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1 ICC 2014 Wireless Powered Communication: Opportunities and Challenges Rui Zhang ECE Department, National University of Singapore ICC 2014, Sydney Rui Zhang, National University of Singapore

Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

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Page 1: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

1 ICC 2014

Wireless Powered Communication:

Opportunities and Challenges

Rui Zhang

ECE Department, National University of Singapore

ICC 2014, Sydney

Rui Zhang, National University of Singapore

Page 2: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

2 ICC 2014

Related Research Areas of Wireless Powered Communications

Introduction

Wireless power transfer

Green communications

Smart grid

Energy harvesting

Rui Zhang, National University of Singapore

Page 3: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

3 ICC 2014

Wireless Powered Communication: Network Architectures

Information flow

Energy flow

Separate energy & info transmitters

Co-located energy & info receiver

Separate energy & info receivers

Introduction Rui Zhang, National University of Singapore

Page 4: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

A Generic UL/DL System Model [1]

Hybrid Access point

Energy and/or Information Receiver

Information flow

Energy flow

Downlink

Uplink

The received baseband-equivalent signal at a receiver

If used for energy harvesting (EH), the harvested power is

If used for information decoding (ID), the achievable data rate is

Energy and/or Information Receiver

In practice, a receiver cannot harvest energy and decode information simultaneously (more details to be given later).

ICC 2014 4

Introduction Rui Zhang, National University of Singapore

Page 5: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Operating Mode 1: WPT

Wireless power transfer (WPT) Only power transfer in one direction Continuous and controllable (vs. ambient RF and other environment

energy harvesting, intermittent and random) Application: mobile device and sensor charging, etc. Technologies available (to be detailed)

Inductive coupling Coupled magnetic resonance EM radiation

Energy flow

ICC 2014 5

Introduction Rui Zhang, National University of Singapore

Page 6: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Operating Mode 2: WPCN

Wireless powered communication network (WPCN) [2] DL: wireless power transfer UL: Information transfer with wireless harvested energy Applications: sensor network charging and info collection, RFID, etc. Power consumptions at the energy receiver

Sensing and info processing UL info transmission

A wireless charging vehicle (WCV) travels inside a sensor network to charge the sensor nodes wirelessly [3].

ICC 2014 6

Introduction Rui Zhang, National University of Singapore

Page 7: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Operating Mode 3: SWIPT

Simultaneous wireless information and power transfer (SWIPT) [1] Info & energy transmit simultaneously in DL Under limited signal power and bandwidth (vs. power-line communication) Applications: heterogeneous EH and ID receivers, simultaneous ID and EH at

one receiver, etc. Rate-and-energy tradeoff Separate or co-located ID and EH receivers

Hybrid Access Point

Energy Flow

Information Flow

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Introduction

Energy Flow

Information Flow

SWIPT with separate ID and EH receivers SWIPT with co-located ID and EH receivers

Rui Zhang, National University of Singapore

Page 8: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Agenda

• Part I: Wireless Power: History and State-of-the-Art

• Part II: Overview of Wireless Powered Communications

• Part III: Case Studies and Extended Work

ICC 2014 8

Introduction Rui Zhang, National University of Singapore

Page 9: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Part I

Wireless Power: History and State-of-the-Art

ICC 2014 9

Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

Page 10: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Microwave Enabled Wireless Power Transfer: Nikola Tesla and his Wardenclyffe Project in early 1900

150 KHz and 300 kW. Unsuccessful and never put into practical use.

ICC 2014 10

Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

Page 11: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

The Invention of ``Rectenna” for Microwave Power Transmission: the Microwave Powered Helicopter by William C. Brown in 1960s

2.45 GHz and less than 1kW. Overall 26% transfer efficiency at 7.6 meters high.

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Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

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Solar Satellite with Microwave Power Transmission (1970s-current)

NASA Sun Tower

Target at GW-level power transfer with more than 50% efficiency

ICC 2014 12

Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

Page 13: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

NASA’s Wireless Power Transfer Project Using Laser Beam

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Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

Page 14: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Induction Coupling Enabled Wireless Power Transfer: Radio Frequency Identification (RFID) in 1970s

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Now some RFID tags can also be powered by harvesting RF energy transmitted by the readers (e.g. Intel WISP tags)

Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

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Wireless Power Transfer via Magnetic Resonant Coupling in 2000s

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Part I: Wireless Power: History and State-of-the-Art

Demonstration of magnetic coupling to power light bulb (Intel Corp.) and charge mobile phones (Witricity Corp.)

Rui Zhang, National University of Singapore

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Wireless RF Power Transfer via Electromagnetic Radiation

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Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

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Wireless Power Transfer: State-of-the-Art Technology

Range

Efficiency

inductive

coupling magnetic

resonant

coupling

Electromagnetic

(EM) radiation

<5cm pre-determined

distance, e.g.,

15-30cm

>1m

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Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

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Summary of performance

Strength Efficiency Distance Multicast Mobility Safety

Inductive Coupling Very high Very high Very short Yes No Magnetic

Magnetic Resonant Coupling

High High Short Difficult No Safe

EM Radiation

Omnidirectional Low Low Long Yes Yes Safe

Unidirectional (microwave/laser)

High High Very long (LOS)

No No EM

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Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore

Page 19: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Application Examples

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Part I: Wireless Power: History and State-of-the-Art

Inductive Coupling

Magnetic Resonant Coupling

EM

Radiation

The Qi wireless mobile device charging Standard

Electric tooth brush Wireless powered medical implants

Qualcomm eZone wireless charging

Qualcomm Halo electric vehicle powered by charging pad

Haier wireless powered HDTV

Intel WISP RFID tags harvest energy from RF radiation

Powercast RF harvesting circuit for sensor networks

The SHARP unmanned plane receives energy beamed from the ground

Rui Zhang, National University of Singapore

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Agenda

• Part I: Wireless Power: History and State-of-the-Art

• Part II: Overview of Wireless Powered Communications

• Part III: Case Studies and Extended Work

ICC 2014 20

Introduction Rui Zhang, National University of Singapore

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Part II

Overview of Wireless Powered Communication

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

Page 22: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Outline of Part II

Microwave Enabled Wireless Power Transfer (WPT) Energy receiver structure Energy beamforming in MIMO channel

