Dynamic Compression-Transmission for                  Energy-Harvesting Multihop Networks                  with Correlated...
Distributed data gathering                         d¨  Collect spatial correlated measurements¨  Route the measurements ...
Distributed data gathering (2)                         d¨    Distributed data gathering for correlated sources      ¤  S...
Distributed data gathering (3)                           d¨    Energy management:      ¤  Acquisition/compression      ¤...
Distributed data gathering (4)                           d¨    Network data queues stability:                            ...
Prior Work¨    Energy Harvesting      ¤  Mostlyaccounts only for the energy consumption of        transmission¨    Ener...
Contributions [Tapparello12]¨    Combine in the same optimization framework:      ¤  Energy       management         n ...
System model¨    Transmission model      ¤  Network  operates in slotted time      ¤  Channel state S(t)      ¤  Trans...
System model (2)  ¨    Data acquisition, compression and distortion model        ¤  Spatial  correlated signal, source s...
System model (3)¨    Energy model      ¤  Energy-harvesting  state H(t)      ¤  Nodes are powered via energy harvesting...
Queuing dynamics¨    Energy      En (t + 1) = En (t)    tx                            En (t)    c            e           ...
Problem formulation                                  N                                  X       T 1                       ...
Solution¨    We addressed the problem using the Lyapunov      optimization technique [Neely10]      ¤  Minimize     a dr...
Main results¨    From theorem 5.1, tunable parameter V:                             En (t)  O(V )                       ...
Numerical results - Scenario(R1 (t), D1 (t))            1                4       d                                2       ...
Numerical results - Scenario(R1 (t), D1 (t))            1                4       d                                2       ...
Numerical results                                                                                            ! = 0.5      ...
Numerical results (2)                                                                                                 ! = ...
Extension with side information at                                           the sink                            d        ...
Extension with side information at                                         the sink (2)¨    Side information affects the ...
Simulation scenario                                                          Rd (t)      (R1 (t), D1 (t))      1          ...
Numerical results                          650                          600                          550                  ...
Numerical results (2)                 0.45                  0.4                 0.35                  0.3      F0 (MSE)   ...
Conclusions¨    Dynamic online optimization for multihop wireless sensor      networks with energy harvesting capabilitie...
Selected references¨    [Tapparello12] C. Tapparello, O. Simeone and M. Rossi,      “Dynamic Compression-Transmission for...
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Dynamic Compression Transmission for Energy Harvesting Networks

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Dynamic Compression-Transmission for Energy-Harvesting Multihop Networks with Correlated Sources.

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Dynamic Compression Transmission for Energy Harvesting Networks

