Ultra-wide band energy harvesting for ultra-low power electronics applications

Received Jul 19, 2020 Revised Sep 9, 2020 Accepted Oct 1, 2020 In this work, the feasibility of energy harvesting in the useful UWB band (i.e., 3.1-10.6 GHz) is analytically investigated. A typical UWB communications/EH chain in this band is modeled and analyzed, considering the spectral constraints imposed by the federal communications commission (FCC) to UWB signaling. Based on the developed model, accurate analytical expressions are derived for the average received powers of two common types of impulse radio UWB (IR-UWB) signaling waveforms. Numerical simulations on the system-level show excellent agreement with the obtained analytical expressions. Moreover, the DC power levels expected from spectrally constrained IR-UWB waveforms are extremely low (less than 0.3 microwatt) and, accordingly, provide useful guidelines for the design and development of ULP electronics applications in the sub-microwatt range.

ISSN: 2088-8708  Ultra-wide band energy harvesting for ultra-low power electronics applications (Nasr Rashid) 1159 than 10 GHz. Such designs are very favorable for EH from different signals occupying different frequency bands of the spectrum, including UWB signals. From the afore-mentioned overview, it is clear that, the majority of the studies reported on the design and development of wide/narrow band energy harvesting rectennas have competed to demonstrate their individual capabilities in terms of the RF-to-DC conversion efficiency. However, according to [10], the RF-to-DC conversion efficiency of a rectenna is, in general, not only a function of the rectenna design, but also of its input waveform. Therefore, in another category of studies reported on RF EH, the signaling waveforms carrying this RF energy have been considered. For different RF waveforms having the same power level, the harvested DC power levels are strongly dependent on the particular RF signaling waveform and some of its time domain characteristics such as the highly desirable peak-to-average-power-ratio (PAPR) [11]. Fortunately, the interests in developing broad band energy harvesters to collect RF energy from high PAPR signals perfectly matches the temporal as well as the spectral characteristics of impulse radio-UWB (IR-UWB) waveforms. Despite the severe spectral constraints imposed by the Federal Communications Commission (FCC) to their spectra (less than -41.3 dBm/MHz), IR-UWB signals are allowed to occupy a bandwidth as large as 7.5 GHz (i.e., 3.1 GHz -10.6 GHz) [12], commonly called the useful UWB band. Moreover, in IR-UWB signaling, the energies of IR-UWB signals are emitted in the form of transient bursts of very short duration (typically, ns or ps) and large voltage amplitudes (compared to the DC levels of IR-UWB waveforms). Meanwhile, due to the poor radiation efficiency of UWB antennas at low frequencies (below 1 GHz), the radiated IR-UWB signals often possess DC-null components [13]. This results in IR-UWB signals with high PAPR levels. To the best of the authors' knowledge, no study has yet been reported to assess the maximum DC power levels that can be extracted from these signals. In this paper, a systemlevel abstraction approach is adopted to evaluate the maximum DC power levels expected from IR-UWB signals under the FCC spectral constraints, regardless of the specific realization of the EH circuit/system. Under this assumption, the calculated DC power levels are guaranteed to be the maximum achievable levels, regardless of the detailed architecture of the EH circuit and/or its RF-to-DC conversion efficiency.
The rest of this paper is organized as follows. A UWB communications/EH chain is described and is modeled in Section 2, considering typical IR-UWB signaling waveforms. In section 3, analytical expressions for the average DC powers harvested from the considered waveform types are developed. The developed expressions are then numerically evaluated and are analyzed in section 4. Based on the obtained results, the whole work provided in this paper is finally concluded in section 5. Figure 1 illustrates the block diagram of a typical IR-UWB signaling/EH chain, inspired from the models provided in [4]. Generally, it consists of an IR-UWB transmitter and an UWB energy harvester at the receiver side, each equipped with a broadband UWB antenna. At the transmitter side, an information source emits a stream of M−ary encoded symbols. Moreover, it is assumed that, the information source and its associated resistance, denoted by Rs, model all signal processing functions that precede the TX antenna. Furthermore, the source resistance Rs is assumed to be matched to the input impedance of the TX antenna. Each of the emitted symbols is assumed to be simultaneously encoded by the pulse amplitude modulation (PAM) and the pulse position modulation (PPM) schemes. Each of the PAM/PPM modulated symbols is further encoded by an IR-UWB signaling waveform, denoted by ( ) t  , assigned to each symbol. The waveform stream at Point B in Figure 1 is expressed as follows:

