Optimal Relay Assignment for Cooperative Communications

1
Optimal Relay Assignment for Cooperative
Communications

• Sushant Sharma
• Virginia Tech
• with
• Yi Shi and Thomas Hou (Virginia Tech)
• Sastry Kompella (NRL)

ACM MOBIHOC 2008
2
Background

• Exploit spatial diversity to improve performance
• MIMO
• Use multiple antennas to increase capacity
• But require multiple antennas at each node
• Depending on wavelength, may not fit well on a
  single node
• Cooperative Communication (CC)
• A recent advance in physical layer technology
• Each node only has a single antenna
• Exploits neighboring nodes antenna for data
  forwarding
• But capacity improvement depends on network
  setting
• E.g., which neighbor to relay

1
3
Cooperative Communication

• Transfer from sender to receiver is done on frame
  by frame basis.
• Each frame is divided into two time slots
• Two slot structure is necessary due to half
  duplex nature of most wireless transceivers.
• Antennas on sender and relay node cooperate to
  achieve spatial diversity.

Relay Node
2nd Time Slot
1st Time Slot
Receiver
1st Time Slot
Sender
4
Two Modes of Operation

• Amplify and Forward (AF)
• Relay node
• Receives the message in first time slot.
• Amplifies and forwards the message to destination
  node in second time slot
• Decode and Forward (DF)
• Relay node
• Receives and decodes the message in first time
  slot.
• Forward the decoded message in second time slot.

3
5
Capacity Equations

• Direct Communication

• Cooperative Communication
• Amplify and Forward
• Decode and Forward

Capacity with cooperative communication may be
higher or lower
Choice of Relay Node is Important !
6
Outline

• Background
• Relay Node Assignment Problem
• Optimal Relay Assignment (ORA) Algorithm.
• Numerical Results

5
7
Problem Setting

• Single Hop Network.
• Number of relay nodes can be greater than or less
  than the number of source-destination pairs.
• Each pair has a dedicated channel assigned for
  CC.
• Channels for different pairs are orthogonal to
  each other.
• Last two settings from Laneman, Tse et.al., 2004.

s2
s1
d5
r1
r2
s3
d4
r3
r4
r6
d3
r5
d1
r7
s5
d2
s4
8
Problem Statement
How to optimally assign these relay nodes to the
source-destination pairs so as to maximize the
minimum capacity in the network.
s2
s1
d5
r1
r2
s3
d4
r3
r4
r6
d3
r5
d1
r7
s5
d2
s4
9
Relay Node Assignment Problem

• Can be solved using exhaustive search
• BUT the complexity is exponential.

• OBJECTIVE
• To design a Polynomial Time Algorithm that
  optimally solves the Relay Node Assignment
  Problem.

10
Outline

• Background
• Relay Node Assignment Problem
• Optimal Relay Assignment (ORA) Algorithm.
• Numerical Results

9
11
Main Contributions

• Optimal Relay Assignment (ORA) Algorithm.
• Key Idea Linear Marking Mechanism
• Guarantees linear time complexity at each
  iteration.
• Overall complexity of ORA algorithm is
  polynomial.
• Formal correctness proof.

12
Highlights of ORA Algorithm

• ORA begins with an initial feasible assignment of
  relay nodes.
• A simple choice is direct transmission.
• ORA then identifies the source-destination pair
  with least capacity, and attempts to find a
  better assignment of relay node for the pair.
• Linear Marking Mechanism ensures that the
  complexity of this iteration is linear.
• If a better assignment cannot be found
• Then the current assignment is optimal.
• Algorithm stops.
• Otherwise, goto step 2.

11
13
An Example
Bottleneck node s3, min 13
Bottleneck node s1, min 15
14
An Example
Bottleneck node s1, min 15
Bottleneck node s3, min 16
15
Complexity Analysis

• Every iteration is linear time due to Linear
  Marking Mechanism O(N)
• Since the minimum capacity in the system always
  increase after an iteration, and there are O(N2)
  different capacities for all pairs
• Number of iterations O(N2).
• So, the worst case complexity is O(N3).

14
16
Correctness Proof

• Based on contradiction.
• Exploits the marking status of the relay nodes at
  the end of last iteration of ORA algorithm.
• Claim the relay node assigned to the bottleneck
  pair is not marked at the end of ORA algorithm.
• Whereas if we assume that a better solution
  exists, then
• We show that the relay node assigned to the
  bottleneck pair will be marked at the end of ORA
  algorithm.
• This contradicts with the claim.

15
17
Correctness Proof (Contd)
16
18
Outline

• Background
• Relay Node Assignment Problem
• Optimal Relay Assignment (ORA) Algorithm.
• Numerical Results

17
19
Simulation Setting

• 50 Node Network
• 15 Source Nodes
• 15 Destination Nodes
• 20 Prospective Relay Nodes
• Preceived Ptransmittedkd-n
• SNR Preceived/s2
• Path Loss Index n 4
• White Gaussian Noise with Variance s2 10-10 W
• Ptransmitted 1 W

20
Network Topology
21
Results
22
Results under Different Initial Assignments
155 Improvement
23
Summary

• Studied the cooperative communications for ad hoc
  networks via a relay node assignment problem.
• Developed a polynomial time algorithm (ORA) to
  solve the problem.
• Key Idea Linear Marking Mechanism
• Offered a formal correctness proof.
• Numerical results showed significant improvement
  in network capacity.

24
Questions !