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

IEEE Global Communications Conference Joint Optimization of Wireless Power Transfer and Collaborative Beamforming for Relay Communications Shimin Gong, PhD Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences

Outline ◼ Introduction ◼ System Model ◼ Robust Multi-Relay Transmission ◼ Numerical Results 2

Introduction Enhance information and power transfer I Beamforming Collaborative III Transmission Leverage diversity S imultaneous W ireless I nformation & II Power Splitting P ower Sustainable T ransfer scheduling 3

Introduction Power Splitting Scheme 1 − 𝜍𝑧 𝑆 Information Receiver 𝑧 𝑆 Power + Splitting Energy Antenna Receiver 𝜍𝑧 𝑆 noise 4

System Model 2 nd Hop: Relays → URx 1 st Hop: HAP → Relays U ser Rx SWIPT 𝐡 Relay 𝐴 𝐠 Hybrid AP Collaborative Cellular Relay Networks Network 5

System Model ◼ Energy Beamforming and Harvesting 𝐼 𝐱𝑡 + 𝜏 𝑜 𝐼 𝐗𝐠 𝑜 𝑧 𝑆 𝑜 = 𝑞 𝑢 𝐠 𝑜 𝑞 𝑜 ≤ 𝜃𝜍 𝑜 𝑞 𝑢 𝐠 𝑜 𝐗 = 𝐱𝐱 𝐼 , Beamforming Matrix 𝐱 , Beamforming Vector 𝑞 𝑢 , HAP Transmit Power 𝜃 , Energy Harvesting Efficiency 𝑡 , HAP Transmit Symbol 𝜍 𝑜 , Power Splitting Ratio 6

System Model ◼ Relays' Transmit Control Amplify-and-Forward 𝐼 𝐱𝑡 + 𝜏 𝑜 1 − 𝜍 𝑜 𝑞 𝑢 𝐠 𝑜 𝑞 𝑜 𝑦 𝑜 = Amplify Coefficient 𝐼 𝐗𝐠 𝑜 𝑂 0 + 1 − 𝜍 𝑜 𝑞 𝑢 𝐠 𝑜 𝑂 𝑂 𝐼 𝐱𝑕 𝑜 𝑡 + ෍ 𝑣 = ෍ 𝑦 𝑜 1 − 𝜍 𝑜 𝑞 𝑢 𝐠 𝑜 𝑦 𝑜 𝜏 𝑜 𝑕 𝑜 + 𝑤 𝑒 URx Reception 𝑜=1 𝑜=1 Signal Noise 7

System Model ◼ Interference to Cellular Users 𝑂 2 𝜚 𝑛 = ෍ 𝑞 𝑜 𝑨 𝑜 𝑜=1 Channel Uncertainty Robust Interference ℙ 𝐴 ∈ 𝒬 𝐯 𝐴 , 𝐓 𝐴 Constraint 𝐯 𝐴 , First Order Moment 𝐴 ℙ 𝜚 𝑛 ≥ ത max 𝜚 ≤ 𝜂 𝐓 𝐴 , Second Order Moment ℙ∈𝒬 8

Robust Multi-Relay Transmission Highly Coupled 𝐲 ∘ 𝐳 𝐼 𝐡 2 URx Throughput 𝜍 𝑜 ,𝐱,𝑞 𝑜 𝑠 = log 1 + max 1 + 𝐲 𝑈 D 𝐡 ∘ 𝐡 𝐲 Maximization 𝐼 𝐗𝐠 𝑜 s. t. 0 ≤ 𝑞 𝑜 ≤ 𝜃𝑞 𝑢 𝜍 𝑜 𝐠 𝑜 Energy Constraint 𝐴 ℙ 𝜚 𝑛 ≥ ത max 𝜚 ≤ 𝜂 Interference Constraint ℙ∈𝒬 Non-Convex 𝐔𝐬 𝐗 ≤ 1, 𝐗 ≽ 0, and 0 ≤ 𝜍 𝑜 ≤ 1 ∘ , Hadamard Product D 𝐲 , Diagonal matrix with the diagonal given by the vector 𝐲 𝐳 = 𝑧 1 , ⋯ , 𝑧 𝑂 𝑈 , 𝑧 𝑜 ≜ 𝐼 𝐱𝑕 𝑜 1 − 𝜍 𝑜 𝑞 𝑢 𝐠 𝑜 9

Robust Multi-Relay Transmission 𝐲 ∘ 𝐳 𝐼 𝐡 2 𝐲 𝑈 D 𝐡 ∘ 𝐡 𝐲 1 + 𝐲 𝑈 D 𝐡 ∘ 𝐡 𝐲 × 𝐳 𝑈 𝐳 𝛿 = 1 + 𝐲 𝑈 D 𝐡 ∘ 𝐡 𝐲 ≤ 𝑌 Cauchy-Schwarz = 1 + 𝑌 𝑍 Inequality ∃𝑑 ≠ 0, s. t. 𝐳 = 𝑑𝐲 ∘ 𝐡 Equivalence Condition 𝑌 max 1 + 𝑌 𝑍 Lower max log 1 + 𝛿 Bounded by s. t. 𝐳 = 𝑑𝐲 ∘ 𝐡, 𝑑 ≠ 0 10

