Wireless Networks Research Seminar April 22nd 2013

Transcription

1 Wireless Networks Research Seminar April 22nd 2013 Distributed Transmit Power Minimization in Wireless Sensor Networks via Cross-Layer Optimization NETS2020 Markus Leinonen, Juha Karjalainen, Marian Codreanu, Markku Juntti

2 2 Outline Scenario & System model 3 main design approaches 1. Distributed source coding 2. Distributed transmission optimization 3. Compressed sensing data gathering

3 Scenario: Single-Sink Data Gathering in Wireless Sensor Networks 3 Multiple battery-powered sensor nodes Spatially correlated data Single destination Distributed cross-layer design over: Application Layer Slepian-Wolf coding Compressed sensing (data compression) Network Layer Multi-path routing, multi-hop Compressed sensing (data gathering) Physical Layer Transmit power allocation Bandwidth allocation Distributed optimization algorithms for improving the overall energy efficiency

4 4 Wireless Sensor Network - System Model Network topology and multi-path routing: N sensors, one sink, L wireless links Flow conservation law (FCL) is assumed to hold Flows (Out) Flows (In) = Rate Communication model FDMA with full-duplex Transmit, receive and relay data Transmit power and bandwidth allocation Resource constraints Pre-allocated frequency bands Wireless communication links with Rayleigh flat fading Inverse-square path loss

5 5 1. Distributed Source Coding (DSC) of Spatially Correlated Sources

6 6 Slepian-Wolf Coding a) Independent encoding a) b) and c) b) Joint encoding c) Distributed source coding (DSC) Slepian-Wolf rate region:

7 7 Slepian-Wolf Coding in Single-Sink Data Gathering Data gathering problem: Minimize the total transportation costs of delivering all the source messages to the destination for joint decoding Solution: 1. Find the shortest path tree (SPT) 2. Assign the SW rates: The closest node Y 1 sends with its entropy H(Y 1 ) The second closest conditions on node Y 1 and sends with H(Y 2 Y 1 ) Nodes far away from the sink transmit communicate with lower rate Gaussian random field Global SW Local SW

8 8 SW Coding in Single-Sink Data Gathering WSN: Reduction in the total transmit power 24 nodes Compares the total transmit power usage in the WSN: SW coding vs. Independent encoding SW performs better With high correlation, significant energy savings Correlation decreases

9 9 2. Distributed Transmission Optimization in Multi-hop WSNs

10 10 Problem: Total Transmit Power Minimization The objective function is to minimize the total transmit power with respect to the data delivery constraint in the wireless sensor network: Flow conservation law (FCL) Capacity constraint (CC) Total power and bandwidth constraints (TPC) (TBC) where the optimization link variables are power, bandwidth and flow: The problem is Convex Coupled across the nodes via the FCL constraint

11 11 Distributed Transmission Optimization: Two alternatives Dual Decomposition Commonly used, state of the art method 2 decomposition levels with layering philosophy (horizontal and vertical) Slow convergence Consensus ADMM Novel approach Based on consensus mechanism 1 decomposition level (horizontal) Fast convergence

12 12 Distributed Transmission Optimization: Dual Decomposition Partial Lagrangian with a proximal regularization term The dual function separates into 1. Routing subproblem in the network layer 2. Resource allocation subproblem in the physical layer The dual problem is solved with the subgradient method Algorithm principles: Iterations - at each node: 1. Find the optimal flow variables (Routing subproblem) 2. Communicate 1 variable across each link 3. Find the optimal power and bandwidth variables 4. Update the dual variables 5. Communicate 1 variable across each link Until convergence (Resource allocation subproblem) 2 variables exchanged per link at each iteration

13 13 Distributed Transmission Optimization: Consensus ADMM (1/2) 1. Consensus optimization framework: Introduce local copies of flow variables 2. ADMM (Alternating Direction Method of Multipliers) Introduce augmented partial Lagrangian Sequential optimization The problem decouples across the nodes Drive the local copies into consensus Duplicates for the end nodes Per-node optimization subproblems ADMM

