Cooperative Broadcast for Maximum Network Lifetime. Ivana Maric and Roy Yates

Transcription

1 Cooperative Broadcast for Maximum Network Lifetime Ivana Maric and Roy Yates

2 Wireless Multihop Network Broadcast N nodes Source transmits at rate R Messages are to be delivered to all the nodes Nodes can choose transmit powers source

3 System Model: Orthogonal Channels Each link is an AWGN channel with bandwidth W Each transmission in an orthogonal channel Nodes can listen to all the channels Motivation: Sensor networks Low-powered nodes, very low data rates Large bandwidth resources Objective: Energy-efficient network broadcast protocols Minimum-energy broadcast Maximum-lifetime broadcast

4 Minimum-energy broadcast Problem: Broadcast at rate R to all nodes using minimum total power Formulated as broadcast tree problem [J. Wieselthier, G. Nguyen, A. Ephremides] Wireless multicast advantage: all the nodes in the range hear a transmission Problem is NP-complete [M. agalj et al., Ahluwalia et al., W. Liang] source

5 Maximum network lifetime Problem: Maximize the amount of time until the first node battery dies [J.H. Chang and L. Tassiulas] Performs load balancing: distributes traffic more evenly among the nodes Static solution given by a broadcast tree Based on the initial battery energy levels Dynamic solution consists of a series of broadcast trees [R.J. Marks et al., I.Kang et al.] suboptimal

6 Accumulative broadcast Conventional broadcast: No interference A node forwards only when reliable Each node retransmits the same message A node receives message from only one transmission as specified by a tree Accumulative broadcast Old Idea: Exploit Overheard (side) Information Allow nodes to collect energy of unreliably received signals As the message is forwarded, a node collects multiple unreliable copies until it accumulates energy needed for reliable reception

7 Accumulative broadcast Allow nodes to collect energy of unreliably received signals Wireless advantage Accumulative broadcast

8 Reliable forwarding More energy-efficient than conventional broadcast because it captures more radiated energy Reliable or unreliable forwarding? Any node can decide to forward as soon as it receives an unreliable copy Problem formulation? A node can forward a message only after reliable decoding Suboptimal Benefits: Simplifies the system architecture Still allows for unreliable overheard information

9 Relays use Repetition Coding All the nodes use the same codebook: relays resend the same codeword After K nodes retransmit a codeword X: p 2 X p 1 source Maximum achievable rate at node m: K r m = W log 2 (1 + h mk p k / N o W) k=1 p 3 X X Y m For a given broadcast rate at the source r = W log 2 (1+P T / N o W) Node m reliable when p K X k h mk p k P T

10 Repetition is OK for Large W Given fixed powers {p 1, p K } and reliable forwarding, the maximum rate achievable from the source to any destination is achieved by the repetition coding in the limit of large W. As W, r m h mk p k / N o ln2 k p 2 p 1 source MAC upper bound: C MAC = W log 2 (1 + h mk p k / N o W) h mk p k / N o ln2 k p 3 p K m Orthogonal channels preclude the coherent combining gain How do we solve the accumulative broadcast problem?

11 Network lifetime A lifetime of a node i - transmission time until node battery is fully drained T i (p i ) = e i / p i e i - initial battery energy p i - transmit power Network lifetime - duration of a data session until the first node battery is fully drained T net (p)= min T i (p i )

12 Transmission schedule Choose a transmission schedule An order in which nodes become reliable For each node, schedule specifies a subset of nodes that contribute to its reliable decoding Represent a schedule with matrix X x ij = 1 node i scheduled to transmit after node j 0 otherwise x ij indicates that node i collects energy from a transmission by node j Define a gain matrix H(X): [H(X)] ij = h ij x ij Problem defined as: min max { p i /e i } H(X)p 1P T p 0

13 Maximum network lifetime problem 5 4 Network of N = 5 nodes Consider a schedule [ ] source Problem is defined as min max { p i /e i } X= h 21 p 1 h 31 p 1 + h 32 p 2 h 41 p 1 + h 42 p 2 + h 43 p 3 P T P T P T h 51 p 1 + h 52 p 2 + h 53 p 3 + h 54 p 4 P T p 1, p 2, p 3, p 4 0

14 LP for Transmit Powers Different node batteries use normalized node powers p i = p i e 1 / e i Problem becomes min max p i H(X)p 1P T p 0 Maximum network lifetime LP q * (X) = min q H(X)p 1P T p 1q p 0

15 Min Power vs. Max Lifetime Minimum Total Power min i p i H(X)p 1P T p 0 Maximum Lifetime min max { p i /e i } H(X)p 1P T p 0 Min Total Power is NP-complete Independently shown by [Y-W. Hong & A. Scaglione] - different physical model Finding the best schedule is hard Max Lifetime is easy Why?

