WO2020039163A1 - A method of inducing amplitude fluctuations in a wireless power transfer channel - Google Patents

Abstract

A method of wirelessly transmitting power from at least one transmit antenna for receiving by at least one rectenna in a Wireless Power Transfer (WPT) system is disclosed. The method comprises transmitting, by the at least one transmit antenna to at least one rectenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal at the at least one rectenna, wherein at least one of the plurality of RF signals has a time-varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal formed at the at least one rectenna, and wherein each of the plurality of RF signals has a common frequency.

Description

A method of inducing amplitude fluctuations in a wireless power transfer channel

Field

The present disclosure relates generally to Wireless Power transfer (WPT) and, in particular, to inducing fluctuations in the channel received by an energy harvester.

Background

Wireless Power Transfer (WPT) via radio-frequency radiation is nowadays regarded as a feasible technology for energising low-power devices in Internet-of-Things (loT) applications. The major challenge with WPT, and therefore any wireless power-based system such as Simultaneous Wireless Information and Power Transfer (SWIPT), Wirelessly Powered Communication Network (WPCN) and Wirelessly Powered Backscatter Communication (WPBC), is to find ways to increase the end-to-end power transfer efficiency, or equivalently the DC power level at the output of the rectenna for a given transmit power. To that end, the traditional line of research in the RF literature has been devoted to the design of efficient rectennas such as in [2], [3] More recently, various WPT signal strategies have been developed which attempt to boost the harvested DC power by modifying some aspect of the transmitted signal(s). However, each technique put forward so far has drawbacks.

A first proposed technique is to use beamforming so as to increase the RF input power to the energy harvester or equivalently increase the RF-to-RF transmission efficiency e_{r -r} [4] One common example of beamforming, multi-antenna beamforming, combines multiple signals to provide a directional aggregate signal and relies on acquiring channel state information at the transmitter (CSIT). Appropriate CSIT acquisition strategies specifically designed for WPT are set out in [5] Alternative techniques to multi-antenna beamforming, also enabling directional/energy focusing transmission, consist in time-modulated arrays and retrodirective arrays [3] and time-reversal techniques [6]

It will be appreciated that, as the complexity of the system grows and the number of signals being combined increases, the complexity of determining the CSIT increases significantly. Therefore, beamforming techniques can quickly become impractical and computationally expensive for WPT in systems having many devices, for example in internet of things (loT) systems. Additionally, because the conditions of transmission channels change at the millisecond level, devices that are moving must report at the millisecond level in order to maintain up-to-date CSIT. This is again computationally expensive and often requires pre-processing at various levels, meaning that beamforming is impractical for low power devices that lack the processing power to perform these steps.

A second proposed technique is to design the energy waveform of a transmitted WPT signal so as to exploit the nonlinearity of the energy harvester (typically a rectenna) and thereby increase the RF-to- DC conversion efficiency e_{r -dc}, as shown in [7] and [8] Waveforms can be designed with and without CSIT depending on the frequency selectivity of the channel. In frequency-selective channels, a channel-adaptive waveform exploits jointly the channel frequency selectivity and the energy harvester nonlinearity so as to maximize e_{r -r} x e_rf-dc. Waveforms can also be designed for a multiantenna transmitter so as to additionally exploit a beamforming gain [8], [9] Channel-adaptive waveforms rely on CSIT and therefore require appropriate channel acquisition strategies, suited for WPT with nonlinear energy harvesting [10]

Due to the harvester nonlinearity, the waveform design commonly results from a non-convex optimization problem, which is very computationally expensive to solve and therefore does not lend itself easily to implementation. While strategies to decrease the waveform design complexity have further appeared in [9], [11], [12], [13], such techniques nevertheless require each transmitted waveform to be designed which adds complexity. As in the case of beamforming techniques, this can again be a burden on low power devices such as those likely to be used in loT settings.

A third proposed technique is to design the energy modulation for single-carrier transmission so as to exploit the nonlinearity of the energy harvester and increase the RF-to-DC conversion efficiency e_rf-dc , as described in [14] and [15] Indeed, as explained in [13] and [16], modulated and deterministic signals do not lead to the same RF-to-DC conversion efficiency due to the energy harvester nonlinearity. However, a problem with such modulation-based techniques is that they lead to large amplitude fluctuations at the input of any power amplifiers used in the system, and therefore require complex and expensive amplifiers and hardware to be used.

It would be advantageous to provide methods and systems for WPT which address one or more of the above-described problems. In particular, it would be advantageous to provide WPT systems which do not require CSIT (in contrast to existing beamforming techniques), do not require complex input waveform design (in contrast to existing energy waveform design techniques) and do not require complex and expensive amplifiers and hardware to be used.

Summary

According to an aspect of the present disclosure, a method of wirelessly transmitting power from at least one transmit antenna suitable for receiving by at least one rectenna in a Wireless Power Transfer (WPT) system is disclosed. While the term“rectenna” is used throughout this disclosure, the rectenna can be considered more generally to be an energy harvester, and this applies wherever the term“rectenna” is used. The method comprises transmitting, by the at least one transmit antenna to at least one rectenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal received by the at least one rectenna. At least one of the plurality of RF signals has a time- varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal formed at the at least one rectenna, and each of the plurality of RF signals has a common frequency. As will be described in detail below, inducing fluctuations of the received combined signal or, in other words, of the transmission channel, increases the energy harvested by the energy harvester of the WPT system (typically a rectenna).

Each of the plurality of RF signals may have a different polarisation. In some arrangements, the transmitting may be by a single transmit antenna. Alternatively, the transmitting may be by a plurality of transmit antennas. As will be described below, using a plurality of transmit antennas has various advantages such as not needing to determine Channel State Information (CSI) for the system and not having to design complex input waveforms to the transmitters.

In arrangements using a plurality of transmit antennas, the plurality of transmit antennas may be colocated or distributed. "Co-located” in this context means that the transmit antennas are typically part of the same physical transmitter and/or are typically spaced apart distances equal to about half the wavelength of the signal being transmitted.“Distributed” in this context means that the transmit antennas typically belong to separate physical transmitters and/or are typically spaced apart by distances greater than half the wavelength of the signal being transmitted, and generally significantly greater than half the wavelength. For example, distributed transmit antennas may be spaced apart by greater than three times the wavelength.

In arrangements using a plurality of transmit antennas, each of the plurality of transmit antennas may transmit only at the common frequency. Each of the plurality of transmit antennas may transmit only a single RF signal at a time. Transmit antennas transmitting only at the common frequency and transmitting on a single RF signal at a time can be considered“dumb” antennas, and are

advantageously typically low in cost, power draw and implementation complexity.

In arrangements using a plurality of transmit antennas there may be M transmit antennas and the signal transmitted by each of the M transmit antennas may be given by:

where x_m(t ) is the signal transmitted by the mth transmit antenna,

P is a fixed total average transmit power across the M transmitters,

w₀ is the signal frequency,

t is time, and

xpm(t) is time varying phase of the signal transmitted by the mth transmit antenna.

The method may further comprise amplitude modulating the combined signal. As will be described below, this means the cost of power amplifiers (PA) used in the system can be balanced against the number of antennas. The amplitude modulating may comprise inducing, over time, fluctuations in the amplitude of the signal transmitted by each of the at least one transmit antennas. The induced fluctuations may be induced in a deterministic manner or in a randomized manner. The induced fluctuations may be induced in a deterministic manner by generating the input signal for each of the at least one transmit antennas such that the amplitude of the signal is specified based on a frequency response of the combined signal. Typically, signals in which randomized fluctuations have been induced will have a small probability of having a large amplitude. Inducing the fluctuations in a randomized manner may comprise inducing the fluctuations in a non-deterministic manner. In some arrangements, the randomized fluctuations may be generated using the pseudo-random outputs of a pseudo-random number generator.

