multicast scaling laws with hierarchical cooperation

Multicast Scaling Laws with Hierarchical CooMulticast Scaling Laws with Hierarchical Cooperationperation

Chenhui Hu, Xinbing Wang, Ding Nie, Jun Zhao

Shanghai Jiao Tong University, China

Multicast Hierarchical Cooperation Presentation 2

OutlineOutline IntroductionIntroduction

MotivationsMotivations ObjectivesObjectives

Models and DefinitionsModels and Definitions

Multi-hop Hierarchical Cooperative SchemesMulti-hop Hierarchical Cooperative Schemes

Achievable Multicast CapacityAchievable Multicast Capacity

Delay and Energy ConsumptionDelay and Energy Consumption

Conclusion and Future WorksConclusion and Future Works


MotivationMotivation

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

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

Protocol Model:Protocol Model:

TDMA Scheduling TDMA Scheduling

)log

1(),( ),

log

1()(

nnkknCap

nnnCap multicastunicast


MotivationMotivation

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

Realize cooperative communication by Realize cooperative communication by Distributed MIMODistributed MIMO..

Two clusters each with M nodes Two clusters each with M nodes 1) Source node distributes its bits 1) Source node distributes its bits

2) Every sender holds a different bit, 2) Every sender holds a different bit,

and transmits simultaneously and transmits simultaneously

3) Receiver nodes interchange their 3) Receiver nodes interchange their

observations to decodeobservations to decode


ObjectivesObjectives

HierarchicalHierarchical Cooperative MIMOCooperative MIMO has been shown in [2,Özgϋr] ach has been shown in [2,Özgϋr] achieves a linear throughput scaling for unicast.ieves a linear throughput scaling for unicast.

In our work, we focus onIn our work, we focus on multicast scaling lawsmulticast scaling laws using using hierarchical hierarchical MIMOMIMO..1. How to hierarchically schedule multicast traffic to optimize the t1. How to hierarchically schedule multicast traffic to optimize the throughput?hroughput?2. Delay performance and energy-efficiency when achieving opti2. Delay performance and energy-efficiency when achieving optimal throughput?mal throughput?3. Delay-throughput tradeoff in our hierarchical cooperative multic3. Delay-throughput tradeoff in our hierarchical cooperative multicast strategies?ast strategies?




Multi-hop Hierarchical Cooperative SchemeMulti-hop Hierarchical Cooperative Scheme





Models and Definitions – I/IIModels and Definitions – I/II Network Model and Traffic: Network Model and Traffic: nn nodes independently & uniformly distributed in a unit suquarenodes independently & uniformly distributed in a unit suquare Randomly and independently choose a set of Randomly and independently choose a set of kk nodes nodes UUi i == { {uui,j i,j | 1 | 1

≤ j ≤ k≤ j ≤ k}} as destination nodes for each node as destination nodes for each node vvii

Physical-layer Model:Physical-layer Model: Channel gain for the transmission from Channel gain for the transmission from vvjj to to vvii

Signal received by node Signal received by node vvii at time at time tt


Models and Definitions – II/IIModels and Definitions – II/II Def. of Throughput: Def. of Throughput: A throughput of bits/sec is feasible if there is a spatial and A throughput of bits/sec is feasible if there is a spatial and

temporal scheme for scheduling, s.t. every node can send temporal scheme for scheduling, s.t. every node can send bits per second on average to all its destination nodes.bits per second on average to all its destination nodes.

Aggregate multicast throughput:Aggregate multicast throughput: Def. of Energy-Per-Bit:Def. of Energy-Per-Bit: Average energy required to carry one bit from a source node to Average energy required to carry one bit from a source node to

one of its destination nodes — one of its destination nodes — Def. of Delay:Def. of Delay: Average time it takes for a bit to reach its destination nodes —Average time it takes for a bit to reach its destination nodes —

),( kn),( kn




Multi-hop Hierarchical Cooperative Scheme Multi-hop Hierarchical Cooperative Scheme General Multicast StructueGeneral Multicast Structue MMM & CMMM schemeMMM & CMMM scheme





General Multicast StructureGeneral Multicast Structure

Divide the network into clusterDivide the network into clusters, with s, with MM nodes in each cluste nodes in each cluster. r.