UWB SIGNALLING/ENERGY HARVESTING MODEL
where  is a log-normal random variable that models the line-of-sight (LoS) path loss of the UWB channel, L is the number of observed clusters, K is the number of rays received within the th l cluster, , l k  is the coefficient of the th k multipath contribution of th l cluster, l T is the time of arrival of the th l cluster, and , l k  the delay of the th k ray within the th l cluster, calculated with respect to l T . The path loss variable  is given by , where T G and R G are the gains of the Tx and the Rx UWB antennas, respectively, c=3×10 8 m/s is the speed of light in free space, D is the Tx-Rx antenna separation (in meters),  is the path loss exponent, and f is the frequency at which the path loss is evaluated. It is important to highlight that T G and R G account for the radiation efficiency, polarization and the Ohmic losses exhibited by the antenna materials at the Tx and the Rx, respectively (Point B to Point C on Figure 1). The channel coefficient , is a discrete random variable that assumes values of 1  with equal probabilities, whereas , l k  is a Rayleigh distributed random variable that models the fading contribution of the th k ray in the th l cluster. The voltage waveform at the input of the Rx rectenna is given by: is the overall ray delay and ( ) is an additive white Gaussian noise (AWGN) process. In the following analysis, a high signalto-noise ratio (SNR) at the receiver front-end is assumed such that the AWGN term in (3) is negligible. This assumption is applicable to close proximity UWB systems where a high SNR is typically observed at the input of an UWB receiver. Moreover, a resolvable set of multipath components is assumed. This can be expressed mathematically as The received waveform is applied to the input of a matching network for maximum power transfer from the Rx antenna output to the input of a high speed full-wave rectifier (FWR)/voltage multiplier (VM). The output of the FWR/VM (Point D in Figure 1) is followed by a low-pass filter (LPF), such that the desired DC power of the received IR-UWB waveform is extracted at the LPF output. Without loss of generality, the FWR/VM applies the absolute value operator . to ( ), whereas the LPF is modeled by an ideal timedomain integrator. The DC power obtained at the LPF output is delivered to a load resistance of ; the Thevenin equivalent of the passive circuits and systems that follow the LPF. The load resistance is assumed to be matched to the output impedance of the rectenna configuration. Since a resolvable set of nonoverlapping multipath components is assumed, the extracted DC power of the received IR-UWB waveform is expressed as follows: the IR-UWB waveform and its associated parameters embedded in E  . In this work, the IR-UWB signaling waveforms; ( ) t  is assumed to be a time and/or amplitude scaled derivatives of a basis function, denoted by ( , ) t   where  is its temporal pulse shaping factor. This basis function is either a typical amplitude-scaled Gaussian pulse which, expressed as  is the Gaussian pulse width, or a typical amplitude-scaled hyperbolic secant (sech) pulse which is given by ( , ) sech( / ) where s  is the sech pulse width. The pulse shaping factor of ( , ) t   is defined as its full width at half maximum (FWHM) pulse width and is related to the Gaussian and sech pulse widths as / 2 log (2) g Consequently, the average DC power of the received IR-UWB waveform is expressed as follows: where m A is the amplitude of the un-modulated th m order IR-UWB waveform is the Fourier transform of ( ) ( , ) m t   ,  is the angular frequency and   .  denotes the Fourier transform operation. For simplicity, 1 L R   to ensure the generality of the conducted analysis and its independence of the particular system design specifications.

