Cooperative Broadcast for Cooperative Broadcast for Maximum Network - PowerPoint PPT Presentation

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

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

System Model: Orthogonal Channels 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

Minimum- -energy broadcast energy broadcast Minimum • 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

Maximum network lifetime 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

Accumulative broadcast 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

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

Reliable forwarding 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 A node can forward a message only after reliable decoding • Suboptimal • Benefits: • Simplifies the system architecture • Still allows for unreliable overheard information

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

Repetition is OK for Large W 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 . source As W → � , • p 1 r m → � h mk p k / N o ln2 p 2 k k • MAC upper bound: p 3 m C MAC = W � log 2 (1 + h mk p k / N o W) � → � h mk p k / N o ln2 p K k k • Orthogonal channels preclude the coherent combining gain • • How do we solve the accumulative broadcast problem? How do we solve the accumulative broadcast problem?

Network lifetime 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 )

Transmission schedule 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 1 node i scheduled to transmit after node j x ij = 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 � 1 P T p � 0

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

LP for Transmit Powers 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 � 1 P T p � 0 • Maximum network lifetime LP q * ( X ) = min q H ( X ) p � 1 P T p � 1 q p � 0

Min Power vs. Max Lifetime Min Power vs. Max Lifetime • Minimum Total Power min � i p i H ( X ) p � 1 P T p � 0 min max { p i /e i } • Maximum Lifetime H ( X ) p � 1 P 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?

Max lifetime 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

The ASAP( ASAP( p p ) distribution ) distribution The • 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

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

ASAP Theorem 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 * )

Maximum Lifetime Accumulative Broadcast Maximum Lifetime Accumulative Broadcast (MLAB) (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

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

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

Conventional Broadcast Comparison 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

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