Wireless Powered Communication Network (WPCN)

Harvest-then-transmit protocol Doubly near-far problem

Simultaneous Wireless Information an Power Transfer (SWIPT)

SWIPT receiver structures Rate-energy tradeoff

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Point-to-Point Wireless Power Transfer: Channel Model

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Modulated vs. Unmodulated Energy Signal

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Part II: Overview of Wireless Powered Communications

Use pseudo-random modulated energy signal to avoid the spike in the power spectral density (PSD) caused by constant unmodulated energy signal

Rui Zhang, National University of Singapore

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Wireless Power Transfer: Receiver Structure (1)

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Wireless Power Transfer: Receiver Structure (2)

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Part II: Overview of Wireless Powered Communications

[4]

Rui Zhang, National University of Singapore

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Scaling Up WPT: Energy Beamforming in MIMO Channel

Antenna gain Path loss Energy conversion efficiency: 30% - 70%

Ga (# of Tx antennas)×(# of Rx antennas) e.g.: 2×1 (3dB gain), 4×1 (6dB gain)…

Diversity gain in fading channel (additional)

Q: What’s the optimal transmitting strategy given a limited power budget?

A: Energy Beamforming (EB)

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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EB for Point-to-Point MIMO Channel

The harvested energy is

Energy beamforming (EB): Tx steers beam(s) towards the Rx(s) to maximize the energy transfer efficiency EB is achieved by adjusting the transmit covariance matrix S The rank of S indicates the number of beams generated

The optimal EB is the principal eigenvector beamforming [1]

Implementation via distributed antennas: collaborative energy beamforming [5]

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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MIMO Wireless Power Multicasting

Utilize the broadcast nature of microwave propagation for energy multicast

Energy near-far problem: fairness is a key issue in the multicast EB design May need to generate multiple beams to balance the energy harvesting performance

In any case, the design of EB requires the accurate knowledge of channel state

information at the transmitter (CSIT)

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Energy Beamforming w/o Full CSIT

Full CSIT is often not available due to Hardware constraints at the energy receivers (rectifiers w/o baseband processing) High channel estimation energy cost that may offset the gain from energy beamforming

Candidate solutions:

Isotropic transmission (no CSIT needed, low efficiency) EB based on reverse-link training (exploiting channel reciprocity) EB based on statistical CSIT (mean, covariance etc.) EB based on limited feedback from the energy receivers

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Part II: Overview of Wireless Powered Communications

A two-phase WPT protocol

Rui Zhang, National University of Singapore

Page 31: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Energy Beamforming Based on One-bit Feedback [6]

Each receiver feeds back one bit information indicating its change of harvested energy compared to the previous time slot

The transmitter adjusts its beamforming strategy based on the feedback bits (more details given later)

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Wireless Powered Communication Network: A General Model

Information flow

Energy flow

RF Powered Wireless Network Downlink (Access Point → Wireless Terminals )

Uplink (Wireless Terminals → Access Point)

“Asymmetric” information/energy flow Need joint energy and communication scheduling and resource allocation

Wireless information and power transfer (DL) Orthogonal vs. simultaneous information and energy transmissions To be detailed in the discussion of SWIPT

Information transfer with wireless harvested energy (UL)

Performance tradeoff between DL (energy + information) vs. UL (information)

Wireless Terminals (each with a rechargeable battery)

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Joint Energy & Information Scheduling and Resource Allocation

Harvest-then-transmit protocol [2] Phase I: mobile terminals harvest energy from AP Phae II: transmit information under the harvested energy budget Similar design applies in frequency division based Energy and Info scheduling

TDMA-based multiple access

EB in the DL User air time allocation in the UL

SDMA-based multiple access EB in the DL Spatial multiplexing in the UL

Joint DL beamforming & UL power control

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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“Doubly” Near-far Problem

Doubly Near-Far Problem Due to distance-dependent signal attenuation in both DL and UL “Near” user harvests more energy in DL but transmits less power in UL “Far” user harvest less energy in DL but transmits more power in UL Unbalanced energy consumptions in the network: need more careful resource allocation

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Part II: Overview of Wireless Powered Communications

Possible Solutions: Adaptive UL time allocation (TDMA) Joint DL EB and UL power control (SDMA) User cooperation (near user helps relay far user's message) [7]

Rui Zhang, National University of Singapore

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Wireless Powered Network Capacity

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Part II: Overview of Wireless Powered Communications

Hybrid cellular network: cellular network + power beacons (PBs) to power mobile devices [8]

Design parameters: p,q: the transmit power of BSs and PBs 𝜆𝑏 , 𝜆𝑝: densities of PPP of BSs and PBs

Objective : optimize (p,q, 𝜆𝑏, 𝜆𝑝) to maximize the

network throughput and yet guarantee the outage performance of information and power transfer

Cognitive radio network [9]: ST can harvest energy from any nearby PT if it is in

the PT’s harvesting zone ST cannot transmit if it is in the guard zone of any PT

Objective: maximize the secondary network throughput under opportunistic energy harvesting

Rui Zhang, National University of Singapore

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Simultaneous Wireless Information and Power Transfer

Wireless Power Transfer vs. Wireless Information Transfer Wireless Power Transfer

Energy (in Joule) is linearly proportional to both time and power

Wireless Information Transfer Information quantity (in bits) increases linearly with time but logarithmically with power

Example: power allocation in frequency selective channel [10]

Tesla’s approach: allocate all power to a single sinusoid tone (zero bandwidth) Shannon’s approach: water-filling power allocation Similar tradeoff exists in spatial domain (MIMO system) power allocation [1]