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

Step 2:Step 2: Conduct MIMO trans Conduct MIMO transmissions along a spanning tremissions along a spanning tree connecting the clusters whee connecting the clusters where the source and its destinatire the source and its destinations nodes locate. ons nodes locate.

Step 3:Step 3: In a cluster having de In a cluster having destination nodes, nodes deliver stination nodes, nodes deliver its observation to the destinatiits observation to the destinations for decoding.ons for decoding.

sM


MMM & CMMM scheme MMM & CMMM scheme

Two methods to schedule transmissions in Two methods to schedule transmissions in Step 3Step 3: : Multi-hop MIMO Multicast (MMM)Multi-hop MIMO Multicast (MMM) Converge based Multi-hop MIMO Multicast (CMMM)Converge based Multi-hop MIMO Multicast (CMMM) Both schemes involve a Both schemes involve a hierarchicalhierarchical solution to the transmission solution to the transmission

problem of Step 3.problem of Step 3. MMM — Treat the traffic in Step 3 as MMM — Treat the traffic in Step 3 as multicast problemmulticast problem CMMM — CMMM — Treat the traffic in Treat the traffic in SStep 3 as tep 3 as converge multicast probleconverge multicast proble

mm, with multi-hop MIMO transmissions, with multi-hop MIMO transmissions

Converge Multicast Problem: Converge Multicast Problem: RRandomly chooseandomly choose a set of nodes a set of nodes as as destinationsdestinations.. EEachach node in the node in thenetwork acts as a source node andnetwork acts as a source node andsends one identical bit to all nodes sends one identical bit to all nodes in in the setthe set..

k


MMM SchemeMMM Scheme

Step 1.Step 1. Preparing for Cooperation: Preparing for Cooperation:

— — Each node distributes data to other nodesEach node distributes data to other nodes Step 2.Step 2. Multi-hop MIMO Transmissions: Multi-hop MIMO Transmissions:

— — Routing on the multicast treeRouting on the multicast tree Step Step 33.. Cooperative Decoding Cooperative Decoding:: To decode, all nodes in the destiTo decode, all nodes in the desti

nation cluster first quantify nation cluster first quantify anan observation into Q bits. Then each observation into Q bits. Then each node conveys the Q bits to all destination nodes in the cluster.node conveys the Q bits to all destination nodes in the cluster.

The multicast problem in step 3 The multicast problem in step 3 can also be solved can also be solved byby the same the same three-step structurethree-step structure. Thus,. Thus, IImplmplementing ementing itit recursively get a hie recursively get a hierarchical solution.rarchical solution.


CMMM SchemeCMMM Scheme

Step Step 3-3-11. Multi-hop MIMO Transmissions:. Multi-hop MIMO Transmissions: Since all nodes must Since all nodes must send one bit to destination nodes, all clusters act as source clustsend one bit to destination nodes, all clusters act as source clusters and transmit to destination clusters by multi-hop MIMO.ers and transmit to destination clusters by multi-hop MIMO.

Step Step 3-3-22. Cooperative Decoding:. Cooperative Decoding: After a destination cluster recei After a destination cluster receives a MIMO transmission, all nodes quantify the observation anves a MIMO transmission, all nodes quantify the observation and converge them to the destination nodes in the cluster.d converge them to the destination nodes in the cluster.

The multicast problem in step The multicast problem in step 3-3-2 is also a converge multic2 is also a converge multicast problem. Implementing the same two-step structure recast problem. Implementing the same two-step structure recursively we get a multi-layer solution to converge multicast ursively we get a multi-layer solution to converge multicast problem.problem.


