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Multicast Scaling Laws with Hierarchical Cooperation. Chenhui Hu, Xinbing Wang, Ding Nie, Jun Zhao Shanghai Jiao Tong University , China. Outline. Introduction Motivations Objectives Models and Definitions Multi-hop Hierarchical Cooperative Schemes Achievable Multicast Capacity

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Multicast scaling laws with hierarchical cooperation

Multicast Scaling Laws with Hierarchical Cooperation

Chenhui Hu, Xinbing Wang, Ding Nie, Jun Zhao

Shanghai Jiao Tong University, China


Outline
Outline

Introduction

Motivations

Objectives

Models and Definitions

Multi-hop Hierarchical Cooperative Schemes

Achievable Multicast Capacity

Delay and Energy Consumption

Conclusion and Future Works

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Motivation
Motivation

  • Non-cooperative wireless networks uses multi-hop transmission E.g. unicast [3, Gupta&Kumar], multicast [19, Li]

  • Capacity of wireless ad hoc networks is constrained by interference between concurrent transmissions.

  • Protocol Model:

  • TDMA Scheduling

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Motivation

  • Cooperative networks obtain capacity gain by turning mutually interfering signals into useful ones. [1,Özgϋr]

  • Realize cooperative communication by Distributed MIMO.

  • Two clusters each with M nodes

  • 1) Source node distributes its bits

    2) Every sender holds a different bit,

    and transmits simultaneously

    3) Receiver nodes interchange their

    observations to decode

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Objectives

  • HierarchicalCooperative MIMO has been shown in [2,Özgϋr] achieves a linear throughput scaling for unicast.

  • In our work, we focus onmulticast scaling laws using hierarchical MIMO.1. How to hierarchically schedule multicast traffic to optimize the throughput?2. Delay performance and energy-efficiency when achieving optimal throughput?3. Delay-throughput tradeoff in our hierarchical cooperative multicast strategies?

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Outline1
Outline

Introduction

Models and Definitions

Multi-hop Hierarchical Cooperative Scheme

Achievable Multicast Capacity

Delay and Energy Consumption

Conclusion and Future Works

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Models and definitions i ii
Models and Definitions – I/II

  • Network Model and Traffic:

  • nnodes independently & uniformly distributed in a unit suquare

  • Randomly and independently choose a set of knodes Ui = {ui,j | 1 ≤ j ≤ k} as destination nodes for each node vi

  • Physical-layer Model:

  • Channel gain for the transmission from vj to vi

  • Signal received by node vi at time t

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Models and definitions ii ii
Models and Definitions – II/II

  • Def. of Throughput:

  • A throughput of bits/sec is feasible if there is a spatial and temporal scheme for scheduling, s.t. every node can send bits per second on average to all its destination nodes.

  • Aggregate multicast throughput:

  • Def. of Energy-Per-Bit:

  • Average energy required to carry one bit from a source node to one of its destination nodes —

  • Def. of Delay:

  • Average time it takes for a bit to reach its destination nodes —

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Outline2
Outline

Introduction

Models and Definitions

Multi-hop Hierarchical Cooperative Scheme

General Multicast Structue

MMM & CMMM scheme

Achievable Multicast Capacity

Delay and Energy Consumption

Conclusion and Future Works

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General multicast structure
General Multicast Structure

  • Divide the network into clusters, with M nodes in each cluster.

  • Step 1: Source node will distribute its bits among the nodes, one for each.

  • Step 2: Conduct MIMO transmissions along a spanning tree connecting the clusters where the source and its destinations nodes locate.

  • Step 3: In a cluster having destination nodes, nodes deliver its observation to the destinations for decoding.

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Mmm cmmm scheme
MMM & CMMM scheme

  • Two methods to schedule transmissions in Step 3:

  • Multi-hop MIMO Multicast (MMM)

  • Converge based Multi-hop MIMO Multicast (CMMM)

  • Both schemes involve a hierarchical solution to the transmission problem of Step 3.

  • MMM — Treat the traffic in Step 3 as multicast problem

  • CMMM — Treat the traffic in Step 3 as converge multicast problem, with multi-hop MIMO transmissions

Converge Multicast Problem: Randomly choosea set of nodes asdestinations.Each node in thenetwork acts as a source node andsends one identical bit to all nodes in the set.