According to a further aspect of the present disclosure, at least one transmit antenna for transmitting power to at least one rectenna in a Wireless Power Transfer (WPT) system is disclosed. The at least one transmit antenna comprises a processing environment configured to perform the method of any method set out herein.

According to a further aspect of the present disclosure, a method of wirelessly transmitting power from at least one transmit antenna to at least one rectenna in a Wireless Power Transfer (WPT) system is disclosed. The method comprises transmitting, by the at least one transmit antenna to the at least one rectenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal received by the at least one rectenna. At least one of the plurality of RF signals has a time- varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal received by the at least one rectenna, and each of the plurality of RF signals has a common frequency. The method further comprises receiving, by the at least one rectenna, the combined signal.

According to a further aspect of the present disclosure, a Wireless Power Transfer (WPT) system is disclosed. The WPT system comprises at least one transmit antenna and at least one rectenna, wherein the at least one transmit antenna and at least one rectenna are configured to perform the method of any method set out herein.

According to a further aspect of the present disclosure, a system comprising one or more transmitters is disclosed, each transmitter comprising at least one transmit antenna for transmitting power to at least one rectenna in a Wireless Power Transfer (WPT) system. The one or more transmitters are configured to transmit, by the at least one transmit antenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal at the at least one rectenna. At least one of the plurality of RF signals has a time-varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal formed at the at least one rectenna, and each of the plurality of RF signals has a common frequency. Brief description of figures

Figure 1 shows an exemplary antenna equivalent circuit (left) and an exemplary single diode rectifier (right) for use in a WPT system. In this arrangement, the rectifier comprises a non-linear device (diode) and a low-pass filter (consisting of a capacitor C and a load RL).

Figure 2 shows the general architecture of an exemplary WPT arrangement of the present disclosure, denoted“transmit diversity” , which comprises M dumb antennas. Signal s(t) is an energy

modulation/waveform.

Figure 3 shows signal gain G_td as a function of the number of transmit antennas M for the transmit diversity arrangement.

Figure 4 shows a rectenna with a single diode and an L-matching network used for circuit simulations to analyse the performance of the transmit diversity arrangement.

Figure 5a shows a curve fitting for input RF power range -40dBm to 20dBm, to be used in computing a nonlinear model of the rectenna. The second degree polynomial is characterized by a = -0.0977, b = -0.9151 , c = -11.1684. The first degree polynomial is characterized by a = 0, b = 0.8848, c = -4.6926.

Figure 5b shows a curve fitting for input RF power range -40dBm to -5dBm, to be used in computing a nonlinear model of the rectenna. The second degree polynomial is characterized by a = -0.0669, b = -0.1317, c = -6.3801. The first degree polynomial is characterized by a = 0, b = 1 .4848, c = 2.9250.

Figure 5c shows corresponding RF-to-DC conversion efficiency P_dc/P_rf , to be used in computing a nonlinear model of the rectenna.

Figure 6a shows a curve fitting for input RF power range -40dBm to 20dBm, to be used in computing a nonlinear model of the rectenna. The second degree polynomial is characterized by a = -0.1089, b = -1.1660, c = -12.0041. The first degree polynomial is characterized by a = 0, b = 0.8396, c = -4.7881.

Figure 6b shows a curve fitting for input RF power range -40dBm to -5dBm, to be used in computing a nonlinear model of the rectenna. The second degree polynomial is characterized by a = -0.1105, b = -1.1468, c = -11.4342. The first degree polynomial is characterized by a = 0, b = 1.5239, c = 3.9400.

Figure 6c shows corresponding RF-to-DC conversion efficiency P_dc/P_rf, to be used in computing a nonlinear model of the rectenna. Figure 7 shows modelled fading gain e_fading for the transmit diversity arrangement with a continuous wave ( N = 1) and multisine ( N = 8) excitation for an average RF input power Pr/ ranging from - 40dBm to -5dBm. The second degree polynomial fitting parameters used are taken from Fig. 5(b) and Fig. 6(b).

Figure 8 shows modelled RF-to-DC conversion efficiency without fading e_rf-dc and with fading e_rf-dc for the transmit diversity arrangement and for a continuous wave ( N = 1) and multisine ( N = 8) excitation in the average RF input power Prr range of -40dBm to -5dBm. The second degree polynomial fitting parameters used are taken from Fig. 5(b) and Fig. 6(b).

Figure 9 shows modelled transmit diversity gain e_td for the transmit diversity arrangement with a continuous wave ( N = 1) and multisine ( N = 8) excitation for an average RF input power Prr ranging from -40dBm to -5dBm. The second degree polynomial fitting parameters used are taken from Fig. 5(b) and Fig. 6(b).

Figure 10 shows modelled RF-to-DC conversion efficiency with one transmit antenna without fading e_rf-dc and with two antenna-transmit diversity e_{rf®c td} for a continuous wave ( N = 1) and multisine ( N = 8) in the average RF input power Prr range of -40dBm to -5dBm. The second degree polynomial fitting parameters used are taken from Fig. 5(b) and Fig. 6(b).

Figure 1 1 shows simulated transmit diversity gain e_td for the transmit diversity arrangement with a continuous wave ( N = 1) and multisine ( N = 8) for an average RF input power P_rr ranging from - 40dBm to 20dBm.

Figure 12 shows simulated RF-to-DC conversion efficiency with one transmit antenna without fading e_rf-dc and with two antenna-transmit diversity e_{rf®c td} for a continuous wave ( N = 1) and multisine ( N = 8) in the average RF input power P_rf range of -40dBm to 20dBm.

Figure 13 shows a rectenna with a single diode and an L-matching network suitable for use in a WPT system of the present disclosure.

Figure 14 shows an experimental setup used to assess the performance of the disclosed methods and arrangements, with an SDR (PXIe-7966R and Nl 5791 R) implementing the transmit diversity arrangement, two PAs linked to Tx antenna 1 and 2, and the Rx antenna connected to the rectifier.

Figure 15 shows measured harvested DC power with a continuous wave (CW), transmit diversity (M = 2) with continuous wave, multisine (N = 8) and transmit diversity with multisine ( N = 8), at distances of 2.5 m and 5 m from the transmitter. Figure 16 shows measured relative gain (in terms of harvested DC power) with transmit diversity (M = 2) with continuous wave, multisine ( N = 8) and transmit diversity with multisine N = 8) over a continuous wave (CW), at distances of 2.5 m and 5 m from the transmitter.

Detailed description

I. INTRODUCTION

The below detailed description sets out particular exemplary arrangements and methods for implementing the present disclosure. It will be appreciated that the arrangements and methods described below are to be considered in all respects only as illustrative and not restrictive. The scope of the present disclosure is set out by the claims, and it will be appreciated that various methods and arrangements not described below will nevertheless fall within the scope of the claims.

