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
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
2
Motivation
 Most works focus on unicast or multicast while convergecast 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
3
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
4
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?
Multicast Hierarchical Cooperation Presentation
5
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
6
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
hij [t ]  Gd
 /2
ij
e
jij [ t ]
 The signal received by node i at time t given by
Yi [t ] 
 h [t ]X [t ]  Z [t ]  I [t ]
jT [t ]
ij
j
i
i
7
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 :
m(t )
  lim inf
t 
t
 The aggregate throughput is
  n
 Delay: The time a destination takes to receive all the packets
from its corresponding k sources.
8
Cooperative MIMO Scheme in Static
Networks
Cooperative MIMO Scheme 1:
Preparing for cooperation with
recursion
Multi-hop MIMO Transmission
Cooperative Reception (each
destination in the cluster can
receive
i i
i
packets at layer i
tk /n
9
Cooperative MIMO Scheme in Static
Networks (cont’)
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.
An example of step 2 in cooperative MIMO scheme 1
10
Cooperative MIMO Scheme in Static
Networks (cont’)
The yellows cells can
be active concurrently.
9-TDMA scheme is adopted to avoid interference.
11
Throughput and Delay for Static Networks
Throughput and delay
In static network, by adopting Cooperative MIMO scheme 1,
we can achieve an aggregate throughput of
 22hh12  2 h11 
   n
k



with the delay of
1
  2 h2  4 h 3  2 h2  2 h 1 


2 h 1
2 h 1
2 h2
k
  n
 k  n



 



E T   
h2  2 h  2
h2  4 h 3 
1




2 h 1
2 h 1
2 h2
k
 k  On

   n



 

12
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.
13
Cooperative MIMO Scheme in MANETs
An illustration of transmission in an active cell in
cooperative MIMO scheme 2
14
Throughput and Delay for MANETs
Throughput and delay
In MANETs, by adopting Cooperative MIMO scheme 2, we
can achieve the per-node throughput and delay of

 1 
   
 , E  DN     log n  k   1

 log n 

   1 , E  DN     k 
k   1

15
Discussion
Delay-Throughput Tradeoff
Static networks:
1
  2 h2  4 h  4  2 h2  2 h 


2 h 1
2 h 1
2h2
k
  n
 k  n



 




h 2  2 h 1
h2  4 h  2 
1




2 h 1
2 h 1
2h2
k
 k  On

   n



 

MANETs:
M k 
2
Optimal network division
 k 
16
Discussion (cont’)
Results extended to unicast, multicast and broadcast under our
schemes.
17
Discussion (cont’)
Comparison with Previous Work and Generalization
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.
19
Thank you !
Reference
Reference
Reference