NotationsNotations

Notations:Notations: : # of layers, : # of layers,

: indicator for a particular layer: indicator for a particular layer : # of nodes, : # of nodes, : # of destination nodes for each source: # of destination nodes for each source denotes # of clustersdenotes # of clusters denotes # of destination clusters at layer denotes # of destination clusters at layer denotes # of multicast sessions at layerdenotes # of multicast sessions at layer We use Knuth's notation in this paper. Also we use We use Knuth's notation in this paper. Also we use to indicate andto indicate and , for any . , for any .




Multi-hop Hierarchical Cooperative Scheme Multi-hop Hierarchical Cooperative Scheme

Achievable Multicast CapacityAchievable Multicast Capacity Upper bound of throughputUpper bound of throughput Achievable throughput of MMMAchievable throughput of MMM



Upper bound of throughputUpper bound of throughput

[The.] Aggregate multicast throughput is whp bounded bywhere is a constant independent of and . where is a constant independent of and .

Can we achieve this optimal bound?Can we achieve this optimal bound?— — Intuition: We need make use of interferenceIntuition: We need make use of interference How can we minimize the delay and energy consumHow can we minimize the delay and energy consum

ption?ption?

Multicast Hierarchical Cooperation Presentation


TThroughputhroughput can be can be improvedimproved by adopting cas by adopting case 2e 2

Achievable Throughput of MMMAchievable Throughput of MMM

Calculate time required in the three stepsCalculate time required in the three steps::

To optimize the throughput, certain To optimize the throughput, certain network divisionnetwork division is use is used:d:



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

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

2 1

2 1, ;

, .

i

h

ii h

nn

n i h

k

2 2

2 1( , )

h

hn

kT n k

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



Results comparison:Results comparison:





Achievable Multicast Capacity Achievable Multicast Capacity

Delay and Energy ConsumptionDelay and Energy Consumption Delay and Energy ConsumptionDelay and Energy Consumption DiscussionDiscussion



Delay of MMM:Delay of MMM:

— Consider the delay of MMM recursively

Delay-Throughput Tradeoff:Delay-Throughput Tradeoff:

Energy Consumption of MMM:Energy Consumption of MMM:


2 22 2 4 3

2 1 2 1( , )h h h h

h hD n k kn

2 24 3 6 4

2 1 2 1( , ) / ,h h h h

h hD n k T n k kn

1 2 3 2

2 1 4 2,h

h hE n k O n k

Poor!Poor!huge bhuge bulk sizeulk size



Delay of CMMM:Delay of CMMM:

Delay-Throughput Tradeoff:Delay-Throughput Tradeoff:

Energy Consumption of CMMM:Energy Consumption of CMMM:

2 31

2 12

2 4 3 1

2 1 2 1 2

, when ( ),

, when ( ),

( , )

h

hh

h

h h h

nk O n

k

n k k n

D n k

1 2 3 2

2 1 4 2,h

h hE n k O n k

11 2

21

2 12

, when ( )

( , )

,

, whe ),

n (/

,

h

hh

k k O n

nk k n

k

D n k T n k

Delay reduces Delay reduces from exponential from exponential

to linear!to linear!

Similar to energy Similar to energy cost of MMMcost of MMM

DiscussionDiscussion

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

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

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

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


/n k

kk n

(/ )D T k

( 2)/2k





Achievable Multicast Capacity Achievable Multicast Capacity





WWe e study the scaling laws for multicast and develop a multstudy the scaling laws for multicast and develop a multi-hop hierarchical cooperation scheme achieving throughpui-hop hierarchical cooperation scheme achieving throughput of , where .t of , where .

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

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

))(( 1 k

n 10

k

n

h

Thank you !Thank you !


ReferenceReference

multicast scaling laws with hierarchical cooperation

Documents

hierarchical mimo

multicast traffic

aggregate multicast

multicast scaling laws

nodes ui

receiver nodes

source node

energy consumptionconclusion