The document proposes a framework for distributed data gathering in multi-hop energy harvesting networks with correlated sources. It combines energy management, data compression and transmission, and queue stability optimization. A distributed algorithm is presented that provides online policies minimizing average distortion with bounded performance guarantees. Simulation results demonstrate the approach under various network conditions.

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, USA
Cristiano Tapparello 12/04/12

2. Distributed data gathering
d
¨ Collect spatial correlated measurements
¨ Route the measurements through the network in
order to gather them through a sink node
Cristiano Tapparello 12/04/12

3. Distributed data gathering (2)
d
¨ Distributed data gathering for correlated sources
¤ Source coding techniques
¤ Lossy compression (distortion)
¤ Rate-distortion region
Cristiano Tapparello 12/04/12

4. Distributed data gathering (3)
d
¨ Energy management:
¤ Acquisition/compression
¤ Transmission
¤ Harvesting
¨ Battery operating devices è energy availability constraint
Cristiano Tapparello 12/04/12

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=1
Cristiano Tapparello 12/04/12

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 process
Cristiano Tapparello 12/04/12

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 distortion
Cristiano Tapparello 12/04/12

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)2L
Cristiano Tapparello 12/04/12

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 ✓ N
n2X n2X
¤ Source acquisition and compression cost
c
En (Rn (t)) = ↵n Rn (t)
Cristiano Tapparello 12/04/12

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)
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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. 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 ✓ N
n2X 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
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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 policies
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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
n2N
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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
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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 ]
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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
V
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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
V
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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 node
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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 5.1
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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. 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 1
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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 1
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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 sizes
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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