Simultaneous Information and Power Transfer For

7/25/2019 Simultaneous Information and Power Transfer For

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5972 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 23, DECEMBER 1, 2013

Simultaneous Information and Power Transfer for Broadband Wireless Systems

Kaibin Huang , Senior Member, IEEE , and Erik Larsson , Senior Member, IEEE

Abstract Far- eld microwave power transfer (MPT) will freewireless sensors and other mobile devices from the constraintsimposed by nite battery capacities. Integrating MPT with wire-less communications to support simultaneous wireless informationand power transfer (SWIPT) allows the same spectrum to be usedfor dual purposes without compromising the quality of service.A novel approach is presented in this paper for realizing SWIPTin a broadband system where orthogonal frequency divisionmultiplexing and transmit beamforming are deployed to create aset of parallel sub-channels for SWIPT, which simpli es resourceallocation. Based on a proposed recon gurable mobile architec-ture, different system con gurations are considered by combiningsingle-user/multi-user systems, downlink/uplink informationtransfer, and variable/ xed coding rates. Optimizing the powercontrol for these con gurations results in a new class of multi-userpower-control problems featuring the circuit-power constraints ,specifying that the transferred power must be suf ciently largeto support the operation of the receiver circuitry. Solving theseproblems gives a set of power-control algorithms that exploitchannel diversity in frequency for simultaneously enhancing thethroughput and the MPT ef ciency. For the system con gura-tions with variable coding rates, the algorithms are variants of water- lling that account for the circuit-power constraints. Theoptimal algorithms for those con gurations with xed codingrates are shown to sequentially allocate mobiles their requ iredpower for decoding in ascending order until the entire budgetedpower is spent. The required power for a mobile is derived assimple functions of the minimum signal-to-noise ratio for correctdecoding, the circuit power and sub-channel gains.

Index Terms Cellular networks, energy harvesting, mobilecommunication, power control, power transmission.

I. I NTRODUCTION

M ICROWAVE power transfer (MPT) refers to wirelesslytransmittin g energy from one place to another. Simulta-neous wireless information and power transfer (SWIPT) refersto using the same emitted electromagnetic (EM) wave eld totranspor t both energy that is harvested at the receiver, and infor-mation that is decoded by the receiver.

In the past decades, much research effort has been directedtowar ds developing MPT for replacing cables in long-distance power transfer either terrestrially [1] or from solar satellites to

Manuscript received April 10, 2013; revised August 12, 2013; acceptedSeptember 01, 2013. Date of publication September 06, 2013; date of currentversion November 01, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Walaa Hamouda.

K. Huang is with the Department of Electrical and Electronic Engi-neering, The University of Hong Kong, Pok Fu Lam, Hong Kong (e-mail:[email protected]).

E. G. Larsson is with the Department of Electrical Engineering (ISY),Linkping University, Linkping 58183, Sweden (e-mail: [email protected]).

Digital Object Identi er 10.1109/TSP.2013.2281026

the earth [2]. This has led to a series of breakthroughs in mi-crowave technology including high-power microwave genera-tors and, more importantly in the current context, the inventionof rectennas (rectifying antennas) for ef cient RF-to-DC con-version [1]. This technology has been applied to the design of helicopters and airplanes powered solely by microwaves [3].Most prior research on MPT focuses on the design of compact and ef cient rectennas or similar energy harvesters [1], [4].More recently there has been interest in the powering of low- power devices and even trickle-recharging of certain personalcommunications devices. There is already equipment availablethat does this [5], by broadcasting omni-directionally with anRF power of about 1 W, and harvesting several mW. With amassive transmitter array, power could be focused so that theharvested power is increased by hundreds of times. The power levels involved are still small, much smaller than the emitted RF power by some cell phones (up to 2 W for GSM), so absorption by the human body does not appear to be a fundamental tech-nological problem. Moreover, various safety precautions could be applied if deemed important.

With SWIPT, one and the same wave- eld is used to transmitenergy and information. This has several advantages. First, sep-arate transmission of power and information by time division is

suboptimal in terms of ef ciently using the available power and bandwidth. SWIPT, by contrast, may exploit integrated trans-ceiver designs. Second, with SWIPT, interference to the com-munication systems can be kept under control. This is espe-cially important in multi-user systems with many potential re-ceivers who would suffer from interference. By contrast, tradi-tional MPT relies on transmission of a single tone (and its un-intended harmonics), wh ich can interfere with communicationlinks. Furthermore, MPT does not have any dedicated spectrum.Hence, as such, for use in existing bands, it must be integratedwith communication s olutions.

A key application of SWIPT that we foresee is to provide power to, and communicate with, sensors for which battery re- placement is dif cult or even impossible [6]. Radio-frequencyidenti cation (RFID) tags are one important example. RFID isalready a very widely used technology, but its full potential is probably not fully exploited. A major limitation is the smallrange of RFID readers with constrained power. Another limita-tion is the ability of readers to correctly resolve different RFIDtag retur ns that arrive at the receiver superimposed on one an-other. Many other applications, for example, in the chemical process industry, in environmental monitoring, in oil platformsand p ipelines and in surveillance and national security applica-tions require sensors with extreme reliability. Often these sen-sors transmit rather modest amounts of data, in some applica-

tions, only a few bits per hour. Typically the sensors are hard

1053-587X 2013 IEEE


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HUANG AND LARSSON: SIMULTANEOUS INFORMATION AND POWER TRANSFER FOR BROADBAND WIRELESS SYSTEMS 597 3

to access and therefore their batteries require long lifetimes andvery low failure rates.

Making SWIPT work will require integration between mul-tiantenna transmission, ef cient energy harvesting, resourcemanagement and signal processing. In particular, theory andmethods for massive MIMO [7] may become fundamentalenablers for SWIPT. Enabling technology for realizing SWIPTin practice is the theme of this paper.

A. Prior Related Work

The concept of SWIPT, in a very basic form, has existed for a long time in applications like RFID and power-line commu-nications. It was rst studied from an information-theoretic per-spective in [8] for a narrow-band noisy channel, and later in[9] for a frequency-selective channel. These papers characterizethe fundamental trade-off between communication capacity and power harvested at the receiver. A similar trade-off was derivedfor a multi-user system in [10]. From a communication theoretic

point of view, the novel aspect here is the new constraint on theminimum received power representing the xed circuit power consumption, called the circuit-power constraint , which resultsin the said fundamental tradeoff.

