Beamforming Design for Simultaneous
Wireless Information and Power Transfer in
MISO Multicasting Systems
숭실대학교 정보통신전자공학부
Thu L. N. Nguyen (응웬뚜랑녹)
E-mail : [email protected]
성균관대 ERC
2015년 8월
CIPLab
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Information Processing
Contents

Overview of RF-based SWIPT

System Model and Problem Formulation

Robust Beamforming Design and Power Splitting
Optimization for the Imperfect CSI

Numerical Results
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Overview of RF-based SWIPT
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RF-based Wireless Power Transfer (1)

Radio Frequency (RF) Sources: every where!!!

RF-based WPT (Wireless Power Transfer)


Originally conceived by Nikola Tesla
Energy is transmitted from a power source to a destination over
the wireless medium.
Energy Transmitter
Energy Receiver
Typical Operation of a Energy Receiver
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RF-based Wireless Power Transfer (2)

Key benefits

Power over distance:

One-to-many

Power is controllable





RF power level
Transmit Frequency/Antenna/Number of transmitters
Distance, cots, etc.
Abundant application in WSNs: building automation, structural
monitoring, defense, data centers, smart grid,…
Limitations

Low received power (e.g., smaller than 1uW* at distance >5m,
transmit power <1W)
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Simultaneous Wireless Information and Power
Transfer (SWIPT)

RF-based SWIPT (Simultaneous Wireless Information and Power Transfer)


Downlink (DL): Access Point  Sensors (Wireless information and power transfer)
Uplink (UL) : Sensors Access Point (Information transfer with wireless harvested
energy)
WPT: Wireless Power Transfer
 Maximize the energy transmission efficiency
Information Flow
WIT: Wireless Information Transfer
 Maximize the information transmission capacity
SWIPT
 Maximize the signal power received for WPT,
also beneficial in maximizing the channel for WIT
against the receiver noise.
Energy Flow
Access Point (AP) with
fixed power supply

Wireless sensors without
fixed power supply
Receiver Architecture Design: Separated information and energy receivers
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System Model and Problem Formulation
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System Model (1)

MISO system model
Notations



Mobile
Station 𝑴𝑺𝟏
𝒉𝟏
Transmitted data symbol 𝒔𝒌
s.t. 𝑬 𝒔𝒌 𝟐 = 𝟏.
Beamforming vector 𝒘𝒌 s.t. 𝒘𝒌 = 𝟏
Channel 𝒉𝒌 between BS and 𝑴𝑺𝒌
Base
Station
(BS)
⋮
⋮
⋮
𝒉𝑲
𝑁𝑡 antennas
Mobile
Station 𝑴𝑺𝑲
At the 𝑴𝑺𝒌
𝟏 − 𝝆𝒌
𝝃
RF-Energy Harvesting
Power
Splitter
Information Decoding
𝒏𝒌 ∼ 𝑪𝑵(𝟎, 𝝈𝟐𝒌 )
𝝆𝒌
The received signal at the 𝑀𝑆𝑘
𝒚𝒌 =
𝒛𝒌 ∼ 𝑪𝑵(𝟎, 𝜹𝟐𝒌 )
𝑷𝒌 𝒉𝑯
𝒌 𝒘𝒌 𝒔𝒌 +
𝑷𝒋 𝒉𝑯
𝒋 𝒘𝒋 𝒔𝒋 + 𝒏𝒌
𝒋≠𝒌
Information
signal
*𝝃∈
*
𝟎, 𝟏 : energy conversion efficiency
𝑷𝒌 : transmit power.
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Noise
Interference
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Problem Formulation (1)

The signal-to-interference-plus-noise ratio (SINR) at the 𝑴𝑺𝒌

𝚪𝐤 =
At the ID
𝝆𝒌 𝑷𝒌 𝒉𝑯
𝒌 𝒘𝒌
𝝆𝒌

𝑯
𝒋≠𝒌 𝑷𝒋 𝒉𝒋 𝒘𝒋
𝟐
𝟐
𝒗𝑘 =
𝑃𝑘 𝒘𝑘
𝒗𝑘 =
𝑃𝑘 𝒘𝑘
+ 𝝆𝒌 𝝈𝟐𝒌 + 𝜹𝟐𝒌
At the EH
𝑲
𝑷𝒋 𝒉𝑯
𝒌 𝒘𝒋
𝚼𝐤 = 𝝃𝒌 𝟏 − 𝝆𝒌
𝟐
+ 𝝈𝟐𝒌
𝒋=𝟏

Optimization problem for beamforming design.
𝑲
min
{𝑷𝒌 ,𝝆𝒌 ,𝒘𝒌 }
subject to
𝑷𝒌
𝒗𝑘 =
𝒌=𝟏
𝚪𝒌 ≥ 𝜸𝒌
𝚼𝐤 ≥ 𝜼𝒌
𝑷𝒌 ≥ 𝟎, 𝒘𝒌
𝟎 < 𝝆𝒌 < 𝟏,
𝒌 = 𝟏, ⋯ , 𝑲.
𝟐
𝑃𝑘 𝒘𝑘
=𝟏
𝜸𝒌 , 𝜼𝒌 : Given thresholds
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Problem Formulation (2)

