Convergecast with MIMO Luoyi Fu, Yi Qin, Xinbing Wang Department of Electronic Engineering Shanghai Jiao Tong University, China Xue Liu Department of Computer Science and Engineering University of Nebraska Lincoln, USA

2 Outline Introduction  Motivation  Objectives Progress  Cooperative MIMO Schemes in Static Networks  Throughput and Delay in Static Networks  Cooperative MIMO Schemes in Mobile Networks  Throughput and Delay in Mobile Networks  Discussion

Multicast Hierarchical Cooperation Presentation 3 Motivation  Most works focus on unicast or multicast while converge- cast is relatively new.  Some relative existing work about converge-cast focuses on the traffic in sensor networks where all nodes flow data to a single sink. However, a wide range of applications require multiple such converge-cast session in the network.  Machine failure diagnosis  pollutant detection  supply chain management  Stringent capacity-delay requirements imposed on Converge-cast.

Multicast Hierarchical Cooperation Presentation 4 Motivation (cont’)  Vast space of improvement on throughput for converge-cast due to its convergent property.  Converge-cast can be treated as a generalized reversed “multicast”.  Hierarchical Cooperative MIMO has been shown to achieve a linear throughput scaling for unicast [14,Özgϋr] and multicast [13,Hu].

Multicast Hierarchical Cooperation Presentation 5 Objective  In our work, we focus on converge-cast scaling laws in both static and mobile ad hoc networks.  We jointly consider converge-cast traffic with cooperative MIMO schemes. 1. How to schedule converge-cast traffic to optimize the throughput in static networks, using MIMO? 2. How to schedule converge-cast traffic to optimize the throughput in mobile networks, using MIMO? 3. Delay performance when achieving optimal throughput? And the corresponding delay-throughput tradeoff? 4. Relationship between our achieved converge-cast results and those in other traffic patterns? 2. How to schedule converge-cast traffic to optimize the throughput in mobile networks, using MIMO? 3. Delay performance when achieving optimal throughput? And the corresponding delay-throughput tradeoff? 4. Relationship between our achieved converge-cast results and those in other traffic patterns?

6 Outline Introduction  Motivation  Objectives Progress  Models and Definitions  Cooperative MIMO Schemes in Static Networks  Throughput and Delay in Static Networks  Cooperative MIMO Schemes in Mobile Networks  Throughput and Delay in Mobile Networks  Discussion

7 Models and Definitions  Network Model: An Ad Hoc network where n nodes are randomly positioned in a unit square.  Traffic Pattern: n destinations with each one corresponding to k randomly and independently chosen sources. (converge-cast)  Communication model: Physical layer model.  The channel gain between node i and j given by  The signal received by node i at time t given by

8 Models and Definitions (cont’)  Definitions:  Throughput: Denote m(t) as the number of packets (bits) from sources that a destination receives in t time slots. Then the long-term per-node throughput is defined as :  The aggregate throughput is  Delay: The time a destination takes to receive all the packets from its corresponding k sources.

9 Cooperative MIMO Scheme in Static Networks Cooperative MIMO Scheme 1: Cooperative MIMO Scheme 1: Preparing for cooperation with recursion Multi-hop MIMO Transmission Cooperative Reception (each destination in the cluster can receive packets at layer i

10 Cooperative MIMO Scheme in Static Networks (cont’) An example of step 2 in cooperative MIMO scheme 1 Convergecast: 3 sources per destination The yellow cell is the one where destination is located. The red cells are the ones where sources are located. Red parts in the cell indicates the percentage of the number of active nodes in this source cell.

11 Cooperative MIMO Scheme in Static Networks (cont’) 9-TDMA scheme is adopted to avoid interference. The yellows cells can be active concurrently.

12 Throughput and Delay for Static Networks In static network, by adopting Cooperative MIMO scheme 1, we can achieve an aggregate throughput of with the delay of Throughput and delay

13 Cooperative MIMO Scheme in MANETs  Nodes move according to i.i.d. mobility model.  The network is divided into c cells in the way that each cell contains M nodes on average.  9-TDMA strategy is adopted again to avoid interference of nearby transmission.

14 Cooperative MIMO Scheme in MANETs An illustration of transmission in an active cell in cooperative MIMO scheme 2

15 Throughput and Delay for MANETs In MANETs, by adopting Cooperative MIMO scheme 2, we can achieve the per-node throughput and delay of Throughput and delay

16 Discussion Delay-Throughput Tradeoff Static networks: MANETs: MANETs: Optimal network division

17 Discussion (cont’) Results extended to unicast, multicast and broadcast under our schemes.

Discussion (cont’) Comparison with Previous Work and Generalization Comparison with Previous Work and Generalization

19 Conclusion  Our cooperative MIMO scheme in static networks breaks the bottleneck and can achieve an aggregate throughput of order 1.  Our cooperative MIMO scheme in MANETs can achieve a per-node throughput of Θ(1) while the delay is reduced to Θ(k).  Our results well cover other traffic patterns and act as a generalization.

Thank you !

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