These aforementioned studies implicitly assumed that thereceived energy can be still harvested after passing throughan information decoder, which is infeasible given the cur-rent state-of-the-art of electronic circuits. This motivatedthe design of practical SWIPT-enabled receivers that split the received microwave signal from each antenna and feedit to two separate circuits, one for information decodingand one for energy harvesting [11], [12]. The correspondingcapacity-and-energy tradeoffs are characterized for the mul-tiple-input-multiple-output (MIMO) channels with perfecttransmitter channel state information (CSIT) [11], [12] andfurther investigated for the case of imperfect CSIT [13]. Anadditional scenario considered in [11] is broadcasting froma base station to two receivers taking turns for informationdecoding and energy harvesting, corresponding to time-division-information-and-power transfer (TD-IPT). This protocolsimpli es the receiver design but compromises the ef cienciesof MPT and information transfer (IT) since they cannot operatesimultaneously. The systems considered in the aforementioned prior works share the common setting that a transmitter drawsenergy from a reliable source such as the electric grid and then

delivers it to passive devices by MPT. A different scenariorelated to distributive networks such as sensor networks is onewhere devices exchange energy in addition to peer-to-peer communication. Transmission strategies are proposed in [14]for two devices to exchange information and energy basedon TD-IPT over a two-way channel. The principle of energysharing is also re ected in a relay system studied in [15] wherea source node transfers energy to a relay node in return for itsassistance in transmission. It is shown that jointly managingthe energy queues at these nodes that both harvest energy fromexternal sources can enhance the end-to-end throughput.

Realizing SWIPT in practice requires not only suitable hard-ware and physical-layer algorithmsbut also the support of an ap- propriate network architecture. One such architecture, proposedin [16], overlays a traditional cellular network with additional

base stations dedicated for MPT to mobiles. Based on a sto-chastic-geometry network model and under a quality-of-serviceconstraint on the data links, a tradeoff is derived between thedensities of the base stations for MPT and those for IT, givinginsight into the optimal network deployment.

A popular modulation method called orthogonal frequencydivision multiplexing (OFDM) divides a broadband channelinto decoupled narrowband sub-channels. OFDM simpli esthe channel equalization and multiple access [facilitat ingorthogonal frequency division multiple access (OFDMA)],which has motivated its adoption in modern communicationstandards such as 3GPP and WiFi [17]. Designing SWI PT based on OFDM not only retains its existing advantages butalso enables simultaneous wireless recharging of multipledevices. The current work represents a rst attempt to developa practical framework for OFDM-based SWIPT that features a practical mobile architecture and a matching set of power-con-trol algorithms that exploit fre quency diversity to enhance theef ciency of SWIPT. In parallel with our initial results in [18],

an independent study on the same topic was reported in [19].The practicality of the S WIPT system proposed in [19] seemsto be limited in several respects. First, the use of a single-an-tenna base station for SWIPT leads to isotropic radiation of the transmission p ower and hence an extremely low MPTef ciency. This is the reason that beamforming is the primarytechnology for practical MPT solutions [1][3]. Isotropic MPTalso couples the multi-user MPT links and results in dif cult power control problems [19]. Second, the design in [19] is based on the assumption that information decoding causesno loss in harvesting the total received energy. While thisassumption is common (see, e.g., [8][10]), we know of nocompelling arguments for its practicality. Lastly, a sub-optimalTD -IPT protocol instead of SWIPT is adopted in [19]. Thesedrawbacks of existing approaches may be overcome by theSWIPT framework proposed in this paper.

B. Summary of Contributions and Organization

This workassumes a noise-limited broadband system where amulti-antenna base station not only communicates with but alsowirelessly powers the mobile devices. The broadband channelis partitioned into orthogonal sub-channels by OFDM and the base station transmits/receives one data stream per sub-channel.

Streams are encoded with either variable rates adapted to there-ceive signal-to-noise ratios (SNRs) or xed rates for which suc-cessful decoding requires the receive SNRs to exceed a giventhreshold. The constraint and threshold are referred to as theminimum-SNR constraint and the SNR threshold , respectively.Assuming sparse scattering and perfect CSIT, the base stationsteers beams for different sub-channels towards associated mobiles, creating a set of parallel channels for SWIPT. Note thatOFDM alone without beamforming can decouple only the ITlinks but not the MPT links. The transmission powers for dif-ferent sub-channels are controlled subject to a constraint on thetotal power. We consider both a single-user system where themobile is assigned all sub-channels and a multi-user systemwhere each mobile is assigned a single sub-channel based onOFDMA. Two practical scenarios for SWIPT are considered


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TABLE ISUMMARY OF POWER CONTROL A LGORITHMS

depending on if IT is in the downlink or the uplink direction.For SWIPT with downlink IT, the OFDM signal transmitted bythe base station is used both for IT and for MPT. For SWIPTwith uplink IT, MPT and IT are in the opposite directions wheredownlink MPT relies on the transmission of unmodulated tones[20], called power tones , and uplink data signals are OFDMmodulated. In this scenario, the base station is assumed to support full-duplex SWIPT basedon the same principle as proposed

in [20]. More speci cally, the antenna array at the base stationis partitioned into two sub-arrays for transmit beamforming andreceive combining and the cross-coupled power tones in the re-ceived uplink s ignal is perfectly canceled. This is viable sincethe base station has perfect knowledge of the phases and fre-quencies of the power tones.

