathrm {in}}=0$ dBm. Similarly, a Multitone ASK waveform with a larger number of tones $N=6$ carrying a higher number of 10 information bits $[{0~1~1~1~1~0~1~0~1~0}]$ is shown in Fig. 19 for $L=4$ , $l_{\min }=0.3$ , and $P_{\mathrm {in}}=0$ dBm. Hundreds of such multitone streams are transmitted to evaluate WPT and WIT performances for a particular minimum symbol level $l_{\min }$ , the number of tones N, and input power $P_{\mathrm {in}}$ by varying the tones’ amplitudes according to the transmitted information patterns.

FIGURE 18.

4-tone Multitone ASK waveform $x(t)$ centred around 2.45 GHz for $l_{\min }=0.1$ and $L=4$ for a data transfer of $[{0~0~1~1~0~1}]$ .

FIGURE 19.

6-tone Multitone ASK waveform $x(t)$ centred around 2.45 GHz for $l_{\min }=0.3$ and $L=4$ for a data transfer of $[{0~1~1~1~1~0~1~0~1~0}]$ .

PCE of the obtained time-domain output waveform $y(t)$ in terms of $P_{\mathrm {avg}}$ , received output dc power $y_{\mathrm {dc}}$ , and output load $R_{\mathrm {load}}$ of RC-LPF can be represented as\begin{equation*} \textrm {PCE}=\frac {|y_{\mathrm {dc}}|^{2}/R_{\mathrm {load}}}{P_{\mathrm {avg}}}\times 100. \tag {27}\end{equation*}

Fig. 20 shows the achieved simulated PCE for 4-tone Multitone ASK transmission signals with $L=4$ and multiple cases of the minimum information level $l_{\min }$ of 0.1, 0.3, 0.5, and 0.7. Here, PCE is analyzed for 600 Multitone ASK streams, i.e., for a data transfer of 3600 bits. It can be observed that PCE is maximum when no information is being transferred over a multitone signal, i.e., when the signal is solely being used for WPT transfer. The input power levels $P_{\mathrm {in}}$ are considered to be in the range of −20 dBm to 10 dBm. For a 4-tone Multitone ASK with $P_{\mathrm {in}}=0$ dBm, an output power of −4 dBm is received when no information is being transferred. PCE further reduces with the inclusion of WIT transmission according to the selected $l_{\min }$ level. For $P_{\mathrm {in}}=0$ dBm and $l_{\min }=0.5$ , an output power of −4.33 dBm is received. Therefore, a full SWIPT operation with the inclusion of WIT transfer in addition to WPT transfer reduces the overall system PCE. However, a full SWIPT communication provides an additional advantage of data transfer over the same transmitted communication signal while extracting the signal power for signal processing usages at the receiver.

FIGURE 20.

PCE for 4-tone Multitone ASK centred around 2.45 GHz with $L=4$ for 600 multitone streams, i.e., 3600 bits data transfer for $l_{\min }=0.1$ , $l_{\min }=0.3$ , $l_{\min }=0.5$ , and $l_{\min }=0.7$ .

From Fig. 20, it can be seen that as $l_{\min }$ increases from 0.1 to 0.7, PCE increases towards the maximum attainable levels. This is due to the increment of the average signal power of the Multitone ASK signal as well as the increment in PAPR levels as discussed in Section II and Section III. PCE variation for 4-tone Multitone ASK for $L=4$ and $P_{\mathrm {in}}=0$ dBm with the increase in minimum symbol level $l_{\min }$ is also shown in Fig. 21 where PCE is increasing linearly with the increase in the minimum symbol level. Therefore, the system WPT performance can be increased by choosing an increased minimum symbol level $l_{\min }$ .

FIGURE 21.

PCE for 4-tone Multitone ASK centred around 2.45 GHz with $L=4$ and $P_{\mathrm {in}}=0$ dBm for 600 multitone streams, i.e., 1800 symbols with the variation in $l_{\min }$ .

PCE for Multitone ASK signal consisting of different numbers of tones is shown in Fig. 22. Multitone ASK signals with minimum symbol levels of $l_{\min }=0.1$ and $L=4$ with the 600 multitone streams transmission of 3-tones, 4-tones, and 6-tones are compared. It can be observed that PCE reduces slightly with the increase in the number of tones. This is due to the LPF at the rectifier output. With the increase in the number of tones, now the relevant baseband tones at the output lie in a wider band. Therefore, the relevant tones for Multitone ASK having a higher number of tones face higher attenuation due to the output bandwidth. PCE reduces slightly by around 2.5% from $N=3$ to $N=6$ . Therefore, to operate a Multitone ASK signal with a larger number of tones for higher throughput, it is required to design the rectifier with a larger output bandwidth.