In the below detailed description, Section II introduces a physics-based diode nonlinear model of an energy harvester for use in a WPT system. Section III analyzes the impact of fading on harvested DC power in a WPT system. Section IV introduces a particular arrangement utilising multiple transmit antennas for WPT, referred to as“transmit diversity”, and analyzes its performance. Section V shows that transmit diversity can be combined with energy waveform and modulation to provide further performance benefits. Section VI revisits the impact of fading and transmit diversity using a curve fitting-based nonlinear model, in order to demonstrate that the obtained results are independent of the energy harvester model being employed. Section VII provides circuit simulation, prototyping and experimentation results, and Section VIII concludes the disclosure.

In view of the drawbacks of existing methods for WPT described above, three questions are considered herein: 1 . Is fading beneficial or detrimental to WPT? 2. Can diversity play a role in WPT? 3. Can multiple transmit antennas be useful to WPT in the absence of CSIT?

At first, if the energy harvester (typically a rectenna) is modelled in the traditional manner, using the so-called linear model, which assumes a constant RF-to-DC conversion efficiency independent of the harvester’s input signal (power and shape), maximizing the output DC power is equivalent to maximizing the average RF input power to the energy harvester, as described in [4] and [8] Since fading does not increase the average RF input power, we may be tempted, in view of these prior disclosures, to answer that fading does not impact the harvested DC power. Similarly, since multiple transmit antennas do not increase the average RF input power in the absence of CSIT, we may be tempted, in view of the previous disclosures, to answer that multiple antennas are useless in the absence of CSIT. Following the same line of thoughts prompted by previous disclosures, diversity would appear to be useless either since fading would not have any impact on the harvested DC performance. However, in this disclosure it is shown that on the contrary, as a consequence of the energy harvester nonlinearity, fading is in fact beneficial to the harvested DC power, multiple transmit antennas are useful even in the absence of CSIT and diversity has a role to play in WPT. These discoveries mark a significant departure from the prior art.

Notations; In this disclosure, scalars are denoted by italic letters. Boldface lower- and upper-case letters denote vectors and matrices, respectively j denotes the imaginary unit, i.e. , j² = -1.

£[ ] denotes statistical expectation and ¾{·} represents the real part of a complex number. |. land ||. || refer to the absolute value of a scalar and the 2-norm of a vector. In the context of random variables, i.i.d. stands for independent and identically distributed. The distribution of a Circularly Symmetric Complex Gaussian (CSCG) random variable with zero-mean and variance s2 is denoted by C (0, s2); hence with the real/imaginary part distributed as (0, s²/2). ~ stands for“distributed as” log is in N /

base e. means approximately equal as N grows large.

II.THE NONLINEAR RECTENNA MODEL

In the following, a rectenna model which takes into account the nonlinear characteristics of the rectenna is set out.

We assume the same rectenna model as in [8] The rectenna is made of an antenna and a rectifier. The antenna model reflects the power transfer from the antenna to the rectifier through the matching network. A lossless antenna is modelled as a voltage source v_s(t ) followed by a series resistance (assumed real for simplicity; a more general model can be found in [11]) R_ant - see Fig. 1 left hand side. Let Z_ln = R_ln + jX_ln denote the input impedance of the rectifier and the matching network. Let y(t) also denote the RF signal impinging on the receive antenna. Assuming perfect matching ( R_ln = R_an_t’ ^xin = 0), the available RF power ^prr is transferred to the rectifier and absorbed by R_ln, so that

also assume that the antenna noise is too small to be harvested.

We consider for simplicity a rectifier composed of a single diode followed by a low-pass filter with a load ( R_l ), as illustrated in Fig. 1 (right hand side). We consider this setup as it is the simplest rectifier configuration. Nevertheless the model presented in this subsection is not limited to a single series diode but also holds for more general rectifiers with many diodes, as, for example, shown in [11] Denote the voltage drop across the diode as v_d (t ) = v_ln(t) - v_out(t) where v_ln(t) is the input voltage to the diode and v_out(t) is the output voltage across the load resistor. A tractable behavioural diode model is obtained by Taylor series expansion of the diode characteristic function

with the reverse bias saturation current i_s, the thermal voltage v_t, the ideality factor n assumed to be equal to 1.05, around a quiescent operating point v_d(t ) = a. We have

The DC current delivered to the load and the harvested DC power are then given by i_ou_t E[i_d (t)] , P_dc i-_ou_tRi

(4) respectively.

We here assume a steady-state response and an ideal rectification. Namely the low pass filter is ideal such that v_out(t) is at constant DC level v_out (we drop the dependency on t). Similarly the output current is also at constant DC level i_out.

Note that the operator £[·] has the effect of taking the DC component of the diode current i_d t) but also averaging over the potential randomness carried by the input signal y(t) [13]

The classical linear model is obtained by truncating to the second order term. This is however inaccurate and inefficient as studied in numerous works [2], [8], [1 1 ], [13], [17] The nonlinearity of the rectifier is characterized by the fourth and higher order terms [8] Truncating the expansion to order 4 (and therefore accounting for the rectifier nonlinearity), we can write

iou_t ~ K + k₂'R_ant [y(t)²] + k₄R _ntE\y(t)⁴].

Following [8], i_out, and therefore ^R _dc are directly related to the quantity

Zac = k₂R_antE[y(t)²] + k₄R_a ² _ntE\y(t)⁴] (5) i = 2, 4 , assuming i_s = 5m^, a diode ideality factor n = 1.05 and v_t = 25.86mF ,

typical values are given by k₂ = 0.0034 and k₄ = 0.3829 [8] Hence, any increase in z_dc would lead to an increase in i_out and P_dc. III. EFFECT OF FADING ON HARVESTED ENERGY

Now that the nonlinear nature of the energy harvester has been modelled, the effect of fading on z_dc, and thus the output power at the energy harvester, is considered.. Fading can be considered as the variation or (amplitude) fluctuation in a transmission channel caused by attenuation and interference of the signals of the channel with the environment and one another.

In the field of communications, fading is a known problem which degrades performance and causes loss of signal power - see, for example, [1 ] However, as will be shown in detail in this section, the inventors have discovered that fading is in fact beneficial to transmission efficiency in WPT systems. This counterintuitive finding opens the door to the possibility of deliberately inducing fading-like effects in WPT transmission channels in order to improve WPT output voltages. One exemplary method of doing this is to use multiple antennas transmitting signals in such a manner that the signals interfere and cause fluctuations in the signal channel. Such an exemplary arrangement will be described below in relation to Section IV.

Turning back to the effect of fading on z_dc, we consider the simplest scenario of a transmitter with a single antenna whose transmit signal at time t is given by an unmodulated continuous-wave x(t ) = V P cos(w_Qt) = V2P¾{e^JWot}

(6) with w₀ the carrier frequency. The average transmit power is fixed to P, namely E [x(t)²] = P.

Denoting the wireless channel between the transmit and receive antenna as A^~1/2h with L the path loss and h the complex fading coefficient (it varies very slowly over time, hence we omit the time dependency), the received signal can be written as y(t) = J2P3i{A^~1/2he^1Wot}.

(7)

The RF received power (RF input power to the energy harvester) is given by

P_rf = E[y(t)²] = L ¹ \h\²P.

(8)

The average RF received power (average RF input power to the energy harvester), where the average is taken over the distribution of h, is given by

where we assume that the fading coefficient h is normalized such that E[|/i|²] = 1. Hence, fading does not change the RF input power to the energy harvester on average. Let us plug (7) in the rectenna model (5). We first consider the deterministic case where h does not change in time and is given by \h\² = 1. Recalling the analysis in [8], we can write

We now consider the same unmodulated continuous-wave transmission but over a fading channel, with h modelled as CSCG with E[|/i|²] = 1. According to [8], after taking the expectation over the fading process, we have

¾c,cw Eii [¾c,cw]>

because E[|/i|⁴] = 2. We note that the second order term has not changed between (10) and (11), while the fourth order term in the fading case is twice as large as in the deterministic case.