A SWIPT-ena bled mobile architecture is proposed that can be recon gured according to the direction of the IT. The archi-tecture consists of dual antennas, one information transceiver and one e nergy harvester. The harvester continuously convertsincoming microwaves to DC power which is used to operatethe mobile circuit and to supply transmission power for the up-link IT. This is feasible by using existing energy harvester de-signs such as those in [12], [16]. When con gured for SWIPTwith downlink IT, the outputs of the two antennas are combined

and then split using a power splitter with an adjustable ratio toyield the inputs of the receiver and harvester, similarly to thedesigns in [11], [12]. The po wer splitting ratio provides a de-gree-of-freedom for managing the received power for IT andMPT. When the architecture is recon gured for SWIPT withuplink IT, the two antenn as are separately attached to the trans-mitter and harvester to support full-duplex SWIPT in oppositedirections. The mobile architecture is assumed to consume xed

circuit power, foll owing practical models [21]. Based on thetransmission scheme and mobile architecture described earlier,algorithms for power control at the base station are designedfor a comprehen sive set of system con gurations combiningsingle-user/multi-user systems, downlink/uplink IT, and vari-able/ xed coding rates. The key features of the proposed algo-rithms are summarized in Table I.

The remainder of the paper is organized as follows. Thesystem model is described in Section II. The SWIPT-enabledmobile a rchitecture is proposed in Section III. Based on thearchitecture, power-control algorithms are designed separatelyfor the four scenarios combining single-user/multi-user systemsand d ownlink/uplink IT in Sections IV VII. Their performanceis evaluated by simulation in Section VIII, followed by con-cluding remarks in Section IX.


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Fig. 1. SWIPT in a broadband single-cell system where a base station serves passive mobiles based on OFDMA. Power is transferred from the base station tomobiles. Information transfer can be in either the downlink or uplink direction.

II. SYSTEM MODEL

In the single-cell system as illustrated in Fig. 1, a multi-an-tenna base station communicates with and supplies power tomobiles in a sparse-scattering environment. IT takes place ineither the downlink or uplink direction but the MPT is alwaysfrom the base station to the mobiles. SWIPT uses a wide spec-trum partitioned into sub-channels. For a single-user system

, all sub-channels are assigned to a single mobile; for a multi-user system, each mobile is assigned one sub-channel

. Note that the problem formulation for the case of assigning variable numbers of sub-channels to mobiles differsfrom the current one in having more complex circuit-power constraints, but the solution methods are similar. Ideally, the

sub-channel assignments for the multi-user system should be jointly optimized with the power control (see, e.g., [22] for tra-ditional OFDMA systems) but the optimal design for the cur-rent scenario seems intractable due to multi-user-circuit-power constraints. For tractability, we assume given sub-channel as-signments and focus on the power control. Furthermore, time isslotted and it is assumed for simplicity that the energy storageof all mobiles are empty at the beginning of each slot. Conse-quently, the instantaneous power harvested by an active mobileis required to meet the circuit-power constraint. Relaxing thesaid assumption requires generalizing the homogeneous circuit- power constraint to heterogeneous ones, which requires only astraightforward extension of the current results. A. Coding Rates

Information streams are transmitted over separate sub-chan-nels and independently encoded with either variable [17] or xed coding rates [23]. Given variable coding rates and perfectCSIT, the rate of a stream is adapted to the receive SNR, denotedas , and given as . Alternatively, the codingrates can be xed to where the constant spec-i es the minimum receive SNR required for correct decoding.

B. Multi-Antenna Beamforming and Combining

We assume an environment with sparse scattering that is nec-essary for ef cient MPT. For SWIPT with downlink IT, theantenna array at the base station is used to reduce the propa-gation loss by steering beams towards intended mobiles. Con-

Fig. 2. (a) Spectrumfor SWIPT with downlinkIT where the downlinksignal isOFDM modulated and there is no uplink transmission. (b) Spectrum for SWIPTwith uplink IT realized by OFDMA signals transmitted by mobiles while down-link MPT uses power tones transmitted by the base station.

sidering an arbitrary slot, let the vectors and represent particular realizations of the -th multiple-input-single-output(MISO) sub-channels from the base station to antenna 1 and 2of the -th mobile, respectively. Moreover, the transmit beam-forming vector for the -th sub-channel is denoted as andcomputed by estimating the mobiles direction by training. The beamforming vectors are assumed given and their designsare outside the scope of this paper. Then the effective SISO-channel gains resulting from beamforming can be de ned as

and .For SWIPT with uplink IT, the antenna array at the BS is di-

vided into two sub-arrays. These sub-arrays and the dual an-tennas at a particular mobile create a downlink MISO channeland an uplink single-input-multiple-output (SIMO) channel for supporting the full-duplex operation of SWIPT. Abusing thenotation, let denote the -th downlink vector sub-channeland the -th uplink vector sub-channel. Beamforming andmaximum-ratio combining are applied at corresponding sub-ar-rays to enhance the MPT ef ciency and the receive SNR of theuplink signal, respectively. Let denote the transmit beam-

forming vector for the -th downlink sub-channel and thecombining vector for the -th uplink sub-channel. The effectiveSISO channels in the opposite directions have the gains de nedas and .

C. Broadband Signals

Consider SWIPT with downlink IT. For this scenario, thedata-bearing signal transmitted by the base station is OFDMmodulated as illustrated in Fig. 2(a). Due to either safety regula-tions or limitations of the base-station hardware, the powers al-located ov er the sub-channels, denoted as , satisfy a power constraint:

(1)


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Fig. 3. Recon gurable mobile architecture that supports the dual-modeSWIPT, namely, SWIPT with downlink or uplink IT.

where represents the maximum total transmission power. A mobile extracts information and energy from thesame received signal using the receiver architecture discussedin the next section.

Next, consider SWIPT with uplink IT. As illustrated inFig. 2(b), downlink MPT relies on the transmission of power tones at the centers of the corresponding sub-channels and

their sum power satis es the power constraint in (1). For asingle-user system, the power tones are beamed by the basestation to a mobile. Besides operating the circuit, the mobileuses part of the harvested power to enable uplink IT where theuplink data signal is OFDM modulated as shown in Fig. 2(b).For a multi-user system, the power tones are beamed tocorresponding mobiles. The uplink transmission by the mobilesis based on OFDMA.

III. S WIPT -E NABLED MOBILE A RCHITECTURE

In this section, we proposea dual-antenna mobile architectureas illustrated in Fig. 3 for supporting the dual-mode SWIPT.The architecture comprises a transceiver and an energy har-vester. The transceiver demodulates and decodes received datafor downlink IT or encodes and modulates data for uplink IT.The energy harvester converts the input signal into DC power for operating the circuitry. The architecture can be recon gureddepending on whether the IT takes place in the uplink or down-link direction.

