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Efficient Multihop Broadcast for Wideband Systems

Efficient Multihop Broadcast for Wideband Systems. Ivana Maric and Roy Yates. source. Wireless Broadcast. Wireless network of N nodes Source transmits with rate R Messages are to be delivered to all the nodes Nodes can choose a power level for each transmission

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Efficient Multihop Broadcast for Wideband Systems

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  1. Efficient Multihop Broadcast for Wideband Systems Ivana Maric and Roy Yates

  2. source Wireless Broadcast • Wireless network of N nodes • Source transmits with rate R • Messages are to be delivered to all the nodes • Nodes can choose a power level for each transmission • Problem: Broadcast at rate R to all nodes with minimum total power • Comment: N=3 nodes is a single relay channel • How many simplifications are needed?

  3. System Model: Orthogonal Channels • A link: AWGN channel with bandwidth W • Large bandwidth resources • Each transmission in an orthogonal channel • Nodes can listen to all the channels • Motivation: Sensor networks • Low-powered nodes, very low data rates

  4. Minimum-energy broadcast problem • Min-energy broadcast tree problem [J. Wieselthier, G. Nguyen, A. Ephremides] • Wired network: Min-cost spanning tree problem • ‘Wireless multicast advantage’: all the nodes in the transmission range will benefit from a transmission • Problem is NP-complete [M. Čagalj et al., Ahluwalia et al., W. Liang] source source

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

  6. Accumulative broadcast • As the message is forwarded, a node has multiple opportunities to receive energy needed for reliable reception of that message • Key issue: Who do you listen to? source

  7. source Reliable forwarding • A node can forward a message only after reliable decoding • Disadvantage: suboptimal • Benefits: • Simplifies the system architecture • Still allows for unreliable overheard information • Imposes an ordering on the node transmissions source

  8. After K nodes retransmit a codeword X: • Received signal for a symbol x: Y = hx + n • Maximum rate: I(x;y) = W log2(1 + Σ hmkPk/NoW) • Upper bound: CMAC = W Σ log2(1 + hmkPk/NoW) K k=1 K k=1 Relays Use Repetition Coding • Relays resend the same codeword • A node m will decode a codeword using transmissions of a subset of nodes that became reliable prior to node m P1 source X P2 X P3 Y … X m PK X

  9. Repetition is OK for Large W • 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. • As W ∞,I(x;y) Σ hmkPk/Noln2 • MAC Upper bound: CMAC= W Σ log2(1 + hmkPk/NoW) Σ hmkPk/Noln2 source P1 k P2 P3 m … k PK • In such a network, how do we solve the broadcast problem?

  10. 5 3 2 1 4 source source Difference from Min-Energy Broadcast Tree • The total transmit power of the minimum-energy broadcast tree upper bounds the total transmit power of accumulative broadcasting • In the MBT problem, knowing the broadcast tree solves the problem completely: power levels are uniquely determined • For accumulative broadcast, tree is not meaningful • Different total power for orders: 1-2-3 and 1-3-2

  11. Approach • Divide the problem into two subproblems: • Choose a reliability schedule • An order in which nodes become reliable • Also, an order in which nodes are given a chance to transmit • For each node, schedule specifies a subset of nodes that contribute to its reliable decoding • Given a schedule, find the best power levels • Can be formulated as LP

  12. 4 • Fix a schedule: 1 2 3 4 5 • We know which nodes contribute to the energy collected at a node 2 1 3 source 5 LP for Transmit Powers min (p1 + p2 + p3 + p4) h21p1 ≥ PT h31p1+ h32p2 ≥ PT h41p1+ h42p2 + h43p3 ≥ PT h51p1+ h52p2 + h53p3 + h54p4 ≥ PT p1, p2, p3, p4 ≥ 0 • But, finding the optimal schedule is NP-complete.

  13. k = arg max Σ hji jєU iєS Greedy Filling Heuristic • Given S={reliable nodes}, U={unreliable nodes} • Choose node k to maximize “filling rate” of the unreliable nodes • Choose power Pkto make one more node reliable • Offline Optimization: • If node k transmits multiple times, Pk1, Pk2…, set Pk=Σ Pkiand transmit once • Readjust schedule

  14. Simple Experiments • Throw N nodes in a square (100 trials) • Propagation exponent=2 • For small N: • Enumerate all schedules, find optimal AB powers • Compare with • greedy heuristic • BIP [Wieselthier, Nguyen, Ephremides](ignores unreliable overheard messages) • For large N: • Compare greedy heuristic, BIP

  15. Performance results Note: Powers normalized by optimal sol’n

  16. Performance results

  17. Conclusion • Accumulative broadcast: Nodes collect energy of unreliably received signals • Only reliable forwarding is allowed • Large BW, relays can use repetition coding • Formulate problem as two subproblems: • Find a reliable schedule • LP to find the optimum power levels for a given schedule • Finding the optimum schedule is NP-complete • Proposed a heuristics to find a good schedule • Compared the algorithm performance with the optimum solution and BIP performance

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