As can be seen, therefore, fading is beneficial in WPT if the rectifier nonlinearity is taken into account. This is due to the fact that the rectifier nonlinearity leads to the convexity of the expression of the diode current (3) with respect to y(t). As noted above, this finding is in contrast to findings in the field of communications, where fading is known to be detrimental. Indeed, the ergodic capacity of a fast fading channel is lower than the AWGN capacity due to the concavity of the log function in the rate expression.

Expression (11) was obtained under the assumption of a continuous wave (CW) as per (6).

Nevertheless, if the CW is modulated using energy modulation or replaced by an energy waveform, the factor of 2 in the fourth order term originating from fading would still appear on top of an additional gain originating from the use of energy modulation/waveform, showing that the benefit of fading for WPT is a model-independent finding. This will be discussed in more detail in Section V.

IV. BASIC TRANSMIT DIVERSITY

Motivated by the above observation that fading is beneficial to the harvested output energy, in this section an exemplary arrangement is described which induces fading-like effects in the transmission channel so as to benefit from the above-described effect. In particular, the disclosed arrangement induces channel fluctuations and creates an effective fast fading channel. During a given energy harvesting period, the rectenna will therefore effectively“see” a fast varying channel that will lead to a higher harvested energy.

In some arrangements, a single transmit antenna is used to transmit a plurality of RF signals, which combine and interfere to produce the desired fluctuations in the transmit channel. In one exemplary arrangement, the transmit antenna transmits a plurality of RF signals having different polarisations. It will be apparent that a variety of different polarisations can be used. A theoretical exception is the transmission of signals with orthogonal polarisations, as such signals will not interfere. However, in practice the polarisations of the signals may change as the signal travels towards the rectenna, due to interaction with the environment leading to scattering. Therefore, in principle any combination of initial signal polarisations may be used.

The particular exemplary arrangement described below comprises multiple transmit antennas and utilises the interference caused by the interference of the signals transmitted by each transmit antenna to induce the rapid fluctuations in the transmit channel referred to above. It will be apparent however that this is merely an exemplary arrangement, and other systems, including single antenna systems, which induce fluctuations in the transmit channel by other means may also be used and fall within the scope of the appended claims.

Given the use of multiple transmitter antennas in the arrangement set out below, the term“transmit diversity” is used to describe the specific arrangement set out in this section. The transmit diversity scheme uses dumb antennas to boost the harvested energy of rectennas by exposing the rectenna to slow fading channels. A dumb antenna is one that transmits a simple sin wave at a single frequency. Using dumb antennas reduces the complexity of the systems, because simple, low-cost antenna systems can be used and no complex design of the input signal is required, in contrast to other WPT methods described above. However, it will be apparent that more complex antenna and signal designs can be used instead of dumb antennas.

A. Phase Sweeping Transmit Diversity

In its simplest form, the disclosed transmit diversity arrangement for WPT induces fast fading of the transmission channel by transmitting a continuous wave on each antenna with an antenna dependent time varying phase xpm(t) . Considering M transmit antennas and one receive antenna, we can write the transmit signal on antenna m as

The average total transmit power is kept fixed to P. Denoting the wireless channel between antenna m and the receive antenna as L ^1/2 h_m (it varies very slowly over time, hence we omit the time dependency), the received signal can be written as

2 p

y(t) = — ¾{A ^1/2 h(t)e^iWot

N

(13) where

is the effective time-varying channel. The rate of change of h t ) is determined by the rate of change of the phases Fig. 2 illustrates the general architecture of transmit diversity for WPT. As can be seen, a transmitter 101 generates a transmit signal s(t). For the basic transmit diversity in equation (12), s(t) = 1. Each of the transmit antennas102a-c then transmits a copy of s(t) with an additional time-varying phase term, in accordance with equation (12) above. The signals interfere and the combined signal is received by the energy harvester 103, in this case a rectenna.

Fig. 2 illustrates an arrangement in which a single transmitter 101 is provided with multiple transmit antennas102a-c. In an alternative arrangement, a plurality of transmitters can be provided, each transmitter having at least one transmit antenna. Each transmit antenna may transmit a copy of s(t) with an additional time-varying phase term, in accordance with equation (12) above.

In order to get some insights into the performance benefit of the transmit diversity strategy, we assume the phases are uniformly distributed over 2p and are independent. Moreover, we assume for simplicity h_m = 1. We can then compute

The quantity G_td = l +

is obtained from computing E[\h(t)\⁴]/M² over the uniform distribution of the phases The derivations are similar to those used to compute the scaling laws in [8]

G_td can be viewed as the diversity gain offered by the transmit diversity strategy. It ranges from 1 for M = 1 (i.e. no gain) to 2 in the limit of large M (which corresponds to the gain offered by CSCG fading in Section III). The evolution of G_td as a function of M is illustrated in Fig. 3. For M = 2 and M = 4, the scheme boosts the fourth order term by a factor of 1.5 and 1.75, respectively.

This is remarkable as it shows that inducing fluctuations in the channel, in this arrangement by using multiple transmit antennas, is beneficial to WPT even in the absence of CSIT. Advantageously, in a multi-user setup, transmit diversity benefits all users by providing a diversity gain to all of them simultaneously. In other words, adding more energy receivers comes for free and does not compromise each receiver’s performance.

It is important to recall that the transmit diversity gain is deeply rooted in the realisation that the rectifier exhibits nonlinearity, as set out in Section II. If the nonlinearity modelled by the fourth order term is ignored, as has traditionally been done in prior disclosures, the transmit diversity gain disappears. With the linear model, there is no benefit in using transmit diversity since the second order term in equation (15) is constant irrespective of M in the absence of CSIT. In other words, the second order term can only by increased by the use of directional transmission (e.g. beamforming), which requires CSIT. This is disadvantageous in systems comprising numerous or low-power devices, as detailed above.

Transmit diversity has a number of practical benefits leading to low cost deployments. First, it can be implemented using dumb transmit antennas fed with a low peak-to-average power ratio (PAPR) continuous wave at a single carrier frequency w₀. Second, it does not require any form of

synchronization among transmit antennas since a time-varying phase is applied to each of them.

Third, it can be easily applied to co-located and distributed antenna deployments. Fourth, it is completely transparent to the energy receivers, meaning that no communication to or from the receiver, other than that involved in the actual transmission of the wireless power signal itself, is required. This eases system implementation and is in contrast to other methods such as beamforming where additional communication with the receiver is required because the receiver must acquire the CSI from the transmitter antannas. Fifth, for deployments with a large number of devices to be charged, it provides a transmit gain simultaneously to all users without any need for CSIT.