Robust Multi-Relay Transmission 𝑌 1 + 𝑌 𝑍 Increasing with both 𝑌 and 𝑍 Monotonic Optimization Polyblock Approximation 1. Initialize 𝑊 0 = 𝑌 0 , 𝑍 0 , 𝑊 = 𝑊 0 , 𝑄 0 = Rectangle 0, 0 , 𝑊 0 , 𝑙 = 0, 𝑠 𝑉 = 𝑌 0 0 , 𝑠 𝑀 = 0 𝑌 0 +1 𝑍 2. WHILE 𝑠 𝑉 − 𝑠 𝑀 ≥ 𝜗 3. 𝑙 ⟵ 𝑙 + 1 𝑊 𝑘 1 𝑘 2 , 𝑠 𝑉 = 𝑊 𝑙 1 𝑊 𝑙 2 Select 𝑊 𝑙 = arg max 𝑊 𝑘 1 +1 𝑊 4. 𝑊 𝑙 1 +1 𝑙 onto the edge of Feasible Region as 𝑃 𝑙 , 𝑠 𝑀 = 𝑃 𝑙 1 𝑃 𝑙 2 Project 𝑊 5. 𝑃 𝑙 1 +1 Crop 𝑄 𝑙 = 𝑄 𝑙−1 \Rectangle(𝑃 𝑙 , 𝑊 6. 𝑙 ) Update 𝑊 according to 𝑃 𝑙 7. 8. END WHILE 11

Robust Multi-Relay Transmission 𝑂 max σ 𝑜=1 𝑡 𝑜 Convex Projection Bisection 𝐼 ഥ SDP s. t. 𝑞 𝑜 ≤ 𝜃𝑞 𝑢 𝐠 𝑜 𝐗𝐠 𝑜 , 𝐼 𝐗 − ഥ 𝑡 𝑜 ≤ 𝑞 𝑢 𝐠 𝑜 𝐗 𝐠 𝑜 , 𝐳 2 ≥ 𝑟 𝑙 𝑍 𝑙 , 2 − 𝑡 𝑜 𝑑 2 𝑞 𝑜 𝑕 𝑜 𝑡 𝑜 ≽ 0 , 𝑡 𝑜 1 𝐲 𝑈 D 𝐡 ∘ 𝐡 𝐲 ≥ 𝑟 𝑙 𝑌 𝑙 , 𝐍 ≽ D 𝐪 0 𝜚 , 𝐴 ℙ 𝜚 𝑛 ≥ ത max 𝜚 ≤ 𝜂 , 𝜉 − ത 0 ℙ∈𝒬 𝐔𝐬 𝚻 𝒜 𝐍 ≤ 𝜉𝜂, 𝑁 ≽ 0, 𝜉 ≥ 0, 𝑑𝑦 ∘ 𝑕 = 𝑧, 𝐔𝐬 𝐗 ≤ 1, 𝐔𝐬 ഥ 𝐗 ≤ 1 . 𝐼 𝐗𝐠 𝑜 ≥ 𝑞 𝑜 . 𝜃𝜍 𝑜 𝑞 𝑢 𝐠 𝑜 𝐼 ഥ 2 , 𝜍 𝑜 = 𝐠 𝑜 𝐼 𝐗𝐠 𝑜 * 𝑡 𝑜 = 𝑧 𝑜 𝐗𝐠 𝑜 /𝐠 𝑜 12

Numerical Results 𝑆 2 2 3 𝑆 1 2 2 2 4 𝑆 3 Path Loss: 𝑀 = 25 + 20 log 10 𝑒 HAP Transmit Power: 𝑞 𝑢 ∈ 10, 100 mW Noise Power: −90 dBm Bandwidth: 100 kHz Energy harvesting efficient: 𝜃 = 0.5 13

Numerical Results Throughput and Relays’ Transmit Power limited by Cellular Users’ Interference Constraint 14

Numerical Results HAP’s beamforming and Relays’ PS ratio Optimization 15

Conclusions Pros: Jointly Optimizing Power Transfer and Relay Strategy ◼ We formulate a throughput maximization problem that jointly ✓ optimizes the relay strategy (PS ratio and transmit power) and the beamforming of HAP. A lower bounded SDP reformulation is deduced via monotonic ✓ optimization. Near optimal result is found via Polyblock iteration algorithm ✓ according to numerical results. Cons: ◼ No direct link considered ✓ 16

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