Consider the architecture con gured for downlink IT.The an-tenna outputs are then coherently combined to enhance the re-ceived signal power (see Fig. 3). The combiner output is splitinto inputs to the receiver and to the energy harvester [12]. To be speci c, the received signal is split using a power splitter that multiplies the signal with the adjustable factors and

, where , in order to obtain the inputs to thereceiver and the energy harvester, respectively. Consequently,the received power is divided into two parts of relative magni-tudes and . Let and represent the variances of the noise for a sub-channel, as accumulated in the path beforeand after the splitter, respectively. To simplify notation, we as-sume that the total noise has unit variance and thus .Using these de nitions, the receive SNR for the -th stream can be written as [11]

(2)

where due to the maximum-ratio combining. Ne-glecting the small contributions from noise and beam sidelobes,and assuming lossless RF-to-DC conversion, the harvested power at a mobile is for a single-user system and for a multi-user system where themobile is assigned the -th sub-channel.

Next, for the mobile architecture con gured for uplink IT,two antennas are separately attached to the transceiver and en-ergy harvester to support the full-duplex operation of the in-formation and power transfers in the opposite directions (seeFig. 3). Under the assumption of unit noise variance, the receiveSNR at the base station for the -th stream iswhere represents the uplink-transmission power allocatedto the -th sub-channel. The harvested power at a mobile is

for the single-user system and for the multi-user system when the mobile is assigned the -th sub-channel.

Finally, it is worth mentioning that adding more antennasat a mobile enhances the received signal power by increasingthe total antenna aperture as well as providing an array gainfor the uplink transmission. Nevertheless, spatial multiplexingis dif cult since a typical environment for ef cient MPT hasline-of-sight and the corresponding channel matrix is practicallyrank-one.

IV. P OWER CONTROL FOR SINGLE -U SER SWIPT SYSTEMSW ITH DOWNLINK IT

A. Single-User Downlink IT With Variable Coding Rates

1) Problem Formulation: Given the receive SNR in (2), thedownlink throughput, denoted as , can be written as

(3)

where the indicator function gives 1 if the event oc-curs and 0 otherwise. The indicator function in (3) representsthe circuit power constraint. The problem of maximizing thethroughput in (3) by power control is formulated as:

2) Solution: P1 is non-convex but can be approximated by aconvex problem as follows. Since, by assumption, ,the rate function in P1 is bounded as

(4)


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Approximating the objective function in P1 using the lower bound in (4) yields

The alternative approximation using the upper bound in (4) hasthe same structure as P1.1 and hence is omitted for brevity.Moreover, both approximations give nearly optimal power control policies as showed by simulation. P1.1 is a convex problem and can be solved numerically by standard algorithmsfor convex optimization [24]. In the remainder of this section,

we investigate the structure of the power control policy thatsolves P1.1.First, it is necessary to test the feasibility of powering the

receiver given transmission power . This requires computingthe limit of the harvested power by solving the followingoptimization problem:

By inspecting P1.1, it is found that . It fol-lows that SWIPT is feasible if and only if

(5)

Next, given the feasibility condition in (5), xing in P1.1 leadsto

P1.3 can be solved using the method of duality and the solutionis [24]

otherwise(6)

where the set is chosen to ensure being non-neg-ative, and the positive scalars and are the Lagrangemultipliers solving the dual problemthe unconstrained mini-mization of the following convex function [24]:

Note that the index set in (6) can be obtained byrepetitively removing from the index of the mobilecorresponding to the smallest negative element of and then recomputing and till the set

contains only non-negative elements. It follows from(6) that there exists a such that the solution to P1.1,denoted as , can be written as

otherwise(7)

where , and . As aresult, the optimal power-control policy for the currentcase can be approximated as for all . Simulationshows that such an approximation yields a throughput very closeto the maximum possible. The power allocation in (7) can beinterpreted as water- lling in frequency with a water level thatdecreases with an increasing sub-channel gain or vice versa.This agrees with the intuition that less transmission power isrequired for turning on a receiver if the MPT loss is smaller. Incontrast, the classic water- lling has a constant water level.

B. Single-User Downlink IT With Fixed Coding Rates

1) Problem Formulation: The downlink throughput,denotedas , is proportional to the number of successfully transmittedstreams. Speci cally, using the receive SNR in (2), is writtenas

(8)

where the rst indicator function represents the circuit-power constraint and the sum gives the number of correctly decodedstreams. The problem of maximizing by power control ishence formulated as:

2) Solution: Solving P2 is equivalent to nding the max-imum number of successfully transmitted streams, denoted as

and derived as follows. First, rearrange the sequence of channel gains in descending order and denote the resultas . The corresponding transmission powersare . This reordering can be represented by the permutation matrix such that

(9)

where the superscript denotes the matrix transposition. As-sume that streams are successfully transmitted. Letrepresent the power needed to successfully transmit the -thstream such that the total power is minimized. To this end, itis desirable to transmit the streams over sub-channels withthe largest channel gains, namely, . Therefore,


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considering the minimum-SNR constraint, solves thefollowing optimization problem:

Replacing the inequality constraints in P2.1 results in an opti-mization problem with a smaller domain:

(10)

Comparing P2.1 and P2.2 reveals that if the domain of P2.2 isnonempty, the solution to P2.2 must also solve P2.1. The exis-tence of a solution for P2.2 can be tested by solving the systemof linear equations from the equality constraints. As a result,satis es the following quadratic equation:

(11)

where the coef cients and are

(12)

Solving the equation in (11) and choosing the positive root givethe optimal value of for a given , denoted as :

(13)

Since the quadratic function on the left hand side of (11) is neg-ative for and positive for , lies in the range

and hence is a valid value for the splitting ratio. This con- rms the existence of a unique solution for P2.2 (equivalentlyP2.1) that follows from the equality constraints in P2.2 as

(14)

and the minimum transmission power for supporting streamsis hence . In other words, the optimal policy per-forms greedy channel inversion.