UWB-TO-DC ENERGY HARVESTING UNDER THE FCC SPECTRAL CONSTRAINTS
An IR-UWB signal is subject to power spectral density (PSD) constraints, denoted by ( ) FCC S  , imposed by the FCC on its effective isotropic radiated power (EIRP) [12]. Therefore, to maximize the DC power extracted from an IR-UWB signal, is to maximize its peak PSD by adapting m A to The FCC-compliant Fourier transform of the th m order Gaussian-based derivative is given by: where n denotes a normalized version of ( ) ( , ) where m s A is the normalization constant of the th m order derivative of a sech-based IR-UWB waveform.
Throughout the following analysis, m n FCC j   is given by either the definitions in (6) or (7) as required.
It is important to highlight that, the values of   (6) and (7) along with the FCC spectral constraints. A closer look at this figure reveals that, it is reasonable to employ IR-UWB signaling waveforms who's PSDs are mostly concentrated in the 3.1-10.6 GHz band, where most of the EIRP of a UWB signal is permitted. Consequently, the average received power in (5) is approximated as follows: , and L f and H f are the lower and the upper frequencies that determine the bandwidth over which the maximum FCC PSD is allowed. The DC power extracted from a Gaussian-based IR-UWB waveform at the LPF output is analytically obtained by substituting (6) in (8) as follows: and   Q u are the conventional Gamma function and the Gaussian Q -function, respectively. Similarly, the average received DC power of a sech-based IR-UWB waveform is obtained analytically by substituting (7) in (8) as follows: (a) (b) Figure 2. Spectra of (a) Gaussian-based IR-UWB waveforms and (b) sech-based IR-UWB waveforms

SIMULATION RESULTS AND ANALYSIS
In this section, the analytical expressions for the average received DC power predicted by (9) and (11) [12]. Throughout simulations, on-off keying (OOK) modulation is considered. The value of the relative time shift is set to zero. A pseudo-random binary sequence (PRBS) of 2 31 − 1 bits length is generated in MATLAB. Each of the generated symbols is encoded by an IR-UWB waveform using the values of the afore-mentioned parameters. For each pulse width, the duration of the waveform (symbol) is defined over a symbol duration that includes, at least, 90% of the waveform energy. A number of 100 realizations of the channel impulse response is generated. For each realization, the power of the received signal is evaluated. The calculated DC power levels are averaged over the number of realizations of the channel impulse response. Both Gaussian and sech-based monocycles outperform their corresponding higher order derivatives in terms of the maximum extractable DC powers. These observations recommend IR-UWB waveforms for energy harvesting applications that need sub-µWatt power levels [15].

POTENTIAL APPLICATION SCENARIOS
It should be highlited that, the particular application scenario to which an EH is integrable depends strongly on the power levels achievable from this EH. Table 1 [16] the lists a number of power resources from, including the UWB spectrum. Obviously, the power level expected from an IR-UWB EH is comparable to the range expected from an RF signal emitted by a building-top basestation employed for mobile services. This competitive performance is attributed to the huge bandwidth dedicated to these signals, which compensates the extremely low PSD limits imposed to UWB signals. Such kind of μ-power converters is highly recommended for microelectronic mechanical systems (MEMS) relying on the CMOS technology.  Table 1 and an effective antenna area of = 1 2 , results in a theoretically estimated spatial power density of = 0.3 / 2 . The hypothesized antenna size is comparable to many of the state-of-the-art antenna designs published on UWB energy harvesting [17][18][19][20][21][22][23][24][25]. Moreover, it is clear that the theoretically expected value of = 0.3 / 2 is comparable to the values listed in Table 1 for RF EH techniques, which are based on much narrower frequency bands and much larger antenna dimensions, accordingly.

CONCLUSION
This paper investigates the feasibility of energy harvesting in the useful ultrawide band of the spectrum (i.e., 3.1-10.6 GHz). Analytical expressions for the maximum DC power levels that can be extracted from these waveforms are derived. Simulation results indicate that energy harvesting in this band finds its best applications where there is a need for − power levels. These applications include, but are not limited to, micro-electro-mechanical systems (MEMS), especially robotic-based MEMS developed for in-body medical missions, where the accessibility to these nodes is essentially impossible after deployment. The reported analysis provides a good starting point for further theoretical and/or experimental investigations that consider specific realizations of ultrawide band communication/energy harvesting systems. Ongoing research on the realizability of UWB energy harvesters is being conducted in ordre to assess the feasibility of these techniqes for the recommended potential applications.