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 Wireless Multihop Multihop Network Broadcast Network Broadcast

• 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 Minimum-

• energy broadcast

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

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

Wireless advantage Wireless advantage Accumulative broadcast Accumulative broadcast

• Allow nodes to collect energy of unreliably received signals

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

• After K nodes retransmit a codeword X:

Maximum achievable rate at node m: rm = W log2(1 + hmk pk / NoW)

• For a given broadcast rate at the source

r = W log2(1+PT / NoW)

• Node m reliable when

k

hmk pk PT

Relays use Relays use “ “Repetition Coding Repetition Coding” ”

p1 p2 p3 pK

source

• All the nodes use the same codebook: relays resend the same code

All the nodes use the same codebook: relays resend the same codeword word

Y Y

X X X X X X X X

m k=1 K

• As W → ,

rm → hmk pk / Noln2

• MAC upper bound:

CMAC = W log2(1 + hmk pk / NoW) → hmk pk / Noln2

• Orthogonal channels preclude the coherent combining gain

Repetition is OK for Large W Repetition is OK for Large W

source

• Given fixed powers {p1,…pK } 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.

• How do we solve the accumulative broadcast problem?

How do we solve the accumulative broadcast problem?

m p1 p2 p3 pK

• k

k k k

Network lifetime Network lifetime

• A lifetime of a node i - transmission time until node battery is fully drained

Ti (pi ) = ei / pi

ei - initial battery energy pi - transmit power

• Network lifetime - duration of a data session until the first node battery is

fully drained

Tnet (p)= min Ti (pi )

• 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

xij=

• xij indicates that node i collects energy from a transmission by node j
• Define a gain matrix H(X): [H(X)]ij = hij xij
• Problem defined as:

Transmission schedule Transmission schedule

min max { pi /ei } H(X)p 1PT p 0

1 node i scheduled to transmit after node j 0 otherwise

min max { pi /ei } h21 p1 PT h31 p1 + h32 p2 PT h41 p1 + h42 p2 + h43 p3 PT h51 p1 + h52 p2 + h53 p3 + h54 p4 PT p1, p2, p3, p4

• Network of N = 5 nodes
• Consider a schedule [1 2 3 4 5]
• Problem is defined as

Maximum network lifetime problem Maximum network lifetime problem

1 4 5 2 3 source

X=

0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0

• Different node batteries use normalized node powers
• Problem becomes
• Maximum network lifetime LP

min max pi H(X)p 1PT p 0

LP for Transmit Powers LP for Transmit Powers

pi = pi e1 / ei q*(X) = min q H(X)p 1PT p 1q p 0

• Minimum Total Power
• Maximum Lifetime
• 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?

Min Power vs. Max Lifetime Min Power vs. Max Lifetime

min i pi H(X)p 1PT p 0 min max { pi /ei } H(X)p 1PT p 0

Max lifetime Max lifetime

• Identifying one best schedule is not crucial
• Solution: Power p*=minX q*(X) and a schedule for which p* is feasible
• Power p*=minX 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 The ASAP( ASAP(p p) distribution ) distribution

• Use the observation:
• 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 As soon as one node transmits with p: every reliable node can use p with no impact on the network lifetime

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

source power p reliable reliable

• Source transmits with power p

any node can transmit with p no impact on the network lifetime

• At each stage:

Set of nodes that became reliable in the previous stage transmit with p

• 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

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=PT / h21
• 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

MLAB MLAB – – the ASAP( the ASAP( p p*

*) distribution

) distribution

source power p reliable reliable

1. Initialize power: p=PT / h21

• 2. Apply ASAP(p)
• 3. If ASAP(p) stalls:
• 4. For all j unreliable find j:

PT = (p+j) hjk set: * =min j increase: p ← p+* go to 2.

ASAP(p) stalls power p reliable reliable

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 with the most disadvantaged child

• Accumulative broadcast:

Nodes cooperatively transmit to increase the shortest lifetime in the network All relay nodes have the same lifetime

network lifetime transmitted energy source

Accumulative broadcast enables load balancing Accumulative broadcast enables load balancing

2 transmitted energy network lifetime 3 4 5 6 source

• Conventional broadcast:

Network lifetime determined by node with the most disadvantaged child

• Accumulative broadcast:

Nodes cooperatively transmit to increase the shortest lifetime in the network All relay nodes have the same lifetime

Total power Total power

• Min energy algorithms:

Conventional broadcast

• BIP

[J. Wieselthier, G. Nguyen &

• A. Ephremides]

Accumulative broadcast

• Greedy filling algorithm

Maximum power Maximum power

• Min energy algorithms:

Conventional broadcast

• BIP

[J. Wieselthier, G. Nguyen &

• A. Ephremides]

Accumulative broadcast

• Greedy filling algorithm

Conclusion 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 *