It is worth again contrasting the disclosed method with those of (energy) beamforming, waveform design and modulation. Note that in the presently disclosed method, the transmit diversity gain G_td is obtained without any CSIT. This contrasts with a (energy) beamforming approach for WPT that always relies on CSIT in order to beam energy in the channel direction. The philosophy behind transmit diversity is also different from energy waveform design [8] and energy modulation [15] that transmit specific signals with suitable characteristics. Energy waveform design in [8] relies on deterministic provision of multisine signals at the transmitter whose amplitudes and phases are carefully selected (as a function of the wireless channel in general settings) so as to excite the rectifier in a periodic manner by sending high energy pulses. The present disclosure negates the need to design such complex input waveforms. Energy modulation in [13]-[15] relies on single-carrier transmission but whose input follows a probability distribution that boosts the fourth order term in the Taylor expansion of the diode. One of such distribution, proposed in [15] and reminiscent of flash signalling, exhibits a low probability of high amplitude transmit signals. In contrast, the presently disclosed method is designed to generate amplitude fluctuations of the wireless channel, not amplitude fluctuations of the transmit signal. This is beneficial because a drawback of energy modulation-based techniques is that they lead to large amplitude fluctuations at the input of any power amplifiers used in the system, and therefore require complex and expensive amplifiers and hardware to be used.

B. Comparisons with Fading and Diversity in Communications

The notion of fading and diversity has a long history in communications. It is interesting to compare the effect of fading in communications and in WPT, as well as contrast the proposed transmit diversity for WPT with various forms of diversity strategies used in communications.

1) Fading: Channel fading in point-to-point scenarios is commonly viewed as a source of unreliability in communications that has to be mitigated [20] In contrast, from Section III, it can be seen that channel fading for both point-to-point and multi-user scenarios is a source of randomization in WPT that can be exploited to improve power transfer efficiency.

2) Time Diversity : In [21 ], a phase-rotated/sweeping transmit diversity strategy was proposed for point-to-point transmission so as to convert spatial diversity into time diversity. The effective SISO channel resulting from the addition of multiple branches seen by the receiver fades over time, and this selective fading can be exploited by channel coding. In the proposed transmit diversity for WPT, there is no information transmission and therefore no channel coding. Time- selective fading is also induced by a phase rotation/sweeping, but it is exploited by the rectifier rather than channel coding.

3) Multi-User Diversity : In [20], [22], multi-user diversity was introduced as a new form of diversity at the system level that leverages the independent time-varying channels across the different users. By tracking the channel fluctuations using a limited channel feedback and selecting the best user at a time (typically when its instantaneous channel is near its peak), a multi-user diversity gain is exploited that translates into a sum-rate scaling double logarithmically with the number of users at high SNR. By increasing the number of users, the sum-rate increases, though each user gets access to a smaller portion of the resources. Such a multi-user diversity strategy can also be applied in multiuser WPT in the same way as communications, as investigated in [23] The proposed disclosed method however differs from multi-user diversity as it does not rely on independent channels across users and does not require any form of tracking and scheduling. Moreover, all users do not have access to a portion of the resources but rather benefit simultaneously from the channel fluctuations. Therefore adding more users comes for free and does not compromise each user’s harvested DC power.

V. TRANSMIT DIVERSITY WITH ENERGY MODULATION/WAVEFORM

In section IV, a new method for WPT was described and contrasted with existing methods such as energy modulation and signal design.

Energy modulation and energy waveform are two different techniques to also boost the amount of DC power at the output of the rectenna. Similarly to transmit diversity, they both exploit the nonlinearity of the energy harvester. However, in contrast to transmit diversity, both create large amplitude fluctuations of the transmit signal. Energy waveform design in [7], [8] relies on providing a deterministic multisine input signal at the transmitter so as to excite the rectifier in a periodic manner by sending high energy pulses. Energy modulation in [13]— [15] relies on single-carrier transmission but whose input follows a probability distribution that boosts the fourth order term in the Taylor expansion of the diode.

Whereas section IV described a transmit diversity arrangement in contrast to these existing techniques, transmit diversity, and the presently disclosed methods and arrangements in general, can also be used in combination with such techniques. As will become clear, such a combination can jointly generate amplitude fluctuations of the wireless channel and amplitude fluctuations of the transmit signal. This combined effect leads to a joint diversity and modulation/waveform gain and can be leveraged in practice to balance the cost of the power amplifiers versus the number of antennas.

One extreme consists in using one single transmit antenna to generate energy waveform/modulation. Such an arrangement would require an expensive PA to cope with the high PAPR transmit signal and would not benefit from a transmit diversity gain. Another extreme would consist in using transmit diversity with multiple dumb antennas with cheap PAs and low PAPR continuous wave signal, as described in the previous section. Such an arrangement would not benefit from a

modulation/waveform gain.

In between those two extremes, it is possible to use a mixture of transmit diversity and energy modulation/waveform and partially trade the transmit diversity gain with the modulation/waveform gain so as to balance the cost of the PAs and the number of transmit antennas. In this section, it is demonstrated that an intermediate arrangement of this nature can be provided.

A. Transmit Diversity with Energy Modulation

Turning first to the combination of transmit diversity and energy modulation, rather than transmitting an unmodulated continuous wave with a time-varying phase on each antenna, as in pure transmit diversity, the carrier can instead be modulated using a suitable input distribution. The transmit signal on antenna m can be written as

where s(t) is the complex energy symbol drawn from a given distribution with E[|s(t) |²] = 1 and transmitted on all antennas. s(t) can be drawn for instance from a CSCG distribution, real distribution or any other distribution with high energy content [15] The received signal becomes

with h(t) given in (14). In order to analyze the performance gain, let us again assume h_m = 1. Following [13], we can then compute

where G_td

G_mod varies depending on the input distribution, namely G_mod = 2 for a CSCG input s(t) ~ CN(0,1), G_mod = 3 for s(t) ~ (0,1) and G_mod = l² for the flash signaling distribution of [15] characterized by s = re¹⁰ with the phase Q uniformly distributed over [0,2p) and the amplitude distributed according to the probability mass function

with l > 1.

Hence, transmit diversity with energy modulation brings a total gain in the fourth order term equal to the product of the diversity gain G_td and the modulation gain G_mod . In other words, the disclosed methods in combination with modulation can provide additional performance benefits compared to the disclosed methods in isolation.

B. Transmit Diversity with Energy Waveform design

Turning now to the combination of transmit diversity and energy waveform design, instead of using an energy modulated single-carrier signal, a deterministic in-phase multisine waveform with uniform power allocation on each antenna can be used. Recall from [8] that allocating power uniformly across all sinewaves was shown to lead to performance very close to the optimum in frequency flat channels. In such a case, (16) still holds but s(t) is replaced by the baseband multisine waveform s(t) =

A = 2nA_f the inter-carrier frequency spacing. Assuming a frequency-flat

channel, the received signal writes as in (17). Following [8], we can then compute

(20)

Hence, transmit diversity in combination with energy waveform design brings a total gain in the fourth order term equal to the product of the diversity gain G_td and the waveform gain G_wf. In other words, the disclosed methods in combination with energy waveform design can provide additional performance benefits compared to the disclosed methods in isolation.

VI. PERFORMANCE ANALYSIS WITH CURVE FITTING-BASED NONLINEAR RECTENNA MODEL

The previous sections were based on a diode nonlinear rectenna model driven by the physics of the rectenna. We here study another rectenna model that is based on fitting data using a polynomial. We use this model to assess the impact of fading on the harvested DC power and the potential gain of transmit diversity. Observations made in this section confirm those made in previous sections, demonstrating that the finding that fading is beneficial for WPT is a model-independent finding.

A. Curve Fitting-based Nonlinear Rectenna Model

Since a curve fitting-based model requires actual data, the rectenna circuit of Fig.4 is designed, optimized and simulated as described below.