  1. 1. Dynamic Compression-Transmission for Energy-Harvesting Multihop Networks with Correlated Sources Cristiano Tapparello*, Osvaldo Simeone† and Michele Rossi* * Department of Information Engineering, University of Padova, Italy † CWCSPR, New Jersey Institute of Technology, New Jersey, USACristiano Tapparello 12/04/12
  2. 2. Distributed data gathering d¨  Collect spatial correlated measurements¨  Route the measurements through the network in order to gather them through a sink nodeCristiano Tapparello 12/04/12
  3. 3. Distributed data gathering (2) d¨  Distributed data gathering for correlated sources ¤  Source coding techniques ¤  Lossy compression (distortion) ¤  Rate-distortion regionCristiano Tapparello 12/04/12
  4. 4. Distributed data gathering (3) d¨  Energy management: ¤  Acquisition/compression ¤  Transmission ¤  Harvesting¨  Battery operating devices è energy availability constraintCristiano Tapparello 12/04/12
  5. 5. Distributed data gathering (4) d¨  Network data queues stability: T 1 N 1 XX lim sup E[Un (t)] < 1 T !1 T t=0 n=1Cristiano Tapparello 12/04/12
  6. 6. Prior Work¨  Energy Harvesting ¤  Mostlyaccounts only for the energy consumption of transmission¨  Energy trade-offs between source coding and transmission ¤  Donot model the additional constraints arising from energy harvesting¨  Distributed source coding techniques ¤  Donot consider energy harvesting nor the energy consumption of the sensing processCristiano Tapparello 12/04/12
  7. 7. Contributions [Tapparello12]¨  Combine in the same optimization framework: ¤  Energy management n  Acquisition/compression n  Transmission n  Harvesting n  Energy availability constraint ¤  Data gathering with lossy compression (distortion) ¤  Multi-hop routing and scheduling ¤  Subject to queue stability¨  Goal: Obtain online policies that minimize the total average distortionCristiano Tapparello 12/04/12
  8. 8. System model¨  Transmission model ¤  Network operates in slotted time ¤  Channel state S(t) ¤  Transmission rate µn,m (t) = Cn,m (P(t), S(t)) ¤  Outgoing transmission rate X µn,⇤ (t) = µn,m (t) m: (n,m)2L ¤  Incoming transmission rate X µ⇤,n (t) = µm,n (t) m: (n,m)2LCristiano Tapparello 12/04/12
  9. 9. System model (2) ¨  Data acquisition, compression and distortion model ¤  Spatial correlated signal, source state O(t) ¤  Each node compress the measured source with rate, Rn (t) ¤  Distortion at the sink (MSE), Dn (t) ¤  Rate-Distortion constraints [Zamir99] !X Y |X | Rn (t) g(X , O(t)) log (2⇡e) Dn (t) , for all X ✓ Nn2X n2X ¤  Source acquisition and compression cost c En (Rn (t)) = ↵n Rn (t) Cristiano Tapparello 12/04/12
  10. 10. System model (3)¨  Energy model ¤  Energy-harvesting state H(t) ¤  Nodes are powered via energy harvesting è energy harvesting decisions e 0  Hn (t)  Hn (t) ¤  Energy availability constraints tx c En (t) + En (Rn (t))  En (t)Cristiano Tapparello 12/04/12
  11. 11. Queuing dynamics¨  Energy En (t + 1) = En (t) tx En (t) c e En (Rn (t)) + Hn (t)¨  Data Un (t + 1)  max{Un (t) µn,⇤ (t), 0} + µ⇤,n (t) + Rn (t)Cristiano Tapparello 12/04/12
  12. 12. Problem formulation N X T 1 ⇡ 1 X minimize F0 = lim sup E[fn (Dn (t))] ⇡ n=1 T !1 T t=0 subject to: !X Y |X | Rn (t) g(X , O(t)) log (2⇡e) Dn (t) , for all X ✓ Nn2X n2X tx c En (t) + En (Rn (t))  En (t) T 1X X N 1 lim sup E[Un (t)] < 1 T !1 T t=0 n=1 Cristiano Tapparello 12/04/12
  13. 13. Solution¨  We addressed the problem using the Lyapunov optimization technique [Neely10] ¤  Minimize a drift-plus-penalty function¨  We propose a distributed algorithm ¤  Energy harvesting ¤  Rate-Distortion optimization ¤  Power allocation¨  The algorithm returns online policies with tunable and bounded performance guarantees with respect to the optimal policiesCristiano Tapparello 12/04/12
  14. 14. Main results¨  From theorem 5.1, tunable parameter V: En (t)  O(V ) Un (t)  O(V ) X T 1 X ✓ ◆ ⇡ 1 ⇤ 1 F0 = limsup E[fn (Dn (t))]  F0 +O T !1 T t=0 V n2NCristiano Tapparello 12/04/12
  15. 15. Numerical results - Scenario(R1 (t), D1 (t)) 1 4 d 2 5 (R2 (t), D2 (t)) N 3 (R3 (t), D3 (t)) ¨  Jointly Gaussian signal samples with zero mean and correlation matrix 2 3 1 ! ! O(t) = 4 ! 1 ! 5 ! ! 1 Cristiano Tapparello 12/04/12
  16. 16. Numerical results - Scenario(R1 (t), D1 (t)) 1 4 d 2 5 (R2 (t), D2 (t)) N 3 (R3 (t), D3 (t)) ¨  Channel state matrix S(t) has independent and Rayleigh distributed entries ¨  Energy-harvesting vector H(t) has independent entries, uniformly distributed in [0, Hmax ] Cristiano Tapparello 12/04/12
  17. 17. Numerical results ! = 0.5 0.65 0.6 0.55 0.5 F0 (MSE) 0.45 0.4 0.35 0.3 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 VCristiano Tapparello 12/04/12
  18. 18. Numerical results (2) ! = 0.5 6000 Max Average 5000 4000 Queue size 3000 2000 1000 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 VCristiano Tapparello 12/04/12
  19. 19. Extension with side information at the sink d c¨  Role of side information available at the sink ¤  Acquiring the side information entails an energy cost¨  Sink transmits to a network collector nodeCristiano Tapparello 12/04/12
  20. 20. Extension with side information at the sink (2)¨  Side information affects the Rate-Distortion region ¤  Entropy function is conditioned on the side information available at the receiver¨  Additional constraints for the sink ¤  Energy management n  Acquisition n  Transmission ¤  Data queue stability¨  Similar optimality properties as theorem 5.1Cristiano Tapparello 12/04/12
  21. 21. Simulation scenario Rd (t) (R1 (t), D1 (t)) 1 4 d c 2 5 (R2 (t), D2 (t)) N 3 (R3 (t), D3 (t))¨  Simple source model for which 2 3 1 !!d (t) !(1 !d (t)) !(1 !d (t)) Rd (t)O(t) = 4 !(1 !d (t)) 1 !!d (t) !(1 !d (t)) 5 , !d (t) = 1 2 !(1 !d (t)) !(1 !d (t)) 1 !!d (t)Cristiano Tapparello 12/04/12
  22. 22. Numerical results 650 600 550 500 Queue Size [bits] 450 Rd(t) = 0 400 Optimized Rd(t) 350 300 250 200 150 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cristiano Tapparello 12/04/12
  23. 23. Numerical results (2) 0.45 0.4 0.35 0.3 F0 (MSE) Rd(t) = 0 0.25 Optimized Rd(t) 0.2 0.15 0.1 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cristiano Tapparello 12/04/12
  24. 24. Conclusions¨  Dynamic online optimization for multihop wireless sensor networks with energy harvesting capabilities¨  Joint optimization of source coding and data transmission for time varying sources and channels¨  The proposed scheme achieve explicit and controllable trade-off between optimality gap and queue sizesCristiano Tapparello 12/04/12
  25. 25. Selected references¨  [Tapparello12] C. Tapparello, O. Simeone and M. Rossi, “Dynamic Compression-Transmission for Energy-Harvesting Multihop Networks with Correlated Sources”, submitted for publication (technical report arXiv:1203.3143).¨  [Zamir99] R. Zamir and T. Berger, “Multiterminal source coding with high resolution,” IEEE Transactions on Information Theory, vol. 45, no. 1, pp. 106–117, Jan. 1999.¨  [Neely10] M. J. Neely, “Stochastic Network Optimization with Application to Communication and Queuing Systems”, Morgan & Claypool Publishers, 2010.Cristiano Tapparello 12/04/12

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