Multicast Scaling Laws with Hierarchical Cooperation Chenhui Hu, Xinbing Wang, Ding Nie, Jun Zhao Shanghai Jiao Tong University, China

Multicast Hierarchical Cooperation Presentation 2 Outline Introduction  Motivations  Objectives Models and Definitions Multi-hop Hierarchical Cooperative Schemes Achievable Multicast Capacity Delay and Energy Consumption Conclusion and Future Works

Multicast Hierarchical Cooperation Presentation 3 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

Multicast Hierarchical Cooperation Presentation 4 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, 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 decode observations to decode

Multicast Hierarchical Cooperation Presentation 5 Objectives  Hierarchical Cooperative MIMO has been shown in [2,Özgϋr] achieves a linear throughput scaling for unicast.  In our work, we focus on multicast 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?

Multicast Hierarchical Cooperation Presentation 6 Outline Introduction Models and Definitions Multi-hop Hierarchical Cooperative Scheme Achievable Multicast Capacity Delay and Energy Consumption Conclusion and Future Works

Multicast Hierarchical Cooperation Presentation 7 Models and Definitions – I/II  Network Model and Traffic:  n nodes independently & uniformly distributed in a unit suquare  Randomly and independently choose a set of k nodes U i = {u i,j | 1 ≤ j ≤ k} as destination nodes for each node v i  Physical-layer Model:  Channel gain for the transmission from v j to v i  Signal received by node v i at time t

Multicast Hierarchical Cooperation Presentation 8 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 —

Multicast Hierarchical Cooperation Presentation 9 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

Multicast Hierarchical Cooperation Presentation 10 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.

Multicast Hierarchical Cooperation Presentation 11 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 choose a set of nodes as destinations. Each node in the network acts as a source node and sends one identical bit to all nodes in the set.

Multicast Hierarchical Cooperation Presentation 12 MMM Scheme  Step 1. Preparing for Cooperation: — Each node distributes data to other nodes — Each node distributes data to other nodes  Step 2. Multi-hop MIMO Transmissions: — Routing on the multicast tree — 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.

Multicast Hierarchical Cooperation Presentation 13 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.

Multicast Hierarchical Cooperation Presentation 14 Notations  Notations:  : # of layers, : indicator for a particular layer : indicator for a particular layer  : # of nodes, : # of destination nodes for each source : # 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 to indicate and, for any., for any.

Multicast Hierarchical Cooperation Presentation 15 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

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? Multicast Hierarchical Cooperation Presentation

17 Throughput can be improved by adopting case 2 Achievable Throughput of MMM  Calculate time required in the three steps:  To optimize the throughput, certain network division is used:

Multicast Hierarchical Cooperation Presentation 18 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

Multicast Hierarchical Cooperation Presentation 19 Achievable Throughput of MMM  Results comparison:

Multicast Hierarchical Cooperation Presentation 20 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

Delay and Energy Consumption  Delay of MMM: — Consider the delay of MMM recursively  Delay-Throughput Tradeoff:  Energy Consumption of MMM: Multicast Hierarchical Cooperation Presentation 21 Poor! huge bulk size

Delay and Energy Consumption Multicast Hierarchical Cooperation Presentation 22  Delay of CMMM:  Delay-Throughput Tradeoff:  Energy Consumption of CMMM: Delay reduces from exponential to linear! Similar to energy cost of MMM

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. Multicast Hierarchical Cooperation Presentation 23

Multicast Hierarchical Cooperation Presentation 24 Outline Introduction Models and Definitions Multi-hop Hierarchical Cooperative Scheme Achievable Multicast Capacity Delay and Energy Consumption Conclusion and Future Works

Multicast Hierarchical Cooperation Presentation 25 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.

Thank you !

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