A conventional single series rectifier circuit was used that consists of a rectifying diode, impedance matching circuit, and low pass filter. The Schottky diode Skyworks SMS7630 was chosen for the rectifying diode because it requires low biasing voltage level, which is suitable for low power rectifier. The impedance matching and low pass filter circuits were designed for an in-phase 4-tone ( N = 4) multisine input signal centered around 2.45GHz with an average power of -20dBm and with 2.5MHz inter-carrier frequency spacing. The load impedance R2 was chosen as 10 KW in order to reach maximum RF-to-DC conversion efficiency with the 4-tone multisine waveform. The matching network capacitor C1 , inductor L1 and output capacitor C2 values were optimized (using an iterative process) to maximize the output DC power under a given load impedance and for the given multisine input waveform at -20dBm RF input power. The chosen values were given by 0.4pF for C1 , 8.8 nH for L1 , and InF for C2. The antenna impedance was set as R1 = R_ant = 50W and the voltage source V1 is expressed

Using PSpice circuit simulations, the DC power P_dc harvested at the load as a function of the RF input power Prr for a continuous wave and multisine ( N = 8) input RF signals is evaluated in Fig. 5 and Fig., respectively.

Figs. 5a-c show circuit evaluations of harvested DC power P_dc versus RF input power Prr for a continuous wave ( N = 1) excitation and corresponding curve fitting model for the rectenna in Fig. 4.

Figs. 6a-c. show circuit evaluations of harvested DC power P_dc versus RF input power Prr for a multisine ( N = 8) excitation and corresponding curve fitting model for the rectenna in Fig. 4. Based on the collected data from the circuit simulations, a model that fits the data is chosen. We fit the data (in a least-squares sense) using a polynomial as follows

The coefficients a, b and c of the polynomials are given for two different RF input power ranges in the legends of Fig. 5 and Fig. 6, for continuous wave ( N = 1) and multisine ( N = 8) excitations, respectively. Note that, similarly to [19], the fitting is performed in the log-log scale instead of using a linear scale. Using a sigmoid or a polynomial to fit data in the linear scale, as in [17] and [18] respectively, may lead to severe inaccuracies in the low power regime as highlighted in [16] It is noted that a second degree polynomial fits the data relatively well, especially whenever fitted to the low input power regime -40 dBm to -5 dBm, as per subfigures (b). We are mainly interested in the non-diode breakdown region, i.e. below -5dBm for the considered circuit, for the reasons discussed in Remark 5 of [13] Subfigures (c) also illustrate the RF-to-DC conversion efficiency. Second degree fitting in the low power regime (-40 dBm to -5 dBm) appears relatively accurate, though RF-to-DC conversion efficiency is in general sensitive to any discrepancy in the curve fitting since it describes the ratio between P_dc and Prr We also note that multisine excitation leads to higher harvested DC power and RF-to-DC conversion efficiency compared to continuous wave, as discussed in detail in [7], [8], [1 1 ]

B. Effect of Fading on Harvested Energy

Similarly to Section III, in this section the impact of fading on harvested DC power is assessed, this time based on the curve-fitting rectenna model set out above.

We assume that the fading coefficient h is modelled as CSCG with E[|/i|²] = 1. With a fading channel, Prr will fluctuate as a function of h around its mean Prr As a consequence, P_dc also will fluctuate as a function of h. For a given realization of h' Prr relates to P_dc through (21). Defining the average DC power as P_dc— E_ft [P_dc]. with the expectation taken over the channel distribution, and making use of the nonlinear model (21) with Prr = \h\²P_rf, we can then write

P_dc = E _h[e^pdc Bi

= P_< dc,no fading ® fading

(25) where

= _e ^aPrf,dB ^+bPrf,dB ^+c '

dc.no fading

(26)

It appears from (25) that the average harvested DC power Pdc with fading can be written as the product of the harvested DC power P_dc,_no fading without fading and a fading gain e_fadlng that characterizes the impact of channel fading on the harvested DC power. Interestingly, (25) can be equivalently written as

where e_rf-dc = P_dc,no fa_dmg/Prf i^s the conventional RF-to-DC conversion efficiency (with e.g.

continuous wave or multisine excitation) in the absence of fading and e_rf-dc = P_dc/P_rf is the RF-to- DC conversion efficiency in the presence of fading. Interestingly, the RF-to-DC conversion efficiency in the presence of fading e_rf-dc can be split into two contributions: the conventional RF-to-DC conversion efficiency in the absence of fading e_{r -dc} and a fading gain e _adinathat accounts for the impact of fading on the harvester nonlinearity.

Defining d = 2 aP_{rf dB} + b and X = \h\² and noting that X ~ EXPO{ 1), the fading gain e_fadlng can equivalently be expressed as

Numerical integration can be used to compute the last integral. The fading gain e_fadlng is illustrated in Fig. 7 for continuous wave and multisine excitations using the fitting parameters taken from Fig. 5 and Fig. 6, respectively. It appears that e_fadlng is larger than one for most input power, especially in the low input power regime, suggesting that fading is beneficial to energy harvesting.

This confirms observations made in Section III and demonstrates that the finding was not a mere artefact of the rectenna model used in Section III. Here, the gain can be explained again by the convexity of the P_dc Prf relationship. The fading gain leads to an increase of the RF-to-DC conversion efficiency in the low input power regime as illustrated in Fig. 8.

C. Effect of Transmit Diversity on Harvested Energy

Similarly to Subsection IV-A, in this section the benefits of transmit diversity on the harvested DC power with the curve fitting-based nonlinear model are assessed. Let us consider the simplest case of two transmit antennas (M = 2) with h_m = 1 and the phases x ₁ and ip₂ independent and uniformly distributed over 27T. The effective channel can be written as h(t) = e^^l(t) + e^^z(t) and \h t) \2 =

2(1 + cosi^^t) - y₂ ( ))· Defining the random variable U =

- ^₂(t), also uniformly distributed over 2p, the effect of transmit diversity on harvested DC power can be computed following the same steps as in Subsection Vl-B by replacing \h\ ² with 1 + cos J ).

Following (28), we therefore write

where the transmit diversity gain e_td is obtained by replacing X in (29) by 1 + cos(U), such that

Numerical integration can be used to compute the last integral. The transmit diversity gain e_td is illustrated in Fig. 9 for continuous wave and multisine excitations using the fitting parameters taken from Fig. 5 and Fig. 6, respectively. It appears that e_td is larger than one for most input power, especially in the low input power regime, suggesting that transmit diversity is beneficial to energy harvesting. This is also in line with observations made in subsection IV-A and section V. The transmit diversity gain e_td leads to an RF-to-DC conversion efficiency with transmit diversity e_{rf®c td} larger than the RF-to-DC conversion efficiency achieved with a single transmit antenna e_{r -dc}, as illustrated in Fig. 10.

VII. PERFORMANCE EVALUATIONS

In this section, the performance of transmit diversity is evaluated using circuit simulations and realtime over-the-air experimentation. A. Circuit Simulations

Previous sections highlighted the benefit of transmit diversity in WPT with both continuous wave or more complicated modulation/waveform. The gains were predicted from the analysis using two different nonlinear models of the energy harvester. In this section circuit simulations are used to evaluate the performance benefit of transmit diversity, and the results are contrasted with the analysis set out above.