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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MIMO SWIPT with Two Separate EH and ID Terminals Rate-energy region: all the achievable rate and energy pairs under a given

transmit power constraint P

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Part II: Overview of Wireless Powered Communications

Each terminal has 4 antennas, P = 1W, EH receiver 1m, ID receiver 10m distance

eigenmode transmission + WF

energy beamforming

Rui Zhang, National University of Singapore

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Separate EH and ID Receivers: a Network Perspective

The receiver “sensitivity” issue (different receiver operating power) Wireless information receiver: > -60dBm Wireless energy receiver: > -10dBm

Near-Far based transmission scheduling Harvest energy when user is close to H-AP Receive information when user is far from H-AP

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Part II: Overview of Wireless Powered Communications

Maximize weighted sum energy harvested for EH receivers under SINR constraints for ID receivers

Rui Zhang, National University of Singapore

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Rate-Energy Tradeoff for an Ideal Co-located EH/ID Receiver

An ideal receiver can harvest the energy and decode information simultaneously However, practical receiver cannot achieve both from the same signal

Rate-energy tradeoff in a discrete memoryless channel [11]

Rate-energy performance upper bound

e.g., SISO AWGN channel:

Capacity-energy function

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Separate Information and Energy Receivers: General Structure

In practice, energy cannot be harvested after information decoding Received signal splits at RF band (point A) Power splitting ratio can be set differently over time: Dynamic Power Splitting (DPS)[4]

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Part II: Overview of Wireless Powered Communications

Energy Receiver

Information Receiver

Rui Zhang, National University of Singapore

Page 41: Wireless Powered Communication: Opportunities and Challenges · Wireless Powered Communication: Opportunities and Challenges Rui Zhang ... Introduction Rui Zhang, ... Energy Beamforming

Information Receiver

RF to baseband conversion by mixers, which are active devices (power consuming)

Equivalent AWGN baseband channel

Maximum achievable rate

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Part II: Overview of Wireless Powered Communications

antenna noise

RF-to-baseband conversion noise

Rui Zhang, National University of Singapore

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Dynamic Power Splitting

In a block transmission of N symbols

Information receiver is OFF in the first symbols, and ON in the remaining symbols Dynamic Power Splitting: for the k-th symbol, split the signal into two streams with

power ratio for energy harvesting (EH) and for information decoding (ID).

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Dynamic Power Splitting

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Rate-Energy Region of Separate Receivers

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Numerical Example (Separated Receivers)

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Integrated Information and Energy Receivers Structure

Received signal splits at banseband (point B)

Information is carried in the DC signal Conventional modulation (e.g., QAM) and coherent demodulation thus

not applicable Solution: energy modulation & demodulation

Advantages of integration:

RF to baseband conversion is by passive diode -> less circuit power Integrated EH and ID circuits -> smaller form factor

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Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore

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Rate-Energy Region of Integrated Receivers

Recall that the DC signal is

The input to information decoder is

SNR is in principle independent of the power splitting ratio

Setting , to maximize the harvested energy.

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Rate-Energy Region of Integrated Receivers

The equivalent channel model

The capacity of the above channel is the maximum mutual information over all input distribution satisfying

Energy modulation: information is only modulated to the energy (amplitude) of the signal.

Optimal scheme is SPS with

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Part II: Overview of Wireless Powered Communications

rectifier noise

Rui Zhang, National University of Singapore

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Numerical Example (Integrated Receivers)

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Rate-Energy Region with Receiver Circuit Power Consideration

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Numerical Example (with Receiver Circuit Power Consideration)

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Practical Example

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Point-to-Multipoint SWIPT: Harmful vs. Helpful Interference

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Part II: Overview of Wireless Powered Communications

Co-channel interference exists in downlink information transmission Interference is harmful to wireless information transmission (treated as noise if

not decodable at receiver) But helpful to wireless energy transmission (additional source of energy

harvesting at receiver) Joint energy & Info beamforming for interference management in SWIPT

One energy & Info Tx, many co-located receivers

Rui Zhang, National University of Singapore

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Dynamic Time Switching over Fading Channels

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Part II: Overview of Wireless Powered Communications

Fading channel + Interference

Opportunistic EH and ID [12]: decode information when SNR is

sufficiently high and received signal (information + interference) is weak

Harvest energy otherwise.

Optimal EH and ID operating region characterization.

The region within the triangle is the optimal operating region for information decoding given a pair of channel power and interference power (h,I)

Rui Zhang, National University of Singapore

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DPS over Fading Channels

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Part II: Overview of Wireless Powered Communications

A more general scheme is DPS between EH and ID receivers based on the fading state [13] Time switching is the special case with on/off (binary) power splitting ratio 𝛼.

Optimal power splitting rules: When fading state is “poor”, all received power is allocated to information receiver. When fading state is “good”, received power split between the information and energy receivers

(constant power to the information receiver).

Rui Zhang, National University of Singapore

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Dynamic Power Splitting vs.Dynamic Antenna Switching

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Part II: Overview of Wireless Powered Communications

Dynamic antenna switching between EH and ID is a special case of DPS with on/off (binary) power splitting ratio 𝛼 per receive antenna.

DPS achieves better R-E region than antenna switching, but antenna switching has much lower hardware complexity.

Rui Zhang, National University of Singapore

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Multi-Transmitter Collaborative SWIPT

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An 2×2 interference channel for SWIPT with TS receivers

Receivers can use time switching (TS) from four modes [14]: (EH,EH), (EH,ID), (ID,EH),(ID,ID)

Receivers can also use power splitting to balance the rate-energy performance [15,16]

Interference channel rate-energy tradeoff characterization [5]

Rui Zhang, National University of Singapore

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Part II: Overview of Wireless Powered Communications

SWIPT with Energy/Information Relaying

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Source Relay Destination h g

information transmission

energy transmission

A relay-assisted link, where the relay is wirelessly charged by RF signals from the source [17,18]

S R Information Transmission

S R Energy Transmission

R D Information Transmission

T

αT (1-α)T/2 (1-α)T/2

S R Energy Transmission (1-ρ)P

S R Information Transmission ρP

R D Information Transmission

T

T/2 T/2

TS Relay

PS Relay

Rui Zhang, National University of Singapore

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Part II: Overview of Wireless Powered Communications

SWIPT in Multi-User OFDM

OFDMA with PS receivers : PS is performed before digital OFDM demodulation.