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Mmm scheme
MMM Scheme

  • Step 1. Preparing for Cooperation:

    — Each node distributes data to other nodes

  • Step 2. Multi-hop MIMO Transmissions:

    — Routing on the multicast tree

  • Step 3. Cooperative Decoding: To decode, all nodes in the destination cluster first quantify an observation into Q bits. Then each node conveys the Q bits to all destination nodes in the cluster.

The multicast problem in step 3 can also be solved by the same three-step structure. Thus,Implementing it recursively get a hierarchical solution.

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Cmmm scheme
CMMM Scheme

  • Step 3-1. Multi-hop MIMO Transmissions:Since all nodes must send one bit to destination nodes, all clusters act as source clusters and transmit to destination clusters by multi-hop MIMO.

  • Step 3-2. Cooperative Decoding: After a destination cluster receives a MIMO transmission, all nodes quantify the observation and converge them to the destination nodes in the cluster.

  • The multicast problem in step 3-2 is also a converge multicast problem. Implementing the same two-step structure recursively we get a multi-layer solution to converge multicast problem.

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Notations
Notations

  • Notations:

  • : # of layers,

    : indicator for a particular layer

  • : # of nodes,

    : # of destination nodes for each source

  • denotes # of clusters

  • denotes # of destination clusters at layer

  • denotes # of multicast sessions at layer

  • We use Knuth's notation in this paper. Also we use

    to indicate and

    , for any .

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Outline3
Outline

Introduction

Models and Definitions

Multi-hop Hierarchical Cooperative Scheme

Achievable Multicast Capacity

Upper bound of throughput

Achievable throughput of MMM

Delay and Energy Consumption

Conclusion and Future Works

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Upper bound of throughput
Upper bound of throughput

  • [The.] Aggregate multicast throughput is whp bounded by

    where is a constant independent of and .

    • Can we achieve this optimal bound?

      — Intuition: We need make use of interference

    • How can we minimize the delay and energy consumption?

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Achievable throughput of mmm
Achievable Throughput of MMM

  • Calculate time required in the three steps:

  • To optimize the throughput, certain network division is used:

Throughput can be improved by adopting case 2

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Achievable throughput of mmm1
Achievable Throughput of MMM

  • [Lem.]: When , the number of nodes at each layer to achieve optimal throughput in MMM strategy is given by

  • [The.]: By MMM strategy, we can achieve an aggregate throughput of

Note: Throughput analysis of CMMM is similar to that of MMM

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Achievable throughput of mmm2
Achievable Throughput of MMM

  • Results comparison:

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Outline4
Outline

Introduction

Models and Definitions

Multi-hop Hierarchical Cooperative Scheme

Achievable Multicast Capacity

Delay and Energy Consumption

Delay and Energy Consumption

Discussion

Conclusion and Future Works

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Delay and energy consumption
Delay and Energy Consumption

Poor!

huge bulk size

Delay of MMM:

—Consider the delay of MMM recursively

Delay-Throughput Tradeoff:

Energy Consumption of MMM:

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Delay and energy consumption1
Delay and Energy Consumption

  • Delay of CMMM:

  • Delay-Throughput Tradeoff:

  • Energy Consumption of CMMM:

Delay reduces from exponential to linear!

Similar to energy cost of MMM

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Discussion
Discussion

The Advantage of Cooperation: improve the aggregate throughput by compared to non-cooperative scheme in [19].

The Effect of Different Network Division: we divide the network into fewer clusters as gets bigger.Special case: in broadcast , our cooperative scheme cannot render any gain on throughput.

Delay-Throughput Tradeoff: nearly the same as non-cooperative multicast: .

The Advantage of Multi-hop MIMO Transmission: achieve a gain on throughput compared with direct transmission in [1,Özgϋr]; the energy consumption also decreases by .

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Outline5
Outline

Introduction

Models and Definitions

Multi-hop Hierarchical Cooperative Scheme

Achievable Multicast Capacity

Delay and Energy Consumption

Conclusion and Future Works

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Conclusion and future works
Conclusion and Future Works

  • We study the scaling laws for multicast and develop a multi-hop hierarchical cooperation scheme achieving throughput of , where .

  • Our scheme achieves a capacity gain compared with non-cooperative scheme, and also cuts down the energy consumption and delay.

  • Our converge-based Multi-hop MIMO Multicast scheme achieves the delay-throughput tradeoff identical to that of non-cooperative schemes when .

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Reference
Reference

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Reference1
Reference

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Reference2
Reference

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