FIGURE 22.

PCE for Multitone ASK centred around 2.45 GHz with $l_{\min }=0.1$ and $L=4$ for 600 multitone streams for $N=3$ , $N=4$ , and $N=6$ .

To analyze WIT performance, BER is calculated from the rectified output $y(t)$ . Obtained magnitudes of relevant baseband tones are analyzed. For example, for a 4-tone Multitone ASK signal having tones at 2.446 GHz, 2.447 GHz, 2.449 GHz, and 2.453 GHz centred around 2.45 GHz, the relevant baseband tones containing the transmitted information will be present at 1 MHz, 2 MHz, and 4 MHz and for a 6-tone Multitone ASK signal, the relevant baseband tones containing the transmitted information will be present at 1 MHz, 2 MHz, 4 MHz, 5 MHz, and 8 MHz.

Fig. 23 illustrates the BER for 4-tone and 6-tone Multitone ASK signals with a modulation order of $L=4$ and minimum symbol level $l_{\min }=0.1$ by transmitting hundreds of information streams. It can be seen that BER increases with an increase in input power, and the increase in BER becomes significantly higher for power levels larger than 0 dBm. The reason for this is amplitude-to-amplitude (AM-AM) distortion due to the nonlinearity of the rectifier circuitry. However, the focus of SWIPT applications is more on lower-power regions for low-power IoT devices for which our transmission scheme works properly. To further enhance the performance, encoding schemes and pre-compensation techniques at the transmitter can be utilized.

FIGURE 23.

BER for Multitone ASK centred around 2.45 GHz with $N=6$ , $l_{\min }=0.1$ , and $L=4$ for 600 multitone streams, i.e., 3000 symbols.

From Fig. 23, it can also be observed that BER increases significantly from 4-tone Multitone ASK to 6-tone Multitone ASK. For a 4-tone signal, it is possible to have a good WIT performance with a negligible BER in the desired power region ($P_{\mathrm {in}}\lt 0$ dBm), and it increases significantly above 0 dBm. For $N=6$ , larger BER is observed even for lower input power regions. The reason for this is the output bandwidth of the rectifier, which distorts the now wider desired baseband tones compared to a few narrower baseband tones for Multitone ASK with a smaller number of tones.

In the paper, the trade-off between WPT and WIT performances is discussed in terms of various parameters, such as allocated minimum symbol level $l_{\min }$ , symbol distribution, modulation order L, number of tones N. This trade-off can be utilized according to the low-power sensor application being used. For example, if the low-power sensor is not communicating the data and is sitting idle, this time can be utilized to charge the sensor fully. In the case of Multitone ASK, this can be done by raising the minimum symbol level $l_{\min }$ . On the other hand, if the low-power sensor is transmitting crucial data, then WIT performance is of main concern. In this case, a lower level of $l_{\min }$ is used. Both WPT and WIT can be achieved simultaneously. However, boundary conditions for the operation would depend upon the low-power sensor application requirements.

SECTION V. Conclusion

In this paper, a novel Multitone ASK transmission scheme for an integrated information and energy receiver SWIPT architecture has been proposed. The main advantage is the reduction in power consumption at the receiver by removing the local oscillator, which results in overall increased power performance. Information is embedded by varying the tones’ power levels of the multitone signal. The data rate is increased by transmitting $(N-1)$ symbols over a single N-tone Multitone ASK signal stream. The effect of varying average power of transmitted signal with the varying information patterns is evaluated. The WPT and WIT performances of the proposed transmission scheme are analyzed in terms of PCE and BER, respectively, and a trade-off between WPT and WIT performances is discussed. WPT performance of the designed transmitted signal has been shown to improve with increasing the minimum level of the symbols, which has approached the maximum power efficiency of the designed rectifier. Although logarithmically distributed symbols have been shown to improve WPT compared to linearly distributed symbols in terms of signal PAPR due to the non-linearity of the rectifier circuitry, linearly distributed symbols result in better WIT performance. It is possible to attain a very low bit error rate with a low transmitted signal power.

Practical WSNs consist of various sensors communicating with each other simultaneously. In the future, transmission schemes need to be utilized to meet the different energy and information demands of multiple heterogeneous IoT devices. A hybrid of various transmission schemes can be designed for multimode receivers according to the power and information requirements of the IoT devices and their application.