To that end, a two-antenna (M = 2) transmit diversity system was considered. Using Matlab, the input voltage source V1 to the realistic rectenna of Fig. 4 was generated. This was done by generating the transmit signal s(t), using either a continuous wave (CW) or multisine ( N = 8), passing it through the two-antenna transmit diversity strategy whose phase is randomly swept at a 2.5 MHz rate, and converting the received signal y(t) to the input voltage source V1. The input voltage source V1 is then fed into the PSpice circuit simulator. The duration of the generated signal was determined to be long enough (about 70 mί) for the rectifier to be in a steady state response mode.

For each input power level ranging from 40dBm to 20dBm, the same process was repeated more than 150 times in order to average out over a sufficient number of realizations of the phase.

A transmit diversity phase change rate of 2.5 MHz was chosen, though several phase change rates between 1 MHz and 10 MHz were also considered. The periods of those phase changes range from 0.1 /JS to 1 /JS. As stated in Subsection Vl-A, the rectenna was been optimized for a 4-tone multisine input waveform with an inter-carrier frequency spacing A_f = 2.5 MHz. Such a waveform generates large peaks with a periodicity of 1/A_f = 0.4 /JS. The RC constant of the low pass filter is

10 KW x InF = IOmί. The period of the phase change is therefore smaller than the rectenna’s RC constant. A significant performance gap between different phase change rates was not observed. The phase change rate was set to 2.5 MHz as mentioned above because it is applicable for the simulations and the prototype implementation.

Fig. 1 1 illustrates the simulated gain of transmit diversity with two transmit antennas (M = 2). Hence, in Fig. 9 and Fig. 1 1 , ©w refers to the transmit diversity gain obtained from analysis/modeling and simulations, respectively.

Fig. 12 displays the simulated RF-to-DC conversion efficiency with and without transmit diversity. A performance gain of transmit diversity with a continuous wave input is observed in circuit simulations, therefore validating the prediction from the analysis.

B. Prototyping and Experimentation

Leveraging the early WPT prototype reported in [24], a two-antenna transmit diversity prototype was implemented to verify that transmit diversity provides in real world conditions the performance benefits predicted from the analysis and simulation results described above. The prototype was divided into two parts, Tx and Rx, respectively. Rx part was a simple rectenna. The rectifier printed circuit board (PCB) was fabricated with a 2/4 length of microstrip, 1005 (1.0 mm x 0.5 mm lumped element package size) passive elements pads for 7r-matching network, and followed by a Schottky diode rectifier circuit. The same diode and low pass filter circuit as the rectenna used for the circuit simulations in Fig. 4 were implemented in the prototype. The values of the matching network components were modified to fit the real fabricated PCB. Universal 2.4 GHz band WiFi antennas with 3dBi gain were used. Fig. 13 illustrates the circuit diagram of the prototype rectenna used in the experiment.

The Tx part is an RF signal generator with 2.45GHz center frequency implemented using a software defined radio (SDR) relying on Nl FlexRIO PXIe-7966R and Nl 5791 R transceiver module. Tx signal generator continuously generates the selected signal type such as CW (continuous wave), multisine (N = 8), TD-CW (transmit diversity with CW), and TDmultisine (transmit diversity with multisine). The experiment was carried out at two different locations. The Rx antenna locations were fixed and Tx antennas were moved to the test locations. Both locations exhibited line-of-sight (LoS) between Tx and Rx, but different Tx-Rx distances of 2.5m and 5m. The received DC voltage measurement was carried out five times, and each measurement, non-continuous in time, was one minute long. Final results were averaged value of 5 minutes total for each case. Fig. 14 is a picture of the overall experimental setup with the SDR (PXIe-7966R and Nl 5791 R) implementing the transmit diversity strategy, the two PAs linked to Tx antenna 1 and 2, and the Rx antenna connected to the rectifier.

Fig. 15 illustrates the harvested DC power measured at the load of the rectifier for various transmit strategies, namely a single antenna with continuous wave (CW), a two-antenna transmit diversity (TD) with continuous wave, a single antenna multisine ( N = 8) and a two-antenna transmit diversity with multisine ( N = 8). Two different distances of 2.5 m and 5 m from the transmitter were considered, corresponding to a relatively high and low input power to the energy harvester, respectively. We observe that measurements are in line with theory and circuit simulations, with transmit diversity providing gain with both continuous wave and multisine waveforms, though larger with continuous wave and at a moderate distance of 2.5 m. Fig. 16 plots the same results but in a different way to highlight the relative gain over the DC power harvested with the single antenna continuous wave. TD with CW offers a gain over CW of about 8% and 45%, at 5 m and 2.5 m, respectively. By combining TD with multisine, a combined transmit diversity and multisine ( N = 8) waveform gain is observed of about 58% and 105% over a single antenna CW. Recall that those gains are obtained without any need for CSIT and that, in a multi-user deployment, each device would benefit from this performance enhancement, irrespectively of the number of devices. It is also worth keeping in mind that the prototype uses two transmit antennas. The gain is expected to grow with the number of transmit antennas, as discussed in Subsection IV-A. Gain levels in arrangements using a single transmit antenna will likely be somewhat lower, but such an arrangement would still benefit from the fact that the CSIT would not need to be acquired. VIII. CONCLUSIONS

In summary, the above disclosure makes clear the fact that fading is beneficial for boosting the RF-to- DC conversion efficiency of a WPT system, as a result of the energy harvester nonlinearity, in stark contrast to the field of communications where fading is detrimental.. This finding has been justified using two different models of the energy harvester nonlinearity, namely the physics-based diode nonlinear model of [8] and a curve fitting-based model approach similar to [17]— [19].

Inspired by this finding, a new WPT signal strategy has been disclosed which induces fast fluctuations of the wireless channel, optionally by using multiple antennas. Those fluctuations are shown to replicate fading effects and thereby boost the RF-to-DC conversion efficiency and the harvested DC power. The disclosed methods and arrangements do not rely on CSIT. A particular exemplary arrangement for obtaining channel fluctuations, denoted transmit diversity, was set out and performance analysis of this arrangement highlights that effective WPT is possible even in the absence of CSIT. In particular, real-time over-the-air measurements reveal gains of about 50% to 100% in harvested DC power with a two-antenna transmit diversity strategy over single-antenna setup, without any need for CSIT. The disclosed methods are therefore highly suitable for use in loT- type systems where there are many low power devices, for which CSIT acquisition is unpractical.

The singular terms“a” and“an” should not be taken to mean“one and only one”. Rather, they should be taken to mean“at least one” or“one or more” unless stated otherwise.

The word "comprising" and its derivatives including "comprises" and "comprise" include each of the stated features, but does not exclude the inclusion of one or more further features.

The above implementations have been described by way of example only, and the described implementations are to be considered in all respects only as illustrative and not restrictive. It will be appreciated that variations of the described implementations may be made without departing from the scope of the invention. It will also be apparent that there are many variations that have not been described, but that fall within the scope of the appended claims.

CLAUSES

Aspects and features of the present disclosure are set forth in the following numbered clauses which can be combined with the methods, devices and/or systems disclosed elsewhere herein.

1. A method of wirelessly transmitting power from at least one transmit antenna to at least one rectenna in a Wireless Power Transfer (WPT) system, the method comprising:

transmitting, by the at least one transmit antenna to the at least one rectenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal received by the at least one rectenna,

wherein at least one of the plurality of RF signals has a time-varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal received by the at least one rectenna, and

wherein each of the plurality of RF signals has a common frequency; and

receiving, by the at least one rectenna, the combined signal.

