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) E-mail : thunguyen@ssu.ac.kr 성균관대 ERC 2015년 8월

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

Overview of RF-based SWIPT

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

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)

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

System Model and Problem Formulation

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

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

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

Robust Beamforming Design and Power Splitting Optimization for the Imperfect CSI

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).

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

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.

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

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

Numerical Results

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

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

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