Thus, all subcarriers would have the same PS ratio at each receiver.

TDMA with TS receivers : Each user performs ID when information is scheduled

for that user, and performs EH in all other time slots

R-E tradeoff characterizations for multi-carrier SWIPT [19-21].

Multi-user OFDM OFDM Receiver with Power Splitting (PS)

Rui Zhang, National University of Singapore

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ICC 2014 60

Part II: Overview of Wireless Powered Communications

Summary of Part II

Wireless energy and information transmission are fundamentally different Linear vs. logarithm objective with power

Single tone vs. waterfilling power allocation (frequency and spatial)

Helpful vs. harmful interference

Enhance the efficiency of energy and information transfer MIMO energy beamforming and multicast

SWIPT

Practical receiver structures: Time switching, power splitting, antenna switching, integrated receiver, etc.

Rate-energy tradeoff.

Wireless powered communication networks Need joint energy and communication scheduling and resource allocations

Doubly near-far problem calls for new design and solution

Future research directions Fundamental limits in SWIPT: still open

Practical design in PHY, MAC, and Network layers for wireless powered

communications

Energy beamforming for WPT under limited feedback

Rui Zhang, National University of Singapore

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Agenda

• Part I: Wireless Power: History and State-of-the-Art

• Part II: Overview of Wireless Powered Communications

• Part III: Case Studies and Extended Work

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Part III: Case Studies and Extended Work Rui Zhang, National University of Singapore

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62 ICC 2014

Part III

Case Studies and Extended Work

Part III: Case Studies and Extended Work Rui Zhang, National University of Singapore

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63 ICC 2014

Wireless Power Transfer Wireless Powered Communication

SWIPT: Separate EH/ID Receivers

Energy transfer Information transfer

SWIPT: Co-located EH/ID Receivers

Recap of Part II

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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Outline of Part III

Wireless power transfer (WPT) Energy beamforming (EB) with limited feedback [6]

Wireless powered communication network (WPCN) Joint energy and communication scheduling for throughput

optimization [2]

Simultaneous wireless information and power transfer (SWIPT) Joint energy and information beamforming for separate EH/ID

receivers [22] and co-located EH/ID receivers [23]

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Part III: Case Studies and Extended Work Rui Zhang, National University of Singapore

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Case Study I: EB with Limited Feedback

Wireless power transfer in one direction (DL) only Assume UL communication links available (but not shown here) for energy

scheduling and channel training (to be detailed later)

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Energy transfer

1U

2U

KU

H1

H2

HK Energy Transmitter

One energy transmitter (ET) K energy receivers (ERs): Multiple antennas at ET: Multiple antennas at ER: Quasi-static flat fading channels Block duration:

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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EB in Multiuser MIMO

ET sends energy beams to all ERs:

with transmit covariance matrix Energy harvested by ER k:

with MIMO channel

Weighted sum-energy harvested:

with effective MIMO channel (for all ERs)

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Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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Optimal EB with Perfect CSIT

Problem formulation Weighted sum-energy maximization Convex optimization problem Objective function: linear Constraints: convex

Closed-form optimal solution is rank-one Single-beam EB is optimal

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where and denote dominant eigenvalue and corresponding eigenvector of effective MIMO channel

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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Practical Challenges to Acquire CSIT

Full CSIT is often not available Hardware constraints at ER: rectifiers w/o baseband processing High channel estimation/feedback energy cost that may offset gain from EB

Candidate solutions Isotropic transmission (no CIST needed, low efficiency) EB based on reverse-link training (TDD, assuming channel reciprocity) EB based on statistical CSI (mean, covariance, etc.)

Proposed solution: EB based on one-bit feedbacks from ERs

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Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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EB with One-Bit Feedback

ER k feeds back one-bit information indicating increase or decrease of harvested energy between time slots n and n-1 Need no hardware change at ERs Simultaneous energy harvesting not interrupted

With one-bit feedbacks, ET Adjusts transmit beamforming for next slot Improves estimation of channels (to be detailed later)

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Two-Phase WPT Protocol (1)

Phase 1 Channel Learning: feedback intervals each of length In the nth interval ET sends one or more energy beams with covariance Each ER measures its harvested energy Each ER feeds back one bit to ET based on

ET updates based on ’s

After channel learning phase, ET estimates as , and obtains estimated dominant eigenvector of as

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Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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Two-Phase WPT Protocol (2)

Phase 2 Energy transmission: ET sends one single energy beam with covariance

Total harvested energy over two phases

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energy harvested in Phase 1

energy harvested in Phase 2

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ACCPM Based Channel Learning: Single ER

Objective: find any point in target set Analytic center cutting plane method (ACCPM) [24] : Iteratively shrink working set towards target set. In the nth iteration Find analytic center of working set Find cutting plane whose boundary passes (neutral cutting plane) Cut away half space according to cutting plane to obtain new working set

Q: How to cut half-space? A: Based on one-bit feedback (energy increase or decrease at ER)

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1n P

X

C u tt in g p la n e

nH

1n n nP P H

X

G(n) G(n) ~ ~

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Convergence Analysis: Single-ER Case

ACCPM based single user channel learning algorithm obtains estimation for with in at most intervals Convergence speed only depends on No. of transmit antennas , but

not on No. of receive antennas

Reason: Dimension of :

Theoretical bound only, faster convergence is often observed in simulation

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ACCPM Based Channel Learning: Multiple ERs