We can now solve P2 by obtaining as the maximum valueof under the power constraint from (1), which involves asimple search. To be speci c

(15)

with given in (14). Note that if for which it is infeasible to transmit any stream. It follows from (15)that the solution to P2, is given as

(16)

The main results of this section are summarized in the following proposition.

Proposition 1: For the single-user SWIPT system withdown-link IT and xed coding rates, the optimal power-control policy

is given in (16) and the corresponding power-splittingratio is with and given in (13) and (15), re-spectively.

V. POWER CONTROL FOR SINGLE -USER SWIPTSYSTEMS W ITH UPLINK IT

A. Single-User Uplink IT With Variable Coding Rates

1) Problem Formulation: Uplink transmission is feasible provided that the harvested power exceeds the circuit power:

. Under this condition, the total uplink trans-mission power is that is allocated over sub-channels for maximizing the uplink throughput. In other words,the throughput for the current case can be written as

(17)

where satis es the power constraint in (1) and rep-

resents uplink power control subject to:

(18)

Using (17), the problem of maximizing the uplink throughput isformulated as

2) Solution: By inspecting P3, the optimization problem can be decomposed into two sub-problems:

and


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where solves P3.1. The two problems have different ob- jectives: That of P3.1 is to maximize the downlink transferred power and that of P3.2 is to maximize the uplink throughput.P3.1 is similar to P1.2 and it is straightforward to show that

,otherwise

(19)

and that the transferred power is . It follows that thefeasibility condition for the uplink transmission is

(20)

which is similar to that in (5). Under this condition and given(19), P3.2 reduces to the classic multi-channel power control problem with the water- l ling solution given by

(21)

where the set contains the indices of the uplink sub-channelsassigned nonzero power, and is the water level chosen suchthat . The solution to P3 is sum-marized in the following proposition.

Proposition 2: Consider the single-user SWIPT systems withuplink IT and variable coding rates.

1) The optimal power-control policy at the base stationis to maximize the MPT ef ciency by transferring themaximum power over a single tone in the downlink sub-channel with the maximum effective channel gain,resulting in the transferred power equal to .

2) Uplink transmission is feasible if and only if the conditionin (20) holds. Under this condition, the optimal power-con-trol policy for the uplink transmission distributes the total power over the sub-channels accordingto the water- lling in (21).

B. Single-User Uplink IT With Fixed Coding Rates

1) Problem Formulation: Under the minimum-SNR and thecircuit constraints, the uplink throughput is given as

(22)where the uplink transmission power satis es the sameconstraint as in (18) for the case of variable coding rates. The problem of maximizing the throughput follows from (22) as:

2) Solution: Similar to P3, P4 can be decomposed into twosub-problems. The rst sub-problem maximizes the transferred power in the downlink and is identical to P3.1. It follows thatuplink transmission is feasible if and only if the condition in (20)is satis ed, namely that . Under this condition,the other sub-problem is to maximize the uplink throughput,more exactly:

It can be observed from P4.1 that the optimal power allocationshould be again based on greedy channel inversion. Speci -cally, the optimal policy attempts to meet the minimum-SNR constraints of the streams following the descending order of their corresponding sub-channel gains . To state the policymathematically, let the sequence represent the

values of sorted in descending order. Let represent the permutation matrix such that

Following the earlier discussion, the power allocated to the sub-channels with gains , denoted as , is given as

otherwise (23)

where , , is the maximum number of uplink streams under the uplink-power constraint obtained from the rst constraint in P4.1 as

(24)

The solution to P4 is summarized in the following proposition. Proposition 3: Consider the single-user SWIPT system with

uplink IT and xed coding rates.1) The optimal power-control policy at the base station is

identical to that in Proposition 2.2) Uplink IT is feasible if and only if . Under

this condition, the optimal power-control policy for uplink transmission is given as

with in (23).

VI. P OWER CONTROL FOR MULTI -USER SWIPT SYSTEMSW ITH DOWNLINK IT

A. Multi-User Downlink IT With Variable Coding Rates

1) Problem Formulation: Using the receive SNR in (2), thesum throughput is obtained as

(25)


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In contrast to the single-user counterpart in (3) having a singlecircuit-power constraint, the sum throughput in (25)contains themulti-user circuit-power constraints. The corresponding power-control problem is formulated as follows:

2) Solution: Like P1, P5 is non-convex but can be approxi-mated by a convex problem by replacing the objective function by either the lower or upper bounds in (4). Both approximating problems have the same structure and yield practically the samesolutions as P5, as shown by simulation. For brevity, we con-sider only the approximation of P5 using the lower bound in(4)and hence solving the following problem:

It can be observed from P5.1 that if , it is optimal tochoose such that the input power to the energy harvester is

since additional power contributes no throughput gain, cor-responding to . Consequently, P5.1 can be

rewritten as

Let denote the indices of the mobiles that meet their cir-cuit-power constraints using the power allocation in the solu-tion of P5. Given and de ning , P5.2 can be simpli ed as

As the values of increase, the objective functionin P5.3 increases and the rst constraint is relaxed. It followsthat with , P5.3 is equivalent to

where . The form of P5.4 is similar to that of the traditional multi-channel power control problem with the key difference that the maximum of

increases with decreasing . The reason is that re-ducing the number of streams decreases the total circuit-power consumption of the system and thereby allows more power to be used for IT. Given , combining the traditional water- llingmethod and the constant if yields thesolution to P5.4 as follows:

otherwise.

(26)

The corresponding sum throughput is

Next, the number of streams is determined by a simplesearch. According to the traditional water- lling method, ischosen as where with is thelargest integer such that are positive. Itis important to note that the traditional choice may not be op-timal due to the aforementioned difference between the tradi-tional method and P5.4. In other words, reducing the number of streams below may result in a throughput gain. The op-timal value of , however, has no closed-form solution but can be obtained by a simple search over the range from 1 to . To be speci c, the value of that maximizes the sum throughputis given as

(27)

The above results are summarized in the following lemma. Lemma 1: The solution for P5.1, denoted as , is ob-

tained from in (26) as

with in (26) and the number of active mobiles optimizedas in (27).

Since P5.1 is a convex approximation of P5, the solutionor equivalently the optimal power-control policy for the

current case can be approximated as for all , whichis shown by simulation to be close-to-optimal.