Imperfect channel state information (CSI)
where

Joint transmit beamforming and power splitting optimization
in imperfect CSI cases.
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Robust Beamforming Design and Power
Splitting Optimization for the
Imperfect CSI
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Contribution

We consider two categories
1. Elimination of multi-user interference
 First, we use zero-forcing (ZF) beamforming to select the weights su
ch that the co-channel interference is canceled, i.e., 𝒉𝑯
𝒋 𝒗𝒌 = 𝟎 for all 𝑗
≠ 𝑘.
 Second, we modify the inequality constraints to obtain a new convex
semidefinite program (SDP), then solve it by the interior point metho
d
2. Non-Elimination of multi-user interference



First, we introduce about S-procedure for quadratic forms.
Second, we use S-procedure to approximate the given constraints.
The results is a SDP relaxation problem.
Third, solve this SDP relaxation problem by optimization tools (e.g.,
cvx package in MATLAB).
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Proposed solution:
Elimination of Multi-User Interference

ZF precoding: 𝒉𝑗𝐻 𝒗𝑘 = 𝟎 for all 𝑗 ≠ 𝑘.

New optimization problem

1.
Approximating constraint (C1’)
where
2.
Using the fact
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Proposed solution:
Non-Elimination of Multi-User Interference (1)

S-procedure for quadratics forms


Let 𝑔, ℎ: ℂ𝒏 → ℂ be quadratic functions such that ℎ(𝑥0 ) > 0 at some
point 𝒙𝟎 ∈ ℂ𝒏 . Then 𝑔 is co-positive with ℎ if and only if there exist
s 𝜆 such that 𝑔 𝑥 − 𝜆 ℎ 𝑥 ≥ 0.
Example


𝑯
𝑯
Given 𝒈 𝒙 = 𝒙𝑯 𝑨𝟏 𝒙 + 𝒃𝑯
𝟏 𝒙 + 𝒙𝒃𝟏 + 𝑐1 ≥ 𝟎 and 𝒉 𝒙 = 𝒙 𝑨𝟐 𝒙 + 𝒃𝟐 𝒙 +
𝒙𝑯 𝒃𝟐 + 𝑐2 ≥ 𝟎, where 𝑨𝟏 , 𝑨𝟐 ∈ ℂ𝒏×𝒏 , 𝒃𝟏 , 𝒃𝟐 ∈ ℂ𝒏 and 𝑐1 , 𝑐2 ∈ ℂ.
The coefficients 𝑨𝟏 , 𝒃𝟏 , 𝑐1 of the polynomial 𝒈 play the role of decis
ion variable, the constraints
𝒈 𝒙 ≥ 𝟎, ∀𝒙 ∈ ℂ𝒏 such that 𝒉 𝒙 ≥ 𝟎

(*)
The constraint (*) can be replaced by a single matrix inequality
𝑨𝟏
𝒃𝑯
𝟏
𝒃𝟏
𝑨𝟐
−𝜆 𝑯
𝑐1
𝒃𝟐
𝒃𝟐
≽ 0,
𝑐2
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𝜆 ≥ 0.
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Proposed solution:
Non-Elimination of Multi-User Interference (2)

Define


𝑼𝒌 = 𝒉𝒌 + 𝚫𝐡𝐤
𝚫𝒉𝒌 ≤ 𝝐𝒌 }, 𝒌 = 𝟏, ⋯ , 𝑲
Reformulate beamforming optimization problem
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Proposed solution:
Non-Elimination of Multi-User Interference (3)

Using S-procedure and setting 𝑾𝒌 =
𝒗𝒌 𝒗𝑯
𝒌 (𝒌 = 𝟏, ⋯ , 𝑲)

𝟏
𝑿
𝜸𝒌 𝒌
−
𝒋≠𝒌 𝑿𝒋 ,
where 𝑿𝒌 =
New convex optimization
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Numerical Results
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

Elimination of multi-user interference (Case 1) and non-elimination
of multi-user interference (Case 2).
𝟏
𝟏
𝑲 = 𝟒, 𝜸𝒌 = 𝜸, 𝜼𝒌 = 𝜼, 𝝈𝟐𝒌 = 𝝈𝟐 , 𝜹𝟐𝒌 = 𝜹𝟐 , 𝝐𝒌 = 𝝐, ∀𝒌; 𝝃 = 𝟐 , 𝝈𝟐 = 𝑵 , 𝜹𝟐 = 𝟎. 𝟎𝟏
𝒕
Transmission power vs SINR
threshold with 𝑵𝒕 = 𝟓, 𝝐 = 𝟎. 𝟎𝟏
Transmission power versus the
harvested energy threshold 𝜼
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Transmission power vs the CSI
Error 𝝐
Transmission power vs the number of
BS antennas 𝑵𝒕
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Summary



Simultaneous Wireless Information and Power Transfer
(SWIPT)
Power Splitting
Robust Beamforming Design Problem and Power Splitting
Optimization for the Imperfect CSI
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