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Energy Efficient Transmission Strategies for Sensor Networks with Energy Harvesting

1. Energy Efficient Transmission Strategies for Sensor Networks with Energy Harvesting. Biplab Sikdar, RPI + NUS. Research Interests. 2. MAC protocols for wireless networks Green networks Smart power systems Network security Network protocols Swtich architectures.

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Energy Efficient Transmission Strategies for Sensor Networks with Energy Harvesting

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  1. 1 Energy Efficient Transmission Strategies for Sensor Networks with Energy Harvesting Biplab Sikdar, RPI + NUS

  2. Research Interests 2 • MAC protocols for wireless networks • Green networks • Smart power systems • Network security • Network protocols • Swtich architectures Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  3. Outline 3 • Sensor networks: Applications and challenges • The energy problem • Modeling energy harvesting • Event Loss Probability due to Run-out (ELPR) • Average Time to Run-Out (ATRO) • Harvesting-aware communications for WSNs • Direct transmissions • Choosing transmission modes • Cooperative, relay-based transmissions • Relay scheduling • Conclusions Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  4. Sensor Networks: Applications and Challenges 4 • Applications • Cyber-physical applications • Disaster recovery applications • Medical applications • Military applications • Research Challenges • Limited battery power • Scalability • Reliability • Distributed operation • Security Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  5. The energy problem 5 • A major hurdle in the adoption of sensor networks is the energy problem • Batteries with low cost and suitable form factor do not have sufficiently long life time. • Battery replacement is an inconvenience for user. • Battery replacement is not feasible for in-vivo implants • Battery energy density trend does not promise short term solution • Other energy supply technologies such as fuel cells are not mature enough for near term use Source: J. A. Paradiso, and T. Starner, “Energy scavenging for mobile and wireless electronics,” IEEE Pervasive Computing, vol. 4, issue 1, pp. 18-27, January-March 2005. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  6. Energy Harvesting for WSNs 6 • Energy Harvesting (EH) is one of the most promising solutions for WSNs • Motion based • Thermal/light based • Vibration based • EH brings a new dimension to communications • Channel model • Traffic Model • Energy model • Challenges in EH WSNs • More efficient EH circuits • More efficient, harvesting-aware, communications • Modeling energy availability • Matching energy use to energy availability Source: J. A. Paradiso, “Energy Harvesting for Mobile Computing,” DCU, July 2006. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  7. Harvesting-Aware Communications 7 • Energy harvesting adds a new dimension to the problem • The battery power is not a non-increasing function of time • Decisions to be made based on both the current state as well as expectations in the future • Many tradeoffs possible in terms of energy and communication “quality” • Problem: How to choose the communication mode? • Problem: Direct or relay based transmission? Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  8. Energy model for EH-WSNs 8 • Assume motion based energy harvesting • Model human activity with a K state Markov Model • In each state, si, the EH device in node j harvests energy at the rate of ci,j • Simple, two state model: • Assume only two states (Rest and Walk) • Independent EH in different nodes Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  9. Energy model for EH-WSNs 9 • Assume • Each event (packet TX/RX) requires energy  • During each time slot, an event happens with probability p • Total battery capacity of the device is equal to B=(N-1) • Define time unit as T = /c. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  10. Loss Probability due to Run Out 10 • Loss Probability due to Run-Out (LPRO) • LPRO serves as a long-term performance metric • This metric can be used to determine design parameters (battery size, EH power, etc) • To calculate LPRO we first calculate the steady state probability for each state, n. • The steady state probabilities can be found using the eigen analysis of the transition matrix P: The steady state probabilities are given by the eigen vector  corresponding to eigen value =1. • LPRO is then given by LPRO = p0 • A closed form expression was also derived for the LPRO Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  11. Loss Probability due to Run Out 11 • Five boundaries: Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  12. Loss Probability due to Run Out 12 w = 0.005, r = 0.045 Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  13. Average Time to Run Out 13 • Average Time to Run-Out (ATRO) • ATRO serves as a vulnerability metric for each node • This vulnerability metric can be used in protocols to optimize BAN operation • To calculate ATRO, we use a modified Markov model, where once the chain reaches state 0, it will remain there for ever. • The ATRO for the original model is equivalent to the average absorption time in the modified model Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  14. Average Time to Run Out 14 • The transition matrix P is of the form • The fundamental matrix Q is defined as Q = (I-S)-1 • ij-th entry of Q is the number of times, starting in state i, we expect to visit state j before absorption • The total number of steps before absorption is the total number of visits we expect to make to all the non-absorbing states • The average absorption times can be calculated from summation of rows of Q • A closed form expression was also derived for the ATRO Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  15. Average Time to Run Out 15 p = 0.1,w = 0.005, r = 0.045, N = 20 Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  16. Extensions: Battery Dimensioning 16 Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  17. Harvesting-Aware Communications 17 • Discrete time, slotted operation • Energy harvesting model: • Two state model • {c,0} energy units per time slot • Event generation model: • Two state model • {1,0} events per time slot Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  18. Harvesting-Aware Communications 18 • Battery capacity: infinite • Fixed energy consumption of 0 per slot • Two transmission modes • Mode 1: • Energy consumption: 1 • Packet success rate: 1 • Mode 2: • Energy consumption: 2 • Packet success rate: 2 • 1>2 & 1>2 Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  19. Problem Definition 19 • Tradeoff between energy consumption and successful packet delivery • Transmit at higher power if energy harvesting is expected in the near future • Define: a policy  that selects the mode to be used for a transmission given the state of the energy harvesting and event generation process • Problem: What action at {0,1,2}should be taken at time t in response to a data packet so that the quality of coverage (steady state ratio of events that are detected and correctly reported)is maximized? Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  20. Bound on the Performance 20 • System state at time t:Xt=(Lt,Et,Yt) • Energy level: Lt {0,1,2,…} • Harvesting process: Yt {0,1} • Event process: Et {0,1} • Action taken at time t: at {0,1,2} • Steady state probability of event occurrence • Steady state probability of energy harvesting Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  21. Bound on the Performance 21 • Claim: The performance of the optimal policy OPT is bounded by • Intuition: • Steady state probability of detecting and successfully reporting a packet: PS • First show that • The expected charge level at time t Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  22. Bound on the Performance 22 • Intuition: • Now E[Lt]  0. Then, • Manipulation of the two expressions gives the desired result Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  23. Improvement on the Bound 23 • The previous bound can be loose if the recharge rate is faster than the discharge rate • The fast recharge scenario is characterized by • The performance of the optimal policy OPT is then bounded by Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  24. Aggressive Policy 24 • A policy that always transmits at Mode 1 if L 0 + 1 • The policy transmits at Mode 2 if 0 + 2L < 0 + 1 • Performance of the aggressive policy: • The event generation process strictly alternates between on and off states • Consider the interval between two successive slots where the event process goes to the off state • Renewal period with expected length • Expected energy generated in the renewal period Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  25. Aggressive Policy 25 • Maximum energy that can be spent on circuitry is 0E[TR] • Energy available for communications • The performance of the aggressive policy A is upper bounded by • The performance of the aggressive policy A is lower bounded by Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  26. Energy Balancing Policy 26 • Intuition: Transmission scheduling decisions should be made so that the expected energy generated is equal to the expected energy spent to report all events. • Expected number of events correctly reported in a renewal period is (11 + 22)E[N] • Expected number of events correctly reported in [0,T] • Performance of the energy balancing policy Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  27. Energy Balancing Policy 27 • The optimal energy balancing policy EB is obtained by solving • The performance of the energy balancing policy EB is bounded by Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  28. Energy Balancing Policy 28 • The performance of the aggressive and energy balancing policies are related by • The performance of the aggressive policy cannot exceed that of the energy balancing policy Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  29. MDP formulation 29 • System state at time t:Xt=(Lt,Et,Yt) • Energy level: Lt {0,1,2,…,K} • Harvesting process: Yt {0,1} • Event process: Et {0,1} • Action taken at time t: at {0,1,2} • The device receives a reward of 1 if an event is successfully detected and reported. • Reward function: Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  30. MDP formulation 30 • Energy gained/lost at time t: (gt/lt) • Next state of the system Xt+1=(Lt+1,Et+1,Yt+1): Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  31. Generalization 31 • Possible to generalize to arbitrary number of transmission modes • A. Seyedi and B. Sikdar “Energy Efficient Transmission Strategies for Body Sensor Networks with Energy Harvesting,” IEEE Transactions on Communications, vol. 58, no. 8, August 2010. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  32. Quality of Coverage 32 qon = 0.75, poff=0.9, c=2, 1=0.9, 0=1, 1=2 and 2=1 pon = 0.6, 2=0.4 1/1>2/2 pon = 0.7, 2=0.6 1/1<2/2 Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  33. Tightness of Bound 33 qon = 0.75, pon = 0.7, poff=0.9, c=2, 1=0.9, 2=0.6, 1=2 and 2=1 Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  34. Relay-based Cooperative Communications and EH-WSNs • Three-terminal Relay Network • Cooperation Protocols • Amplify-and-Forward (AF) and Decode-and-Forward (DF) • The use of a relay may dynamically distribute the overall power consumption among the source and the relay • At a given instant of time, should the source transmit directly or use the relay for the next data packet? Relay yr xr hs,r hr,d yd xs Destination Source hs,d Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  35. System Model • Categorize each sensor as either a Source or a Relay • A Source can transmit a packet directly (direct mode) or use a relay (relay mode) • A Relay can help a Source (relay mode) or transmit its own packet on