Challenge beyond single-ER case Update of to satisfy , , i.e., neutral

cutting plane is infeasible if

Solution: ERs grouping Divide ERs into subsets ’s, each with no more than ERs Partition total channel learning slots into subsets ’s For time slots in , ET estimates channels of users in based on their

one-bit feedbacks

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Convergence Analysis: Multi-ER Case

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ACCPM based multiuser channel learning algorithm obtains estimations for all ERs with in at most intervals Recall complexity of single-user case: If , proposed algorithm learns all ERs’ channels

simultaneously w/o reducing convergence speed (in worst-case analysis)

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Simulation Result: Setup

6 ERs, all 5 meters from ET ET with antennas, each ER with antennas Rician fading channels Transmit power: Energy transfer efficiency:

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ET

ER 1

ER 2

ER 3

ER 4

ER 5

ER 6

5 meters

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Simulation Result: Baseline Schemes

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Partial CSIT: existing one-bit feedback based channel learning schemes Cyclic Jacobi technique (CJT) [25]

One-bit feedback: increase or decrease in received power Usage of feedback: perform blind estimate of EVD of MIMO channel Application: MIMO, one receiver only

Gradient sign [26] One-bit feedback: increase or decrease in received power Usage of feedback: adjust transmit beam with random perturbation Application: MIMO, one receiver only

Distributed beamforming [27] One-bit feedback: larger or smaller than prior highest received power Usage of feedback: adjust phase of transmit beam Application: MISO, one receiver only

Perfect CSIT: optimal EB No CSIT: isotropic transmission

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Simulation Result: Single-ER Case

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CJT: discrete error points Gradient sign and distributed beamforming: larger step size yields faster

convergence but more fluctuations ACCPM: best accuracy & convergence

Only ER 1 is active

Absolute error of harvested power versus No. of feedback intervals

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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Simulation Result: Single-ER Case

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ACCPM & CJT: harvested power first increases then decreases with No. of feedback intervals

ET transmits with full rank covariance in channel learning phase, not optimized for wireless power transfer

Gradient sign & distributed beamforming: harvested power increases with

Only ER 1 is active, fixed 200 time intervals

Harvested power versus No. of feedback intervals

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Simulation Result: Single-ER Case

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Harvested energy approaches optimal value with perfect CSIT as block-length increases

More accurate channel estimation with lower training overhead

ACCPM achieves the largest harvested energy (albeit moderately)

Only ER 1 is active, optimal

Harvested power versus No. of total time intervals

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Simulation Result: Multiple-ER Case

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Similar to single-ER case Harvested energy increases with block-length ACCPM achieves maximum harvested energy (but much more substantially, due to

simultaneous estimation of multiple channels)

ERs 1-6 are all active, optimal

Harvested power versus No. of total time intervals

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Summary and Future Work

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Summary Challenges in acquiring CSI for WPT: receiver hardware constraints;

energy cost ACCPM based channel learning

One-bit feedback: based on received energy level only, no baseband processing needed

Estimate multiuser MIMO channels simultaneously

Extension and Future work More than one bits feedback Exploit channel reciprocity [28] Energy transfer and channel learning trade-off Near-far problem and fairness issue

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Case Study II: Resource Allocation in Wireless Powered Communication Networks

Wireless power transfer (WPT) from H-AP to users in DL Wireless information transmission (WIT) from users to H-AP in UL by TDMA

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One hybrid AP (H-AP) K user terminals Single antenna at all nodes Quasi-static flat-fading channels

Energy transfer Information transfer

1h

1U

2U

KU

2h

Kg

1g

2g

Kh

H-AP

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Harvest-then-Transmit-Protocol

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WPT in DL Energy broadcast with time duration Energy harvested by user i: ,

WIT in UL TDMA, each user with time duration Transmit power at user i: Achievable rate of user i:

where is effective channel accounting for both DL and UL channels

Trade-off: rate per user increases with both DL and UL time allocated given a total time constraint:

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DL-UL Time Allocation Trade-off

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Zero throughput with or Throughput increases over when it is small, decreases over otherwise With small , DL WPT time dominates throughput With large , UL WIT time dominates throughput Optimal DL vs. UL time allocation?

Throughput versus DL-UL time allocation, , , in a single-user setup, with effective channel gain

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Sum-Throughput Maximization

Problem formulation Convex optimization problem Objective function: concave Constraints: linear

Closed-form optimal solution Time allocated to DL WPT and

users in UL WIT ’s should be all non-zero

decreases with , increases with

Ratio between time allocated to two users in UL WIT:

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where is the sum of users’ effective channel

gains, is constant satisfying

doubly near-far problem

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Doubly Near-Far Problem

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Doubly near-far problem: Distance-dependent signal attenuation in both DL and UL “Near” user harvests more energy in DL and has less power loss in UL “Far” user harvests less energy in DL but has more power loss in UL

Unfair time and rate allocation among users

Sum-throughput versus time allocation (two-user)

One H-AP Two users: distance to H-AP Channel models: Pathloss exponents: Optimal time allocation: , or Optimal rate allocation:

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Doubly Near-Far Problem

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Rate ratio (user 2 over user 1) decreases twice faster in the logarithm scale than conventional TDMA (with constant transmit power) due to doubly near-far problem

Wireless powered communication network: TDMA network:

Fairness issue needs to be solved

Rate ratio versus pathloss exponent (two-user)

One H-AP Two users: distance to H-AP Channel models: Identical pathloss exponents:

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Common-Throughput Maximization

Problem formulation Convex optimization problem Objective function: single variable Constraints: all convex

Closed-form optimal solution not available

Proposed optimal solution Use bisection method Given , solve a convex feasibility

problem

With optimal solution Equal throughput for all users is

ensured

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Common-Throughput versus Sum-Throughput

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More time allocated to far user, i.e., user 2 Fairness achieved, but sum-throughput reduced

