1. E-mail : thunguyen@ssu.ac.kr
Beamforming Design for Simultaneous Wireless Information and Power Transfer in MISO Multicasting Systems
숭실대학교 정보통신전자공학부
Thu L. N. Nguyen (응웬뚜랑녹)
성균관대 ERC
2015년 8월

2. Contents Overview of RF-based SWIPT
System Model and Problem Formulation
Robust Beamforming Design and Power Splitting Optimization for the Imperfect CSI
Numerical Results

3. Overview of RF-based SWIPT

4. 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

5. 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)

6. 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)
Receiver Architecture Design: Separated information and energy receivers
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

7. System Model and Problem Formulation

8. The received signal at the 𝑀 𝑆 𝑘
System Model (1)
MISO system model
Notations
Transmitted data symbol 𝒔 𝒌 s.t. 𝑬 𝒔 𝒌 𝟐 =𝟏.
Beamforming vector 𝒘 𝒌 s.t. 𝒘 𝒌 =𝟏
Channel 𝒉 𝒌 between BS and 𝑴 𝑺 𝒌
Mobile Station 𝑴 𝑺 𝟏
𝒉 𝟏
Base Station (BS) ⋮ ⋮ ⋮
𝒉 𝑲
Mobile Station 𝑴 𝑺 𝑲
𝑁 𝑡 antennas
At the 𝑴 𝑺 𝒌
𝟏− 𝝆 𝒌 𝝃
RF-Energy Harvesting
Power Splitter
Information Decoding
𝒏 𝒌 ∼𝑪𝑵(𝟎, 𝝈 𝒌 𝟐 )
𝝆 𝒌
𝒛 𝒌 ∼𝑪𝑵(𝟎, 𝜹 𝒌 𝟐 )
𝒚 𝒌 = 𝑷 𝒌 𝒉 𝒌 𝑯 𝒘 𝒌 𝒔 𝒌 + 𝒋≠𝒌 𝑷 𝒋 𝒉 𝒋 𝑯 𝒘 𝒋 𝒔 𝒋 + 𝒏 𝒌
The received signal at the 𝑀 𝑆 𝑘
* 𝝃∈ 𝟎,𝟏 : energy conversion efficiency * 𝑷 𝒌 : transmit power.
Noise
Information signal
Interference

9. Problem Formulation (1)
The signal-to-interference-plus-noise ratio (SINR) at the 𝑴 𝑺 𝒌
At the ID
At the EH
Optimization problem for beamforming design.
𝚪 𝐤 = 𝝆 𝒌 𝑷 𝒌 𝒉 𝒌 𝑯 𝒘 𝒌 𝟐 𝝆 𝒌 𝒋≠𝒌 𝑷 𝒋 𝒉 𝒋 𝑯 𝒘 𝒋 𝟐 + 𝝆 𝒌 𝝈 𝒌 𝟐 + 𝜹 𝒌 𝟐
𝒗 𝑘 = 𝑃 𝑘 𝒘 𝑘
𝚼 𝐤 = 𝝃 𝒌 𝟏− 𝝆 𝒌 𝒋=𝟏 𝑲 𝑷 𝒋 𝒉 𝒌 𝑯 𝒘 𝒋 𝟐 + 𝝈 𝒌 𝟐
𝒗 𝑘 = 𝑃 𝑘 𝒘 𝑘
min { 𝑷 𝒌 , 𝝆 𝒌 , 𝒘 𝒌 } 𝒌=𝟏 𝑲 𝑷 𝒌
subject to 𝚪 𝒌 ≥ 𝜸 𝒌
𝚼 𝐤 ≥ 𝜼 𝒌
𝑷 𝒌 ≥𝟎, 𝒘 𝒌 𝟐 =𝟏
𝟎< 𝝆 𝒌 <𝟏,
𝒌=𝟏,⋯, 𝑲.
𝒗 𝑘 = 𝑃 𝑘 𝒘 𝑘
𝜸 𝒌 , 𝜼 𝒌 : Given thresholds

10. Problem Formulation (2)
Imperfect channel state information (CSI)
Joint transmit beamforming and power splitting optimization in imperfect CSI cases.
where

11. Robust Beamforming Design and Power Splitting Optimization for the Imperfect CSI

12. Contribution We consider two categories
Elimination of multi-user interference
First, we use zero-forcing (ZF) beamforming to select the weights such that the co-channel interference is canceled, i.e., 𝒉 𝒋 𝑯 𝒗 𝒌 =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 method
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).