B. Multi-User Downlink IT With Fixed Coding Rates

1) Problem Formulation: Using the receive SNR in (2), thesum throughput is written as


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that differs from the single-user counterpart in (8) by havingthe multi-user circuit-power constraints. The matching power-control problem can be formulated as

2) Solution: Replacing the inequalities in P6 with equalitieshas no effect on the solution. Hence, P6 can be rewritten as

The splitting ratio forthe -th mobile can be obtained by solving

the following two linear equations:

The resulting optimal value of , which is identical for allmobiles and denoted as , has a similar form as the single-user counterpart in (13):

(28)

where thecoef cients and are as given in (12). With xed as given in (28), it follows from inspecting P6 that the op-

timal power-control policy again performs greedy channel in-version, just like its single-user counterpart. The result is sum-marized in the following proposition.

Proposition 4: For the multi-user SWIPT system with down-link IT, the optimal power-control policy, represented by ,is given as

(29)

where

otherwise.(30)

The optimal splitting ratio is given by (28) and ,

, is the largest integer such that the power constraint

(31)

is satis ed.

VII. P OWER CONTROL FOR MULTI -USER SWIPT SYSTEMSW ITH UPLINK IT

A. Multi-User Uplink IT With Variable Coding Rates

1) Problem Formulation: The sum throughput for the currentcase is given as

(32)

Note that the product in (32) represents the combined lossdue to propagation both in the downlink and in the uplink. Thismust be contrasted with the loss of only in the case of down-link IT [see (25)]. The power-control problem is formulatedusing (32) as

2) Solution: To facilitate a compact exposition, we use thefollowing de nitions. Let denote the downlink sub-channel gains sorted in descending order and let be the corresponding permutation matrix; that is, we have:

(33)

Arranging the uplink sub-channel gains in the same way,i.e., , gives

(34)

The powers are de ned based on in a similar way.Using these de nitions, P7 can be rewritten as

Given that P7.1 is non-convex, a sub-optimal algorithm is proposed as follows. Assume that mobiles are active, that is,they harvest suf cient energy for meeting their circuit-power constraints; all others are allocated zero power. To maximizethe MPT ef ciency, the active mobiles are chosen to bethose corresponding to the largest downlink sub-channel gains

. This choice may not be overall optimal, how-ever, since selecting a mobile with relative small downlink butsuf ciently large uplink sub-channel gains can increase thethroughput. De ne . Given the assumptionsand choices made, the problem of maximizing the uplink sumthroughput reduces to the standard multi-channel power control problem:

This problem is solved by water- lling:

otherwise

(35)

The number of active mobile is optimized. Let ,, be the maximum number of active mobiles such


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that the corresponding multi-user circuit-power constraints andthe power constraint are satis ed:

(36)

For the same reason as discussed when solving P5.4, it maynot be optimal to set the optimal value of , denoted as ,as . Instead, can be found by testing the values

. The above results are summarized in the fol-lowing algorithm for computing a sub-optimal solution for P7.

Algorithm 11) Compute the maximum number of active mobiles .2) Determine the optimal number of streams as

(37)

with given in (35).3) Given , the allocated powers are computed as

otherwise(38)

Then rearrange to give the power allocation :

Algorithm 1 sequentially performs the tasks of schedulingmobiles with high MPT ef ciencies and maximizing the uplink sum rate of the scheduled mobiles by power control. The designexploits the fact that meeting the circuit power constraints is a

prerequisite for IT and hence has high priority. Such a sequen-tial algorithm provides a close-to-optimal solution as shown bysimulation results in the sequel.

B. Multi-User Uplink IT With Fixed Coding Rates

1) Problem Formulation: The sum throughput for thecurrentscenario can be written as

(39)

The corresponding formulation of the optimal power-control problem follows as

2) Solution: Since the rst indicator function in the objectivefunction of P8 yields 1 if and only if the second does so, P8reduces to

For ease of notation, de ne the scalar sequenceaccording to

(40)

and the vector . Let repre-sent the sequence sorted in ascending order, and de nethe vector and the permutation matrixsuch that . By inspecting P8, the optimal power con-trol policy at the base station is found to be the one that attemptsto meet the minimum-SNR requirements of the uplink streamsfollowing the descending order of . To be speci c, the op-timal power allocated to the sub-channel corresponding to ,denoted as , is given as

otherwise (41)

where is the maximum number of uplink streams or equiv-alently the largest integer for which the power constraint ob-tained from (1),

(42)

is satis ed. Note that the policy as speci ed by (41) is avariant of greedy channel inversion where combines theinversion of closed-loop channels and circuit-power consump-tion. Then the solution to P8 follows from rearranging

according to the original order of the sub-channels. In

other words,(43)

with in (41). The key results of this section are summa-rized in the following proposition.

Proposition 5: Consider the multi-user SWIPT system withuplink IT and xed coding rates.

1) The optimal power-control policy at the base station isgiven by (43).

2) It is optimal for each active mobile harvesting nonzero power to apply all available power for uplink transmissionafter deducting the power needed to operate its circuitry.

VIII. S IMULATION R ESULTS

In this section, the performance of SWIPT using the power-control algorithms proposed in the preceding sections is eval-uated by simulation in terms of spectral ef ciency versus cir-cuit power. The channel model is described as follows. Propa-gation is assumed to have line-of-sight and be close to that infree space, which is necessary for making MPT feasible. The propagation model for beamed transmission is modi ed fromthat in [25] and speci ed by the following relation between thetransmission power and received power for an arbitrarylink:

(44)


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Fig. 4. Spectral ef ciency versus circuit power for the scenario of downlink IT. (Top left) Single user and variable coding rates. (Top right) Single user and xedcoding rates. (Bottom left) Multi-user and variable coding rates. (Bottom right) Multi-user and xed coding rates.