Sum-throughput versus time allocation Common-throughput versus time allocation

Two users with distance

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Common-Throughput versus Sum-Throughput

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Time allocation ratio between (far) user 2 and (near) user 1, , increases with in (P2), but decreases with in (P1) (to tackle the more severe doubly near-far problem)

Time allocation ratio versus pathloss exponent

Two users with distance (P1): sum-throughput maximization (P2): common-throughput maximization Comparison of ratio of time allocated to

user 2 and user 1 in (P1) versus (P2)

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Simulation Result

ICC 2014 92

As pathloss increases, Sum-throughput maximization: user 1’s throughput converges to sum-

throughput, user 2’ throughput approaches zero Common-throughput maximization: both users’ throughput decrease

quickly towards zero

Throughput versus pathloss exponent

Two users User 1: 5m away from H-AP User 2: 10m away from H-AP

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Extension: Multi-Antenna Wireless Powered Communication Network [29]

WPT in DL: energy beamforming Higher WPT efficiency than SISO Adjust beam weights to control energy transferred to near/far users: better fairness

WIT in UL: SDMA Higher spectrum efficiency than TDMA Interference mitigation via receive beamforming

ICC 2014 93

Energy transfer Information transfer

1U

2U

KU

h1

g1 h2

g2

hK

gK

One H-AP with M>1 antennas K single-antenna user terminals

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Harvest-then-Transmit Protocol (Revised)

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AP 1

U

DL for WET UL for WIT

KU

τT (1-τ)T

WPT in DL: H-AP sends energy beams: Energy harvested by user k:

WIT in UL: Available transmit power at user k: Each user k sends simultaneously SINR of user k with receive beamforming vector :

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Common-Throughput Maximization

Problem formulation Common-throughput maximization Joint optimization of DL-UL time

allocation, DL energy beamforming, UL power control and receive beamforming (MMSE)

Non-convex optimization problem Objective function: non-concave UL power constraints: non-convex

Proposed optimal solution Non-negative matrix theory (details

omitted here, see [29])

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Summary and Future Work

ICC 2014 96

Summary Sum-throughput maximization in wireless powered communication

network (WPCN) Trade-off in UL-DL time allocations

Better UL channels lead to shorter DL WPT time for both TDMA and SDMA

Trade-off in UL time/power allocations among users (in TDMA/SDMA) Doubly near-far problem

Common-throughput maximization in WPCN More time/power is allocated to far users

Fairness versus throughput trade-off

Extension and Future work Partial/imperfect CSIT Multi-cell and network level optimization Broadband channel with frequency selective fading Full-duplex energy and information transmission [30]

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Case Study III: Joint Information and Energy Beamforming Design for SWIPT

SWIPT with Separate EH/ID Receivers

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SWIPT with Co-located EH/ID Receivers

Energy transfer Information transfer

1U

h1

hK

g1

gK

UK

UK +1

UK +K

E

E

E

E

I

I

Energy transfer Information transfer

1U

2U

KU

h1

g1=h1 h2

hK

g2=h2

gK=hK

AP: M antennas Single-antenna ID receivers: Single-antenna EH receivers:

AP: M antennas K single-antenna receivers with co-located

EH/ID receivers

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Case of Separate EH/ID Receivers

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MISO broadcast system for SWIPT: exploit near-far channel conditions “Near” users are scheduled for energy harvesting (EH) “Far” users are scheduled for information decoding (ID)

A P

Energy transfer

Information transfer

EH Receivers

ID Receivers

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Information and Energy Beamforming

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AP sends information and energy signals simultaneously with transmit beamforming and power control Balance between information and energy transmission

information signal energy signal

: information-bearing (random) signal : energy-carrying (pseudo-random) signal : information beamforming vector : energy beamforming vector

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ID Receivers

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Received signal at ID receivers (harmful interference)

Type I ID receivers: Can not cancel interference from energy signals

Type II ID receivers: Can cancel interference from energy signals

interference from all other information beams

extra (pseudo-random) interference from all energy beams

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EH Receivers

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Energy harvested by EH receivers (useful interference)

Weighted sum-energy harvested by all EH receivers

where denotes effective MIMO channel

energy harvested from all information beams

energy harvested from all energy beams

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Problem Formulation

Weighted sum-energy maximization for EH ERs subject to individual SINR constraints at ID receivers

Challenge: Maximizing convex quadratic functions, thus non-convex quadratically constrained quadratic programs (QCQP)

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Type I ID receiver Type II ID receiver

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SDR-Based Optimal Solution to (P1)

Define ,

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dropping rank-1

constraints

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Tightness of SDR to (P1)

Optimal solution to (SDR1) satisfies (assuming i.i.d. user channels)

, SDR of (P1) is tight

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solvable by CVX

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

no dedicated energy beams used (since Type I ID receivers considered), WPT by adjusting information beams only

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SDR-Based Optimal Solution to (P2)

Similar to (P1), SDR of (P2) is given as

Optimal solution to (SDR2) satisfies (assuming i.i.d. user channels)

, SDR of (P2) is tight

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dominant eigenvector of

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

at most one energy beam used (since Type II ID receivers considered), WPT by adjusting both energy and information beams in general

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Alternative Approach: Uplink-Downlink Duality

Both (P1) and (P2) are equivalent to power minimization problem in dual uplink, with effective noise covariance For (P1), (a new non-trivial case to solve) For (P2),

Both (P1) and (P2) are solvable by well-known fixed point method (details omitted here, see [22])

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Uplink-downlink duality for MISO-BC and SIMO-MAC

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Simulation Result

Type I and Type II receivers have the same performance when When Type I and Type II receivers perform similarly for very small or large Type II receiver outperforms Type I receiver for medium (thanks to

energy signal cancellation at ID receivers)

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No. of transmit antennas: No. of EH receivers: Transmit power at AP: Channel model: 200 random

realizations from Rayleigh fading Same SINR constraints for all ID

receivers,

Harvested energy versus SINR constraints

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Case of Co-located EH/ID Receivers