16 Max lifetime Identifying one best schedule is not crucial Solution: Power p * =min X q * (X) and a schedule for which p * is feasible Power p * =min X q * (X) feasible for a set of schedules X* To identify X* : use a simple procedure that, for any power p, finds the schedules for which p is feasible

17 The ASAP(p) ) distribution Use the observation: As soon as one node transmits with p: every reliable node can use p with no impact on the network lifetime The ASAP(p) distribution: during a broadcast with power p, a node transmits with p as soon as possible as soon as it becomes reliable

18 The ASAP(p) ) distribution reliable Source transmits with power p any node can transmit with p no impact on the network lifetime power p reliable At each stage: Set of nodes that became reliable in the previous stage transmit with p source If p is large enough, ASAP(p) is a feasible broadcast : message is delivered to all nodes All relays transmit with power p Otherwise, ASAP(p) stalls

19 ASAP Theorem Theorem: If p is a feasible power for a schedule X, then ASAP(p) is a feasible broadcast. ASAP(p) finds all the schedules for which p is feasible For the optimum power p *, ASAP(p * ) is feasible If p * were known, we could broadcast with ASAP(p * )

20 Maximum Lifetime Accumulative Broadcast (MLAB) Finds the power p * to maximize the network lifetime Then, broadcasting with ASAP(p * ) maximizes the network lifetime Finds p * through a series of ASAP(p) distributions Start with the smallest possible power p=p T / h 21 If ASAP(p) stalls at stage µ(p): Find the minimum increase * for which ASAP( p+ * ) doesn t stall at µ(p) Set p= p+ * and perform ASAP(p) MLAB finishes when ASAP(p) makes all nodes reliable

21 MLAB the ASAP( p * ) distribution reliable reliable power p reliable power p source ASAP(p) stalls reliable 1. Initialize power: p=p T / h Apply ASAP(p) 3. If ASAP(p) stalls: 4. For all j unreliable find j: P T = (p+ j ) h jk set: * =min j increase: p p+* go to 2.

22 MLAB finds the optimal power Theorem 2: The MLAB algorithm finds the optimum power p * such that ASAP(p * ) maximizes the network lifetime.

23 Conventional Broadcast Comparison Throw N nodes in a square (100 trials) Compared with [I. Kang & R. Poovendran] static problem solution: MST and MSNL dynamic problem solution: WMSTSW

24 Accumulative broadcast enables load balancing transmitted energy Conventional broadcast: Network lifetime determined by node with the most disadvantaged child network lifetime Accumulative broadcast: Nodes cooperatively transmit to increase the shortest lifetime in the network source All relay nodes have the same lifetime

25 Accumulative broadcast enables load balancing transmitted energy Conventional broadcast: Network lifetime determined by node with the most disadvantaged child network lifetime Accumulative broadcast: Nodes cooperatively transmit to increase the shortest lifetime in the network 3 source 2 All relay nodes have the same lifetime 4 5 6

26 Total power Min energy algorithms: Conventional broadcast BIP [J. Wieselthier, G. Nguyen & A. Ephremides] Accumulative broadcast Greedy filling algorithm

27 Maximum power Min energy algorithms: Conventional broadcast BIP [J. Wieselthier, G. Nguyen & A. Ephremides] Accumulative broadcast Greedy filling algorithm

28 Conclusion Accumulative broadcast: Nodes collect energy of unreliably received signals For maximum lifetime problem: ASAP distribution is optimal MLAB finds min power ASAP distribution Performs load balancing No need for updates: solves the static and dynamic problem Distributed implementation When ASAP stalls: no need to restart Reliable nodes retransmit with power increment *