2. The method of clause 1 , wherein each of the plurality of RF signals has a different

polarisation.

3. The method of any preceding clause, wherein the transmitting is by a single transmit antenna.

4. The method of any of clauses 1 or 2, wherein the transmitting is by a plurality of transmit antennas.

5. The method of clause 4 wherein the plurality of transmit antennas are co-located.

6. The method of clause 4 wherein the plurality of transmit antennas are distributed.

7. The method of any of clauses 4-6, wherein each of the plurality of transmit antennas transmits only at the common frequency.

8. The method of any of clauses 4-7, wherein each of the plurality of transmit antennas transmits only a single RF signal.

9. The method of any of clauses 4-8, wherein there are M transmit antennas, and wherein the signal transmitted by each of the M transmit antennas is given by:

2 p

— cos(w₀t + xp_m (t ))

M where x_m(t ) is the signal transmitted by the mth transmit antenna, P is a fixed total average transmit power across the M transmitters,

w₀ is the signal frequency,

t is time, and

xpm(t) is time varying phase of the signal transmitted by the mth transmit antenna.

10. The method of any preceding clause, further comprising amplitude modulating the combined signal.

11. The method of clause 10, wherein amplitude modulating the combined signal comprises inducing, over time, fluctuations in the amplitude of the signal transmitted by each of the at least one transmit antennas.

12. The method of clause 10, wherein the induced fluctuations are induced in a deterministic manner.

13. The method of clause 12, wherein the induced fluctuations are induced in a deterministic manner by generating the input signal for each of the at least one transmit antennas such that the amplitude of the signal is specified based on a frequency response of the combined signal.

14. The method of clause 11 , wherein the induced fluctuations are induced in a randomized

manner.

15. A Wireless Power Transfer (WPT) system comprising at least one transmit antenna and at least one rectenna, wherein the at least one transmit antenna and at least one rectenna are configured to perform the method of any preceding clause.

16. A system comprising one or more transmitters, each transmitter comprising at least one transmit antenna for transmitting power to at least one rectenna in a Wireless Power Transfer (WPT) system, wherein the one or more transmitters are configured to:

transmit, by the at least one transmit antenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal at the at least one rectenna,

wherein at least one of the plurality of RF signals has a time-varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal formed at the at least one rectenna, and

wherein each of the plurality of RF signals has a common frequency.

17. The system of clause 16, wherein each of the plurality of RF signals has a different

polarisation. 18. The system of any of clauses 16 or 17, comprising a single transmitter, wherein the single transmitter comprises a single transmit antenna.

19. The system of any of clauses 16 or 17, wherein each of the one or more transmitters

comprises a plurality of transmit antennas.

20. The system of clause 19, comprising a single transmitter.

21 . The system of clause 19, comprising a plurality of transmitters.

22. The system of any of clauses 19-21 , wherein each of the plurality of transmit antennas is configured to transmit only at the common frequency.

23. The system of any of clauses 19-22, wherein each of the plurality of transmit antennas is configured to transmit only a single RF signal.

24. The system of any of clauses 19-23, wherein there are M transmit antennas, and wherein each of the M transmit antennas is configured to transmit at signal given by:

where x_m(t ) is the signal transmitted by the mth transmit antenna,

P is a fixed total average transmit power across the M transmitters,

w₀ is the signal frequency,

t is time, and

xpm(t) is time varying phase of the signal transmitted by the mth transmit antenna.

25. The system of any of clauses 16-24, wherein the one or more transmitters are further

configured to amplitude modulate the combined signal.

26. The system of clause 25, wherein the one or more transmitters are further configured to

induce, over time, fluctuations in the amplitude of the signal transmitted by each of the at least one transmit antennas.

27. The system of clause 26, wherein the induced fluctuations are induced in a deterministic manner.

28. The system of clause 27, wherein the induced fluctuations are induced in a deterministic manner by generating the input signal for each of the at least one transmit antennas such that the amplitude of the signal is specified based on a frequency response of the combined signal.

29. The system of clause 26, wherein the induced fluctuations are induced in a randomized

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Claims

1 . A method of wirelessly transmitting power from at least one transmit antenna for receiving by at least one rectenna in a Wireless Power Transfer (WPT) system, the method comprising:

transmitting, by the at least one transmit antenna to at least one rectenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal at the at least one rectenna,

wherein at least one of the plurality of RF signals has a time-varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal formed at the at least one rectenna, and

wherein each of the plurality of RF signals has a common frequency.

2. The method of claim 1 , wherein each of the plurality of RF signals has a different polarisation.

3. The method of any preceding claim, wherein the transmitting is by a single transmit antenna.

4. The method of any of claims 1 or 2, wherein the transmitting is by a plurality of transmit antennas.

5. The method of claim 4 wherein the plurality of transmit antennas are co-located.

6. The method of claim 4 wherein the plurality of transmit antennas are distributed.

7. The method of any of claims 4-6, wherein each of the plurality of transmit antennas transmits only at the common frequency.

8. The method of any of claims 4-7, wherein each of the plurality of transmit antennas transmits only a single RF signal.

9. The method of any of claims 4-8, wherein there are M transmit antennas, and wherein the signal transmitted by each of the M transmit antennas is given by:

where x_m(t ) is the signal transmitted by the mth transmit antenna,

P is a fixed total average transmit power across the M transmitters,

w₀ is the signal frequency, t is time, and

xpm(t) is time varying phase of the signal transmitted by the mth transmit antenna.

10. The method of any preceding claim, further comprising amplitude modulating the combined signal.

11. The method of claim 10, wherein amplitude modulating the combined signal

comprises inducing, over time, fluctuations in the amplitude of the signal transmitted by each of the at least one transmit antennas.

12. The method of claim 10, wherein the induced fluctuations are induced in a

deterministic manner.

13. The method of claim 12, wherein the induced fluctuations are induced in a

deterministic manner by generating the input signal for each of the at least one transmit antennas such that the amplitude of the signal is specified based on a frequency response of the combined signal.

14. The method of claim 11 , wherein the induced fluctuations are induced in a

randomized manner.

15. At least one transmit antenna for transmitting power to at least one rectenna in a Wireless Power Transfer (WPT) system, the at least one transmit antenna comprising a processing environment configured to perform the method of any preceding claim.

16. A method of wirelessly transmitting power from at least one transmit antenna to at least one rectenna in a Wireless Power Transfer (WPT) system, the method comprising:

transmitting, by the at least one transmit antenna to the at least one rectenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal received by the at least one rectenna,

wherein at least one of the plurality of RF signals has a time-varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal received by the at least one rectenna, and

wherein each of the plurality of RF signals has a common frequency; and receiving, by the at least one rectenna, the combined signal.

17. A Wireless Power T ransfer (WPT) system comprising at least one transmit antenna and at least one rectenna, wherein the at least one transmit antenna and at least one rectenna are configured to perform the method of claim 16.

18. A system comprising one or more transmitters, each transmitter comprising at least one transmit antenna for transmitting power to at least one rectenna in a Wireless Power Transfer (WPT) system, wherein the one or more transmitters are configured to:

transmit, by the at least one transmit antenna, a plurality of radio frequency (RF) signals which interfere to form a combined signal formed at the at least one rectenna,

wherein at least one of the plurality of RF signals has a time-varying phase, such that interference between the plurality of RF signals induces fluctuations in the amplitude of the combined signal at the at least one rectenna, and

wherein each of the plurality of RF signals has a common frequency.