its own (own-traffic mode). • Different energy consumptions • A Source: • A Relay: • Event Generation Process and Energy Generation Process • Discrete slotted time model • Independent Correlated two-state Markov processes Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  36. Upper Bound on the Performance • Objective – maximizing the quality of coverage • ( )- number of events occurred (detected and correctly reported) in the sensing region of a sensor over a period of T slots in the interval [0, T]. - steady-state probability of event occurrence - steady-state probability of energy harvesting occurrence - energy generation units per slot Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  37. Markov Decision Process Formulation • System State • - energy available at time t. Assuming the battery capacity is K. • - equals 1 if an event to be reported during [t, t+1), 0 o.w. • - equals 1 if being charged at time t, 0 o.w. • Actions • 0 - {no transmission, no transmission}; 1 – {direct, no transmission} 2 – {relay, relay}; 3 – {direct, own-traffic}; 4 – {no tranmsission, own-traffic} • Probability Transition - amount of energy gained in the interval [t, t+1) - amount of energy spent in the interval [t, t+1) Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  38. MDP Formulation (cont.) Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  39. MDP Formulation (cont.) • Reward Function • Value Iteration considering the average expected reward criteria • Optimality equation Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  40. Simulation Results • Three-node-group model (source, relay, and destination) • MATLAB based simulator with energy harvesting • No retransmissions Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  41. Effect of Event Generation Process on the Performance Parameters Used: Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  42. Explaining the Approximation Errors • Let be the number of slots in which action i is taken. Parts of the bound are achieved as follows, , the term is omitted ---(1) , the term is omitted ---(2) • When is low and is high, . The source has enough energy and tends to transmit the packet directly and the relay spends most of its energy and time slots on its own traffic. Consequently, T2 is small and the approximation error from (2) is small. • As increases, errors come from (1) and (2). The high packet generation rate at the source results in a low battery level at the source and a higher use of the relay to transmit the source’s packet. The fraction increases, the bound becomes looser. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  43. Cooperative Transmissions Under Partial State Information 43 • Optimal transmission scheduling with relays relies on the presence of perfect state information of the relays • Assumption: when a relay transmits or relays data, packet headers include the state information. • In periods without data, conveying the state information of the relay in real time represents a significant overhead. • Thus the source may have to base its decision on stale state information. • Problem: determine the optimal decision based on partial information about the system. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  44. System Model • Categorize each sensor as either a Source or a Relay • A Source can transmit a packet directly (direct mode) or use a relay (relay mode) • A Relay can help a Source (relay mode) or transmit its own packet on its own (own-traffic mode). • Different energy consumptions • A Source: • A Relay: • Event Generation Process and Energy Generation Process • Discrete slotted time model • Independent Correlated two-state Markov processes Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  45. Partially Observable MDP Formulation • System State • - energy available at time t. Assuming the battery capacity is K. • - equals 1 if an event to be reported during [t, t+1), 0 o.w. ([t-1,t) for relays) • - equals 1 if being charged at time t, 0 o.w. ([t-1,t) for relays) • Actions • 0 - {no transmission, no transmission}; 1 – {direct, no transmission} 2 – {relay, relay}; 3 – {direct, own-traffic}; 4 – {no transmsission, own-traffic} • System observation at time t is denoted by Yt where denotes that variable is unknown. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  46. POMDP Formulation (cont.) 46 • The observation space is given by with • Approach: convert to equivalent, fully observable MDP • The state space of the equivalent MDP consists of the space of probability distributions on the original state space • Key result: The state space represented by is countable • This guarantees the existence of an optimal solution to the optimal reward function (Cassandra et. al.) • The solution to the equivalent MDP with complete state information provides the optimal actions to take in the POMDP Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  47. POMDP Formulation (cont.) 47 • Denote the state space of the equivalent MDP as ∆, and its state at time t as Zt • Then Zt  ∆ is a information vector of length |X|, whose i-th component is given by • The state Zt+1is recursively computable as • The optimality equations for the equivalent MDP are given by Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  48. POMDP Formulation (cont.) 48 • To complete the formulation: • The reward function: Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  49. Simulation Results • Three-node-group model (source, relay, and destination) • MATLAB based simulator with energy harvesting • No retransmissions • H. Li. N. Jaggi and B. Sikdar, “Relay Scheduling for Cooperative Communications in Sensor Networks with Energy Harvesting,” IEEE Transactions on Wireless Communications, vol. 10, no. 9, pp. 2918-2928, September 2011. Biplab Sikdar: WBUT, Kolkata, June 19, 2014

  50. Effect of Event Generation Process on the Performance Parameters Used: Biplab Sikdar: WBUT, Kolkata, June 19, 2014

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