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MISO broadcast system with co-located ID and EH receivers Unified information and energy beamforming Each receiver coordinates EH and ID based on power splitting (PS)

PS receiver: received signal is split to EH and ID receivers with ratios ,

Multi-antenna AP coordinates information and energy transfer to K single-antenna users

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

1U

2U

KU

h1

g1=h1 h2

hK

g2=h2

gK=hK

Energy transfer Information transfer

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Signal Model (1)

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AP sends one unified information/energy signal for each user

Received signal at each user

: information-bearing signal : beamforming vector

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Signal Model (2)

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Signal split to ER

Harvested energy

Signal split to IR

SINR

zk

: antenna noise : IR’s noise

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Problem Formulation

Objective: Minimize transmit power Subject to: Individual SINR constraints Individual harvested energy constraints

Non-convex problem: Coupled and Quadratic terms with

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Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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SDR-Based Optimal Solution

Define

Optimal solution to SDR satisfies , , i.e., SDR is tight

All constraints are met with equality

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SDR

convex problem, solvable by CVX

Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work

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Suboptimal Solutions

Main idea: fix directions of beamforming, optimize transmit power allocations and receive PS ratios

Suboptimal solution I Zero-forcing beamforming: Applicable when No. of transmit antennas > No. of users

Suboptimal solution II SINR-optimal beamforming: ’s are obtained by ignoring energy

constraints Applicable for arbitrary No. of transmit antennas

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Simulation Result

Transmit power increases substantially with e When is small, performance gap is more significant

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AP is equipped with 4 antennas 4 users, each is 5m away from AP Rician fading channels Energy harvesting efficiency: Antenna noise: IR’s noise:

Fix energy harvesting targets , , and vary SINR targets ,

Transmit power versus SINR

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Extension: SWIPT w/o CSIT [31]

In case of no CIST Random beamforming helps (by generating artificial channel fading) Receivers: threshold-based switching between EH and ID EH when received power is above threshold ID when received power is below threshold

Substantial rate-energy performance gain over periodic switching

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Transmitter and receiver structures for case of no CSIT: random beamforming at transmitter, and threshold based mode switching at receivers.

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Extension: Secure Communication in SWIPT [32]

Security issue in SWIPT Near-far based scheduling: ERs can eavesdrop IRs’ information easily Availability of CSI at AP for both IRs and ERs

Two conflicting goals: Energy transfer: received power at each ER should be large Secure information transfer: received power at each ER should be small

Proposed solution: dual use of energy signals (one IR and K ERs)

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energy signal artificial noise

A P

ERs

IRs

information signal

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Summary and Future Work

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Summary Separate EH/ID receivers in MISO SWIPT

If energy interference not cancelled at ID receivers, no energy beam is used If energy interference cancelled at ID receivers: one energy beam is optimal

Co-located EH/ID receivers in MISO SWIPT Unified information/energy beamforming Joint optimization with receiver power splitting

Rate-energy trade-off characterization

Extension and Future work Fundamental R-E trade-offs in SWIPT (see e.g., [33]) Partial/imperfect CSIT (see e.g., [34]) Other system and network models (see e.g., [35], [36], [37])

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Concluding Remarks

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Wireless RF Powered Communication Fundamental limits: still open Many new design challenges in PHY, MAC, and Network layers

Hardware Development

Wireless power transfer (energy beamforming, high-efficiency rectenna, waveform design,…) Practical receivers for SWIPT (e.g., time switching, power splitting, antenna switching, integrated receiver,…)

Applications

Wireless sensor/M2M networks (IoT, IoE) Cellular networks (small cells? millimeter-wave?) …

Concluding Remarks Rui Zhang, National University of Singapore

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Acknowledgement

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Material preparation Suzhi Bi Liang Liu

Others Jie Xu Hyungsik Ju Xun Zhou Seunghyun Lee

Acknowledgement Rui Zhang, National University of Singapore

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References

References

[1] R. Zhang and C. K. Ho, “MIMO broadcasting for simultaneous wireless information and power transfer,” IEEE Transactions on Wireless Communications, vol. 12, no. 5, pp. 1989-2001, May 2013. [2] H. Ju and R. Zhang, “Throughput maximization in wireless powered communication networks,” IEEE Transactions on Wireless Communications, vol. 13, no. 1, pp. 418-428, Jan. 2014. [3] L. Xie, Y. Shi, Y. T. Hou, and H. D. Sherali, “Making sensor networks immortal: an energy-renewable approach with wireless power transfer,” IEEE/ACM Transactions on Networking, vol. 20, no. 6 pp. 1748-1761, Dec. 2012. [4] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power transfer: architecture design and rate-energy tradeoff,” IEEE Transactions on Communications, vol. 61, no. 11, pp. 4757-4767, Nov. 2013. [5] S. Lee, L. Liu, and R. Zhang, “Collaborative wireless energy and information transfer in interference channel,” submitted to IEEE Transactions on Wireless Communications. (available on-line at arXiv:1402.6441) [6] J. Xu and R. Zhang, “Energy beamforming with one-bit feedback,” submitted to IEEE Transactions on Signal Processing. (Available on-line at arXiv:1312.1444) [7] H. Ju and R. Zhang, “User cooperation in wireless powered communication networks,” submitted to IEEE Global Communications Conference (Globecom), 2014. (available on-line at arXiv:1403.7123)

