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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
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
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
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
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
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
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
ICC 2014 7
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
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
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
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
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.
ICC 2014 11
Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore
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
NASA’s Wireless Power Transfer Project Using Laser Beam
ICC 2014 13
Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore
Induction Coupling Enabled Wireless Power Transfer: Radio Frequency Identification (RFID) in 1970s
ICC 2014 14
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
Wireless Power Transfer via Magnetic Resonant Coupling in 2000s
ICC 2014 15
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
Wireless RF Power Transfer via Electromagnetic Radiation
ICC 2014 16
Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore
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
ICC 2014 17
Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore
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
ICC 2014 18
Part I: Wireless Power: History and State-of-the-Art Rui Zhang, National University of Singapore
Application Examples
ICC 2014 19
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
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
Part II
Overview of Wireless Powered Communication
ICC 2014 21
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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
ICC 2014 22
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Point-to-Point Wireless Power Transfer: Channel Model
ICC 2014 23
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Modulated vs. Unmodulated Energy Signal
ICC 2014 24
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
Wireless Power Transfer: Receiver Structure (1)
ICC 2014 25
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Wireless Power Transfer: Receiver Structure (2)
ICC 2014 26
Part II: Overview of Wireless Powered Communications
[4]
Rui Zhang, National University of Singapore
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)
ICC 2014 27
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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]
ICC 2014 28
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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)
ICC 2014 29
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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
ICC 2014 30
Part II: Overview of Wireless Powered Communications
A two-phase WPT protocol
Rui Zhang, National University of Singapore
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)
ICC 2014 31
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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)
ICC 2014 32
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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
ICC 2014 33
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
“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
ICC 2014 34
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
Wireless Powered Network Capacity
ICC 2014 35
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
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]
ICC 2014 36
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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
ICC 2014 37
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
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
ICC 2014 38
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
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
ICC 2014 39
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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]
ICC 2014 40
Part II: Overview of Wireless Powered Communications
Energy Receiver
Information Receiver
Rui Zhang, National University of Singapore
Information Receiver
RF to baseband conversion by mixers, which are active devices (power consuming)
Equivalent AWGN baseband channel
Maximum achievable rate
ICC 2014 41
Part II: Overview of Wireless Powered Communications
antenna noise
RF-to-baseband conversion noise
Rui Zhang, National University of Singapore
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).
ICC 2014 42
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Dynamic Power Splitting
ICC 2014 43
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Rate-Energy Region of Separate Receivers
ICC 2014 44
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Numerical Example (Separated Receivers)
ICC 2014 45
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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
ICC 2014 46
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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.
ICC 2014 47
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
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
ICC 2014 48
Part II: Overview of Wireless Powered Communications
rectifier noise
Rui Zhang, National University of Singapore
Numerical Example (Integrated Receivers)
ICC 2014 49
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Rate-Energy Region with Receiver Circuit Power Consideration
ICC 2014 50
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Numerical Example (with Receiver Circuit Power Consideration)
ICC 2014 51
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Practical Example
ICC 2014 52
Part II: Overview of Wireless Powered Communications Rui Zhang, National University of Singapore
Point-to-Multipoint SWIPT: Harmful vs. Helpful Interference
ICC 2014 53
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
Dynamic Time Switching over Fading Channels
ICC 2014 54
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
DPS over Fading Channels
ICC 2014 55
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
Dynamic Power Splitting vs.Dynamic Antenna Switching
ICC 2014 56
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
Multi-Transmitter Collaborative SWIPT
ICC 2014 57
Part II: Overview of Wireless Powered Communications
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
ICC 2014 58
Part II: Overview of Wireless Powered Communications
SWIPT with Energy/Information Relaying
ICC 2014 58
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
ICC 2014 59
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
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
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 61
Part III: Case Studies and Extended Work Rui Zhang, National University of Singapore
62 ICC 2014
Part III
Case Studies and Extended Work
Part III: Case Studies and Extended Work Rui Zhang, National University of Singapore
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
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]
ICC 2014 64
Part III: Case Studies and Extended Work Rui Zhang, National University of Singapore
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)
ICC 2014 65
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
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)
ICC 2014 66
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
ICC 2014 67
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
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
ICC 2014 68
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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)
ICC 2014 69
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
ICC 2014 70
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Two-Phase WPT Protocol (2)
Phase 2 Energy transmission: ET sends one single energy beam with covariance
Total harvested energy over two phases
ICC 2014 71
energy harvested in Phase 1
energy harvested in Phase 2
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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)
ICC 2014 72
1n P
X
C u tt in g p la n e
nH
1n n nP P H
X
G(n) G(n) ~ ~
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
ICC 2014 73
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
ICC 2014 74
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Convergence Analysis: Multi-ER Case
ICC 2014 75
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)
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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:
ICC 2014 76
ET
ER 1
ER 2
ER 3
ER 4
ER 5
ER 6
5 meters
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Simulation Result: Baseline Schemes
ICC 2014 77
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Simulation Result: Single-ER Case
ICC 2014 78
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
Simulation Result: Single-ER Case
ICC 2014 79
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Simulation Result: Single-ER Case
ICC 2014 80
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Simulation Result: Multiple-ER Case
ICC 2014 81
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Summary and Future Work
ICC 2014 82
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
ICC 2014 83
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Harvest-then-Transmit-Protocol
ICC 2014 84
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:
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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:
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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:
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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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Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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)
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Simulation Result
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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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
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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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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 :
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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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Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Summary and Future Work
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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]
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
SDR-Based Optimal Solution to (P1)
Define ,
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dropping rank-1
constraints
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
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
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Signal Model (2)
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Signal split to ER
Harvested energy
Signal split to IR
SINR
zk
: antenna noise : IR’s noise
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Problem Formulation
Objective: Minimize transmit power Subject to: Individual SINR constraints Individual harvested energy constraints
Non-convex problem: Coupled and Quadratic terms with
ICC 2014 111
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
SDR-Based Optimal Solution
Define
Optimal solution to SDR satisfies , , i.e., SDR is tight
All constraints are met with equality
ICC 2014 112
SDR
convex problem, solvable by CVX
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
ICC 2014 113
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Simulation Result
Transmit power increases substantially with e When is small, performance gap is more significant
ICC 2014 114
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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.
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
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
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Summary and Future Work
ICC 2014 117
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])
Rui Zhang, National University of Singapore Part III: Case Studies and Extended Work
Concluding Remarks
ICC 2014 118
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
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
ICC 2014 120
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)
Rui Zhang, National University of Singapore
ICC 2014 121
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[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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ICC 2014 122
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[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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[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