Joint Optimization of Wireless Power Transfer and Collaborative - - PowerPoint PPT Presentation

Joint Optimization of Wireless Power Transfer and Collaborative Beamforming for Relay Communications

Shimin Gong, PhD Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences

IEEE Global Communications Conference

◼ Introduction ◼ System Model ◼ Robust Multi-Relay Transmission ◼ Numerical Results

2

Outline

Introduction

3

Simultaneous Wireless Information & Power Transfer Beamforming Power Splitting

Collaborative Transmission

I III II

Enhance information and power transfer Leverage diversity Sustainable scheduling

Introduction

+

Energy Receiver Information Receiver Power Splitting

1 − 𝜍𝑧𝑆 𝜍𝑧𝑆 𝑧𝑆

Antenna noise

Power Splitting Scheme

4

System Model

Cellular Network Collaborative Relay Networks Hybrid AP User Rx Relay

5

SWIPT

1st Hop: HAP → Relays 2nd Hop: Relays → URx

𝐠 𝐡 𝐴

◼ Energy Beamforming and Harvesting 6

System Model

𝑧𝑆 𝑜 = 𝑞𝑢𝐠𝑜

𝐼𝐱𝑡 + 𝜏𝑜

𝑞𝑜 ≤ 𝜃𝜍𝑜𝑞𝑢𝐠𝑜

𝐼𝐗𝐠𝑜

𝐗 = 𝐱𝐱𝐼, Beamforming Matrix 𝐱, Beamforming Vector 𝜃, Energy Harvesting Efficiency 𝜍𝑜, Power Splitting Ratio 𝑞𝑢, HAP Transmit Power 𝑡, HAP Transmit Symbol

◼ Relays' Transmit Control 7

System Model

1 − 𝜍𝑜 𝑞𝑢𝐠𝑜

𝐼𝐱𝑡 + 𝜏𝑜

Amplify-and-Forward 𝑦𝑜 = 𝑞𝑜 𝑂0 + 1 − 𝜍𝑜 𝑞𝑢𝐠𝑜

𝐼𝐗𝐠𝑜

Amplify Coefficient 𝑣 = ෍

𝑜=1 𝑂

𝑦𝑜 1 − 𝜍𝑜 𝑞𝑢𝐠𝑜

𝐼𝐱𝑕𝑜𝑡 + ෍ 𝑜=1 𝑂

𝑦𝑜𝜏𝑜𝑕𝑜 + 𝑤𝑒 Signal Noise

URx Reception

◼ Interference to Cellular Users 8

System Model

𝜚𝑛 = ෍

𝑜=1 𝑂

𝑞𝑜𝑨𝑜

2

ℙ𝐴 ∈ 𝒬 𝐯𝐴, 𝐓𝐴

Channel Uncertainty

𝐯𝐴, First Order Moment 𝐓𝐴, Second Order Moment

max

ℙ∈𝒬

𝐴 ℙ 𝜚𝑛 ≥ ത

𝜚 ≤ 𝜂

Robust Interference Constraint

9

Robust Multi-Relay Transmission

∘, Hadamard Product D 𝐲 , Diagonal matrix with the diagonal given by the vector 𝐲 𝐳 = 𝑧1, ⋯ , 𝑧𝑂 𝑈, 𝑧𝑜 ≜ 1 − 𝜍𝑜 𝑞𝑢𝐠𝑜

𝐼𝐱𝑕𝑜

𝐔𝐬 𝐗 ≤ 1, 𝐗 ≽ 0, and 0 ≤ 𝜍𝑜 ≤ 1

• s. t. 0 ≤ 𝑞𝑜 ≤ 𝜃𝑞𝑢𝜍𝑜𝐠𝑜

𝐼𝐗𝐠𝑜

Energy Constraint

max

ℙ∈𝒬

𝐴 ℙ 𝜚𝑛 ≥ ത

𝜚 ≤ 𝜂

Interference Constraint

max

𝜍𝑜,𝐱,𝑞𝑜 𝑠 = log 1 +

𝐲 ∘ 𝐳 𝐼𝐡 2 1 + 𝐲𝑈D 𝐡 ∘ 𝐡 𝐲

URx Throughput Maximization

Non-Convex Highly Coupled

Robust Multi-Relay Transmission

10

𝛿 = 𝐲 ∘ 𝐳 𝐼𝐡 2 1 + 𝐲𝑈D 𝐡 ∘ 𝐡 𝐲 ≤ 𝐲𝑈D 𝐡 ∘ 𝐡 𝐲 1 + 𝐲𝑈D 𝐡 ∘ 𝐡 𝐲 × 𝐳𝑈𝐳 = 𝑌 1 + 𝑌 𝑍 ∃𝑑 ≠ 0, s. t. 𝐳 = 𝑑𝐲 ∘ 𝐡