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References

[8] K. Huang and V. K. N. Lau, “Enabling wireless power transfer in cellular networks: architecture, modeling and deployment,” IEEE Transactions on Wireless Communications, vol. 13, no. 2, pp. 902-912, Feb. 2014. [9] S. Lee, R. Zhang, and K. B. Huang, “Opportunistic wireless energy harvesting in cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 9, pp. 4788-4799, Sept. 2013. [10] P. Grover and A. Sahai, “Shannon meets Tesla: wireless information and power transfer”, in Proc. IEEE ISIT, pp. 2363-2367, 2010. [11] L. R. Varshney, “Transporting information and energy simultaneously,” in Proc. IEEE ISIT, pp. 1612-1616, 2008. [12] L. Liu, R. Zhang, and K. C. Chua, “Wireless information transfer with opportunistic energy harvesting,” IEEE Transactions on Wireless Communications, vol. 12, no. 1, pp. 288-300, Jan. 2013. [13] L. Liu, R. Zhang, and K. C. Chua, “Wireless information and power transfer: a dynamic power splitting approach,” IEEE Trans. Communications, vol. 61, no. 9, pp. 3990-4001, Sept. 2013. [14] J. Park and B. Clerckx, “Joint wireless information and energy transfer in a two-user MIMO interference channel,” IEEE Trans. Wireless Communications, vol. 12, no. 8, pp. 4210-4221, Aug. 2013. [15] C. Shen, W. C. Li, and T. H. Chang, “Simultaneous information and energy transfer: a two-user MISO interference channel case,” in Proc. IEEE Globecom, 2012. [16] S. Timotheou, I. Krikidis, and B. Ottersten, “MISO interference channel with QoS and RF energy harvesting constraints,” in Proc. IEEE ICC, 2013. [17] A. A. Nasir, X. Zhou, S. Durrani, and R. A. Kennedy, “Relaying protocols for wireless energy harvesting and information processing,” IEEE Trans. Wireless Communications, vol. 12, no. 7, Jul. 2013.

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References

[18] I. Krikidis, S. Timotheou, and S. Sasaki, “RF energy transfer for cooperative networks: data relaying or energy harvesting,” IEEE Wireless Communication Letters, vol. 16, no. 11, pp. 1772-1775, Nov. 2012. [19] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power transfer in multiuser OFDM systems,” IEEE Trans. Wireless Communications, vol. 13, no. 4, pp. 2282-2294, Apr. 2014. [20] K. Huang and E. Larsson, ``Simultaneous information and power transfer for broadband wireless systems", IEEE Trans. Signal Processing, vol. 61, No. 23, pp. 5972-5986, Dec 2013. [21] D. W. K. Ng, E. S. Lo, and R. Schober, ``Wireless information and power transfer: energy efficiency optimization in OFDMA systems," IEEE Trans. Wireless Communications, vol. 12, no. 12, pp. 6352-6370, Dec. 2013. [22] J. Xu, L. Liu, and R. Zhang, “Multiuser MISO beamforming for simultaneous wireless information and power transfer,” submitted to IEEE Transactions on Signal Processing. (Available on-line at arXiv:1303.1911) [23] Q. Shi, L. Liu, W. Xu, and R. Zhang, “Joint transmit beamforming and receive power splitting for MISO SWIPT systems,” to appear in IEEE Transactions on Wireless Communication. (Available on-line at arXiv:1304.0062) [24] S. Boyd, “Convex optimization II,” Stanford University. Available online at http://www.stanford.edu/class/ee364b/lectures.html. [25] Y. Noam and A. Goldsmith, “The one-bit null space learning algorithm and its convergence,” IEEE Transactions on Signal Processing, vol. 61, no. 24, pp. 6135-6149, Dec. 2013. [26] B. C. Banister and J. R. Zeidler, “A simple gradient sign algorithm for transmit antenna weight adaptation with feedback,” IEEE Transactions on Signal Processing, vol. 51, no. 5, pp. 1156-1171, May 2003.

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References

[27] R. Mudumbai, J. Hespanha, U. Madhow, and G. Barriac, “Distributed transmit beamforming using feedback control,” IEEE Transactions on Information Theory, vol. 56, no. 1, pp. 411-426, Jan. 2010. [28] Y. Zeng and R. Zhang, “Optimal training for wireless energy transfer,” submitted to IEEE Global Communications Conference (Globecom), 2014. (available on-line at arXiv:1403.7870) [29] L. Liu, R. Zhang, and K. C. Chua, “Multi-antenna wireless powered communication with energy beamforming,” submitted to IEEE Transactions on Communications. (Available on-line at arXiv:1312.1450) [30] H. Ju and R. Zhang, “Optimal resource allocation in full-duplex wireless powered communication network,” submitted to IEEE Transactions on Communications.(available on-line at arXiv:1403.2580) [31] H. Ju and R. Zhang, “A novel model switching scheme utilizing random beamforming for opportunistic energy harvesting,” IEEE Transactions on Wireless Communication, vol. 13, no. 4, pp. 2150-2162, Apr. 2014. [32] L. Liu, R. Zhang, and K. C. Chua, “Secrecy wireless information and power transfer with MISO beamforming,” IEEE Transactions on Signal Processing, vol. 62, no. 7, pp. 1850-1863, Apr. 2014. [33] P. Popovski, A. M. Fouladgar, and O. Simeone, “Interactive joint transfer of energy and information,” IEEE Transactions on Communications, vol. 61, no. 5, pp. 2086–2097, May 2013. [35] Z. Xiang, and M. Tao, “Robust beamforming for wireless information and power transmission,” IEEE Wireless Communication Letters, vol. 1, no. 4, pp. 372-375, Aug. 2012. [35] A. M. Fouladgar and O. Simeone, “On the transfer of information and energy in multi-user systems,” IEEE Wireless Communication Letters, vol. 16, no. 11, pp. 1733-1736, Nov. 2012.

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References

[36] B. Gurakan, O. Ozel, J. Yang, and S. Ulukus, “Energy cooperation in energy harvesting wireless systems,” in Proc. IEEE ISIT, pp. 965-969, 2012. [37] B. K. Chalise, Y. D. Zhang, and M. G. Amin, “Energy harvesting in an OSTBC based amplify-and-forward MIMO relay system,” in Proc. IEEE ICASSP, 2012.

Rui Zhang, National University of Singapore