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,zgr] 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,zgr] 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,zgr]; 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 ! Multicast Hierarchical Cooperation Presentation 27 Reference Multicast Hierarchical Cooperation Presentation 28 Reference Multicast Hierarchical Cooperation Presentation 29 Reference