14 14 Distributed Transmission Optimization: Consensus ADMM (2/2) At each node iterate until convergence: 1. Find the set of local variables (local flow variables, power and bandwidth variables) 2. Broadcast the obtained local flow variables to the neighboring nodes 3. Set the optimal global flow variables by averaging over the local copies 4. Update the dual variables by the method of multipliers update Obtained variables Local flows Resource variables 2. Global flows Dual variables Iteration steps Input variables Global flows Dual variables Local flows Local flows Global flows Dual variables (previous values) 2 variables exchanged per link at each iteration

15 15 Distributed Transmission Optimization: Convergence with tuned step sizes Solution feasibility Solution accuracy 8 nodes The ADMM algorithm converges significantly faster to near-optimal solution than the dual decomposition

16 16 Distributed Transmission Optimization: Average convergence without step size tuning Average number of iterations for convergence Solution accuracy 500 random channel realizations Order of magnitude smaller number of iterations for the ADMM as compared to DD

17 17 3. Compressed Sensing (CS) Data Gathering in Multi-hop WSNs

18 18 Compressed Sensing Data Gathering in WSNs (1/2) Monitoring applications: Temperature, humidity, light intensity... Spatial correlation Distance dependent Power exponential correlation function Smooth field Sparsity can be revealed by a proper transformation Use compressed sensing (CS) for reducing the amount of transmitted data in the WSN The CS theory: One can recover a signal from much fewer samples or measurements than the conventional signal acquisition and compression limits are stating Spatial correlation Sparsity after transformation Compressed data gathering

19 19 Compressed Sensing Data Gathering in WSNs (2/2) CS in nutshell Encode Decode Perform CS data aggregation at a node when the amount of transmitted data can be reduced Linear random combination of the received data units and node s own data Instance of network coding Energy savings by data aggregation in large networks

20 20 Compressed Sensing Data Gathering in WSNs: Recovery performance & Communication costs Recovery error 100 random drops Comparison to multi-hop forwarding without CS: BCR: Maximum amount of data units of a node for CS Maximum amount of data units of a node for MHF TCR: Total amount of data units in WSN for CS Total amount of data units in WSN for MHF Communication costs With M=90, error is below 3 % and the maximum amount of data a node has to transmit is reduced by ~50 % Potentiality to prolong the network lifetime

21 21 Publications Power Minimization in Single-Sink Data Gathering Wireless Sensor Network via Distributed Source Coding, Markus Leinonen, Master s Thesis, Oulun yliopisto, Distributed Power and Routing Optimization in Single-Sink Data Gathering Wireless Sensor Networks, Markus Leinonen, Juha Karjalainen, and Markku Juntti, European Signal Processing Conference (EUSIPCO) 2011, Aug Sep. 2, Barcelona, Spain. Consensus Based Distributed Joint Power and Routing Optimization in Wireless Sensor Networks, Markus Leinonen, Marian Codreanu, and Markku Juntti, IEEE Global Communication Conference 2012, Dec. 3. 7, Anaheim, USA. Distributed Consensus Based Joint Resource and Routing Optimization in Wireless Sensor Networks, Markus Leinonen, Marian Codreanu, and Markku Juntti, Asilomar Conference on Signals, Systems and Computers 2012, Nov , Pacific Grove, USA. Distributed Joint Resource and Routing Optimization in Wireless Sensor Networks via Alternating Direction Method of Multipliers, Markus Leinonen, Marian Codreanu, and Markku Juntti, IEEE Transactions on Wireless Communications, Submitted in Aug. 2012, Major revision in Jan. 2013, Resubmitted in Mar Distributed Data Gathering in Wireless Sensor Networks via Compressed Sensing, Markus Leinonen, Marian Codreanu, and Markku Juntti, Fourth Nordic Workshop, SNOW, 2013, Apr. 2. 5, Ylläs, Finland, Presented. Presentation only, no proceedings to be published.