where is the wavelength, and the total apertures of the

transmit and receive antenna arrays, respectively, the trans-mission distance and a complex Gaussian random variablewith nonzero mean that models small-scale fading. For simula-tion, it is assumed that the wavelength corresponds to a carrier frequency of 5.8 GHz, the total aperture of the base-station an-tenna array is 1 sq. m, the aperture of each of the two antennasat a mobile is 0.05 sq. m, the base-station transmission power is 10 W in the single-user system and 20 W in the multi-user system, and follows the distribution. For the sce-nario of uplink IT, the two sub-arrays at the base station thatsupport full-duplex MPT/IT are assumed to have equal aper-tures of 0.5 sq. m. For ef cient MPT, transmission distances are

assumed to be short as enabled by dense base-station deploy-ment. To be speci c, the distances are 100 m for the single-user system and m for the multi-user systemwith ve mobiles. Correspondingly, there are ve frequencysub-channels which are assumed to be frequency non-selective.Their bandwidth has no effect on the simulation results since the performance metric is spectral ef ciency. The distributions of the channel coef cients follow from the prop-agation model in (44). To be speci c, each coef cient is given by the expression of in (44) substituted with the cor-responding transmission distance, and all coef cients are as-sumed to be independent. Note that the beamforming gains areaccounted for in the model of the channel coef cients via theantenna apertures [25]. Given short propagation distances andline-of-sight channels, a mobile can be exposed to extremely

strong interference and hence the interference-plus-noise vari-

ance from each sub-channel is chosen to have a large value,namely , where and of the noise power are introduced before and after a power splitter (see Fig. 3), re-spectively. Note that in an interference dominant environment,the interference-plus-noise variance is largely determined by theratio between the main-lobe and side-lobe responses rather thanthe channel bandwidth that affects the thermal noise variance.The SNR threshold for the case of a xed coding rate is set as30 dB for the scenario of downlink IT and 7 dB for the scenarioof uplink IT, which are optimized numerically to enhance thespectral ef ciency. Last, the battery capacity at all mobiles isassumed to be suf ciently large such that there is no energy loss

due to battery over

ow.The proposed SWIPT with power control is compared in thesequel with SWIPT without such control (equal power alloca-tion) as well as the TD-IPT method [11], [19]. It is assumed for TD-IPT that each time slot is divided into two halves for al-ternating MPT and IT. The time sharing reduces the durationfor IT by half but enhances the received signal power by dedi-cating all antennas to either MPT or IT at each time instant. The power control algorithms for TD-IPT follow straightforwardlyfrom those designed for SWIPT and thus the details are omittedfor brevity.

First, consider the scenario of SWIPT with downlink IT. Thecurves of spectral ef ciency versus circuit power are plotted inthe sub- gures in Fig. 4, corresponding to different cases combining single-user/multi-user systems and variable/ xed coding


13/15


Fig. 5. Spectral ef ciency versus circuit power for the scenario of uplink IT. (Top left) Single user and variable coding rates. (Top right) Single user and xedcoding rates. (Bottom left) Multi-user and variable coding rates. (Bottom right) Multi-user and xed coding rates.

rates. For all the curves in the gure, as the circuit power de-creases, the spectral ef ciencies converge to their counterpartsfor the case with reliable power supplies at the mobiles, whichare extremely high ( ) due to the low propa-gation loss. The spectral ef ciencies reduce with increasing cir-cuit power. In particular, the changes exhibit a threshold effectfor the single-user system (see top sub- gures in Fig. 4). Thissuggests that powering one passive mobile by MPT has littleeffect on the spectral ef ciency if the circuit power is belowthe threshold, but otherwise it degrades the ef ciency severely.However, for the multi-user system, since the base-station needs

to power multiple mobiles, the spectral ef

ciency is sensitiveto the changes in the circuit power (see bottom sub- gures inFig. 4). Next, comparing SWIPT with and without power con-trol, it is observed that with the spectral ef ciency xed suchcontrol can increase circuit power substantially e.g., by up toabout 8 dB for the single-user system. Last, though TD-IPTyields spectral ef ciencies about half of those by SWIPT for low to moderate circuit power, the gap narrows as the power increases and TD-IPT can outperform SWIPT for high circuit power as shown in the case of the single-user system with xedcoding rates.

Next, consider the scenario of SWIPT with uplink IT. Asimilar set of curves as those in Fig. 4 are plotted in Fig. 5.Compared with the previous scenario of SWIPT with downlink IT, the power supplied by the base station must overcome a

roundtrip propagation loss, rst for the MPT in the downlink and then for the IT in the uplink, which decreases the spectralef ciencies by more than 10 bit/s/Hz. For the current scenario,TD-IPT is found to outperform SWIPT. This suggests thatgiven severe propagation loss it should be preferable to use alltransmit/receive antennas for either MPT or IT which more thancompensates the time-sharing loss. Last, the performance of the sub-optimal Algorithm 1 designed for the case of multi-user SWIPT with uplink IT is observed to be close-to-optimal,where the curve for the optimal algorithm is obtained byscheduling based on an exhaustive search for maximizing the

spectral ef

ciency.For the same scenario of uplink IT, a further comparison be-tween TD-IPT and SWIPT is provided in Fig. 6 for which theround-trip propagation loss is alleviated by reducing all trans-mission distances by ve times. It is observed that there areintersections between the curves for SWIPT and their TD-IPTcounterparts. This leads to the conclusion that SWIPT is pre-ferred when the propagation loss is not extremely severe (e.g.,for the case of downlink IT) or the circuit power is low; other-wise, TD-IPT should be used for a higher spectral ef ciency.

IX. C ONCLUSIONS

A framework has been proposed for realizing SWIPT in a broadband wireless system that comprises a passive SWIPT-en-abled mobile architecture and a matching set of power-control


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Fig. 6. Spectral ef ciency versus circuit power for the scenario of uplink IT with reduced transmission distances, namely 20 m for the single-user system andfor the multi-user system. (Left) Single user. (Right) Multi-user.

algorithms designed for different system con gurations ac-counting for single-user/multi-user systems, variable/ xedcoding rates, and uplink/downlink information transfer. Thesealgorithms have been optimized for maximizing the systemthroughput under circuit-power constraints at mobiles, inaddition to a power constraint at the base station. It is shown by simulation that power control plays an important role inenhancing the ef ciency of SWIPT.