13. Proposed solution: Elimination of Multi-User Interference
ZF precoding: 𝒉 𝑗 𝐻 𝒗 𝑘 =𝟎 for all 𝑗≠𝑘.
New optimization problem
Approximating constraint (C1’)
Using the fact
where

14. Proposed solution: Non-Elimination of Multi-User Interference (1)
S-procedure for quadratics forms
Let 𝑔, ℎ: ℂ 𝒏 → ℂ be quadratic functions such that ℎ( 𝑥 0 )>0 at some point 𝒙 𝟎 ∈ ℂ 𝒏 . Then 𝑔 is co-positive with ℎ if and only if there exists 𝜆 such that 𝑔 𝑥 −𝜆 ℎ 𝑥 ≥ 0.
Example
Given 𝒈 𝒙 = 𝒙 𝑯 𝑨 𝟏 𝒙+ 𝒃 𝟏 𝑯 𝒙+𝒙 𝒃 𝟏 + 𝑐 1 ≥𝟎 and 𝒉 𝒙 = 𝒙 𝑯 𝑨 𝟐 𝒙+ 𝒃 𝟐 𝑯 𝒙+ 𝒙 𝑯 𝒃 𝟐 + 𝑐 2 ≥𝟎, where 𝑨 𝟏 , 𝑨 𝟐 ∈ ℂ 𝒏×𝒏 , 𝒃 𝟏 , 𝒃 𝟐 ∈ ℂ 𝒏 and 𝑐 1 , 𝑐 2 ∈ℂ.
The coefficients 𝑨 𝟏 , 𝒃 𝟏 , 𝑐 1 of the polynomial 𝒈 play the role of decision variable, the constraints
𝒈 𝒙 ≥𝟎, ∀𝒙∈ ℂ 𝒏 such that 𝒉 𝒙 ≥𝟎 (*)
The constraint (*) can be replaced by a single matrix inequality
𝑨 𝟏 𝒃 𝟏 𝒃 𝟏 𝑯 𝑐 1 −𝜆 𝑨 𝟐 𝒃 𝟐 𝒃 𝟐 𝑯 𝑐 2 ≽0, 𝜆≥0.

15. Proposed solution: Non-Elimination of Multi-User Interference (2)
Define
𝑼 𝒌 = 𝒉 𝒌 +𝚫 𝐡 𝐤 𝚫 𝒉 𝒌 ≤ 𝝐 𝒌 }, 𝒌=𝟏, ⋯, 𝑲
Reformulate beamforming optimization problem

16. Proposed solution: Non-Elimination of Multi-User Interference (3)
Using S-procedure and setting 𝑾 𝒌 = 𝟏 𝜸 𝒌 𝑿 𝒌 − 𝒋≠𝒌 𝑿 𝒋 , where 𝑿 𝒌 = 𝒗 𝒌 𝒗 𝒌 𝑯 (𝒌=𝟏,⋯, 𝑲)
New convex optimization

17. Numerical Results

18. Elimination of multi-user interference (Case 1) and non-elimination of multi-user interference (Case 2).
𝑲=𝟒, 𝜸 𝒌 =𝜸, 𝜼 𝒌 =𝜼, 𝝈 𝒌 𝟐 = 𝝈 𝟐 , 𝜹 𝒌 𝟐 = 𝜹 𝟐 , 𝝐 𝒌 =𝝐, ∀𝒌; 𝝃= 𝟏 𝟐 , 𝝈 𝟐 = 𝟏 𝑵 𝒕 , 𝜹 𝟐 =𝟎.𝟎𝟏
Transmission power vs SINR threshold with 𝑵 𝒕 =𝟓, 𝝐=𝟎.𝟎𝟏
Transmission power versus the harvested energy threshold 𝜼

19. Transmission power vs the CSI Error 𝝐
Transmission power vs the number of BS antennas 𝑵 𝒕

20. Summary Simultaneous Wireless Information and Power Transfer (SWIPT)
Power Splitting
Robust Beamforming Design Problem and Power Splitting Optimization for the Imperfect CSI