Cauchy-Schwarz Inequality

max log 1 + 𝛿 max 𝑌 1 + 𝑌 𝑍

• s. t. 𝐳 = 𝑑𝐲 ∘ 𝐡, 𝑑 ≠ 0

Lower Bounded by Equivalence Condition

Robust Multi-Relay Transmission

11

𝑌 1 + 𝑌 𝑍

Increasing with both 𝑌 and 𝑍 Monotonic Optimization

• 1. Initialize 𝑊

0 = 𝑌0, 𝑍 0 , 𝑊 = 𝑊 0 , 𝑄0 = Rectangle 0, 0 , 𝑊 0 , 𝑙 = 0,

𝑠𝑉 =

𝑌0 𝑌0+1 𝑍 0, 𝑠𝑀 = 0

• 2. WHILE 𝑠𝑉 − 𝑠𝑀 ≥ 𝜗

3. 𝑙 ⟵ 𝑙 + 1 4. Select 𝑊

𝑙 = arg max 𝑊𝑘 1 𝑊𝑘 1 +1 𝑊 𝑘 2 , 𝑠𝑉 = 𝑊𝑙 1 𝑊𝑙 2 𝑊𝑙 1 +1

5. Project 𝑊

𝑙 onto the edge of Feasible Region as 𝑃𝑙, 𝑠𝑀 = 𝑃𝑙 1 𝑃𝑙 2 𝑃𝑙 1 +1

6. Crop 𝑄𝑙 = 𝑄𝑙−1\Rectangle(𝑃𝑙, 𝑊

𝑙)

7. Update 𝑊 according to 𝑃𝑙

• 8. END WHILE

Polyblock Approximation

Robust Multi-Relay Transmission

12

Projection Bisection

𝐳 2 ≥ 𝑟𝑙𝑍

𝑙,

𝐲𝑈D 𝐡 ∘ 𝐡 𝐲 ≥ 𝑟𝑙𝑌𝑙, max

ℙ∈𝒬

𝐴 ℙ 𝜚𝑛 ≥ ത

𝜚 ≤ 𝜂 , 𝑑𝑦 ∘ 𝑕 = 𝑧, 𝜃𝜍𝑜𝑞𝑢𝐠𝑜

𝐼𝐗𝐠𝑜 ≥ 𝑞𝑜.

max σ𝑜=1

𝑂

𝑡𝑜

• s. t. 𝑞𝑜 ≤ 𝜃𝑞𝑢𝐠𝑜

𝐼 ഥ

𝐗𝐠𝑜, 𝑡𝑜 ≤ 𝑞𝑢𝐠𝑜

𝐼 𝐗 − ഥ

𝐗 𝐠𝑜, 𝑑2𝑞𝑜𝑕𝑜

2 − 𝑡𝑜

𝑡𝑜 𝑡𝑜 1 ≽ 0, 𝐍 ≽ D 𝐪 𝜉 − ത 𝜚 , 𝐔𝐬 𝚻𝒜𝐍 ≤ 𝜉𝜂, 𝑁 ≽ 0, 𝜉 ≥ 0, 𝐔𝐬 𝐗 ≤ 1, 𝐔𝐬 ഥ 𝐗 ≤ 1.

*𝑡𝑜 = 𝑧𝑜

2, 𝜍𝑜 = 𝐠𝑜 𝐼 ഥ

𝐗𝐠𝑜/𝐠𝑜

𝐼𝐗𝐠𝑜

Convex SDP

Numerical Results

13

2 4 3 2 2 2

Path Loss: 𝑀 = 25 + 20 log10 𝑒 Noise Power: −90 dBm Bandwidth: 100 kHz Energy harvesting efficient: 𝜃 = 0.5 HAP Transmit Power: 𝑞𝑢 ∈ 10, 100 mW

𝑆2 𝑆1 𝑆3

Numerical Results

14

Throughput and Relays’ Transmit Power limited by Cellular Users’ Interference Constraint

Numerical Results

15

HAP’s beamforming and Relays’ PS ratio Optimization

Conclusions

◼

Pros: Jointly Optimizing Power Transfer and Relay Strategy

✓

We formulate a throughput maximization problem that jointly

• ptimizes the relay strategy (PS ratio and transmit power) and the

beamforming of HAP.

✓

A lower bounded SDP reformulation is deduced via monotonic

• ptimization.

✓

Near optimal result is found via Polyblock iteration algorithm according to numerical results.

◼

Cons:

✓

No direct link considered

16

Questions & Answers Thank you !