This work can be extended in several interesting directions.First, the channel assignment was assumed to be xed here.Jointly assigning channels and performing optimal power con-trol may further increase the SWIPT ef ciency. Second, the cur-rent framework can be modi ed to support multimode opera-tions including MPT or SWIPT to nearby mobiles but only in-formation transfer to mobiles far away. Third, the power controlcan be integrated with intelligent energymanagement policies atthe mobiles, in order to exploit the diversity that originates fromtime-variations of the channels. Finally, it would be interestingto design a framework for cooperative SWIPT in a multi-cellsystem.

R EFERENCES

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[2] J. O. Mcspadden and J. C. Mankins, Space solar power programs andmicrowave wireless power transmission technology, IEEE Microw. Mag. , vol. 3, pp. 4657, Apr. 2002.

[3] J. J. Schlesak, A. Alden, and T. Ohno, A microwave powered highaltitude platform, IEEE MTT-S Dig. , pp. 283286, 1988.

[4] T. Le, K. Mayaram, and T. Fiez, Ef cient far- eld radio frequencyenergy harvesting for passively powered sensor networks, IEEE J.Solid-State Circuits , vol. 43, pp. 12871302, May 2008.

[5] P2110 915MHz RF powerharvester receiver, Product Datasheet,Powercast Corp., Pittsburgh, PA, USA, 2010, pp. 112.

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Edfors, and F. Tufvesson, Scaling up MIMO: Opportunities and chal-lenges with very large arrays, IEEE Signal Process. Mag. , vol. 30, pp.

4060, Jan. 2013.[8] L. R. Varshney, Transportinginformation and energysimultaneously,

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[9] P. Grover and A. Sahai, Shannon meets tesla: Wireless informa-tion and power transfer, Proc., IEEE Int. Symp. Inf. Theory , pp.23632367, Jun. 2010.

[10] A. Fouladgar and O. Simeone, On the transfer of information andenergy in multi-user systems, IEEE Commun. Lett. , vol. 16, pp.17331736, Nov. 2012.

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[18] K. Huang and E. G. Larsson, Simultaneous information-and-power transfer for broadband downlink systems, presented at the IEEE Int.Conf. Acoust., Speech, Signal Process., Vancouver, Canada, May2631, 2013.

[19] D. W. Ng, E. S. Lo, and R. Schober, Energy-ef cient resource al-location in multiuser OFDM systems with wireless information and power transfer, presented at the IEEE Wireless Commun. Netw. Conf.,Shanghai, China, Apr. 710, 2013.

[20] J. Choi, M. Jain, K. Srinivasan, P. Levis, and S. Katti, Achievingsingle channel, full duplex wireless communication, presented at theACM MobiCom, Chicago, IL, USA, Sep. 2024, 2010.

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Kaibin Huang (S05M08SM13) received theB.Eng. ( rst-class hons.) and the M.Eng. degreesfrom the National University of Singapore in 1998and 2000, respectively, and the Ph.D. degree fromThe University of Texas at Austin (UT Austin) in2008, all in electrical engineering.

Since Jan. 2014, he has been an assistant professor in the Dept. of Electrical and Electronic Engineering(EEE) at The University of Hong Kong. He is an ad- junct professor in the School of EEE at Yonsei Uni-versity in S. Korea. He used to be a faculty member

in the Dept. of Applied Mathematics at The Hong Kong Polytechnic University(PolyU) and the Dept. of EEE at Yonsei University. He had been a PostdoctoralResearch Fellow in the Department of Electrical and Computer Engineering atthe Hong Kong University of Science and Technology from Jun. 2008 to Feb.2009 and an Associate Scientist at the Institute for Infocomm Research in Sin-gapore from Nov. 1999 to Jul. 2004. His research interests focus on the analysisand design of wireless networks using stochastic geometry and multi-antennatechniques.

He frequently serves on the technical program committees of major IEEEconferences in wireless communications. He chairs the Comm. TheorySymp. of IEEE GLOBECOM 2014 and the Adv. Topics in Wireless Comm.Symp. of IEEE/CIC ICCC 2014 and has been the technical co-chair for IEEE CTW 2013, the track chair for IEEE Asilomar 2011, and the track co-chair for IEE VTC Spring 2013 and IEEE WCNC 2011. He is a guest

editor for the IEEE J OURNAL ON SELECTED A REAS IN COMMUNICATIONS , aneditor for the IEEE T RANSACTIONS ON WIRELESS COMMUNICATIONS , IEEEW IRELESS COMMUNICATIONS LETTERS and also IEEE/KICS J OURNAL OFCOMMUNICATION AND NETWORKS . He is an elected member of the SPCOMTechnical Committee of the IEEE Signal Processing Society. Dr. Huangreceived the Outstanding Teaching Award from Yonsei, Motorola Partnershipsin Research Grant, the University Continuing Fellowship at UT Austin, andBest Paper Awards from IEEE GLOBECOM 2006 and PolyU AMA in 2013.

Erik G. Larsson (S99AM02M03SM10)received the Ph.D. degree from Uppsala University,Sweden, in 2002.

Since 2007, he is a Professor and Head of the Di-vision for Communication Systems, Department of Electrical Engineering (ISY), Linkping University(LiU), Linkping, Sweden. He has previously beenan Associate Professor (Docent) at the Royal Insti-tute of Technology (KTH), Stockholm, Sweden, andAssistant Professor at the University of Florida andthe George Washington University. His main profes-

sional interests are within the areas of wireless communications and signal pro-cessing. He has published some 100 journal papers on these topics, he is a coau-thor of the textbook Space-Time Block Coding for Wireless Communications(Cambridge Univ. Press, 2003) and he holds 10 patents on wireless technology.

Dr. Larsson is an Associate Editor for the IEEE T RANSACTIONS ONCOMMUNICATIONS and he has previously been Associate Editor for severalother IEEE journals. He is a member of the IEEE Signal Processing SocietySPCOM Technical Committee. He is active in conference organization, mostrecently as the Technical Chair of the Asilomar Conference on Signals, Systemsand Computers 2012 and Technical Program Co-Chair of the InternationalSymposium on Turbo Codes and Iterative Information Processing 2012. Hereceived the IEEE S IGNAL PROCESSING MAGAZINE Best Column Award 2012.

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