What is ECG

1
What is ECG?

• A capacity graph that represents a physical state
  to represents a snapshot of all nodes in the
  physical layer, such as which nodes are
  transmitting and what transmitting powers are
  being used
• Loosely speaking, a graph that can be directly
  realized in the physical layer

2
ECG Example

• ECG1 (G1) Corresponds to the physical state
  where s is transmitting at a power just enough to
  reach a and b
• ECG2 (G2) Corresponds to the physical state
  where s is transmitting at a power just enough to
  a, b, c, d
• Number between arc means associated bit rate

3
Initialization of ECG

• R Communication range, Ri Interference range
• 1) Randomly choose a node as the transmitter
• 2) Draw two circles originated from it with R
  and Ri
• 3) If some receivers associated with other
  transmitter overlap with this Ri, stop go to step
  1), otherwise go to step 4)
• 4) Choose the receivers that are inside the R
• 5) Include the link into the linear program for
  power control (Next slide), if a feasible
  solution exists, then the link is packed.
  Otherwise, go to step 1)

4
Example
3
5
1
2
4

• There are 5 nodes
• Step 1) Randomly choose a transmitter (Suppose
  node 1)
• Step 2) Draw 2 circles (R, Ri)

5
Example
3
Ri
5
R
1
2
4

• Step 1) Randomly choose a transmitter (Suppose
  node 1)
• Step 2) Draw 2 circles (R, Ri)
• R Communication range, Ri Interference range

6
Example
3
5
1
2
4

• Step 3) In this case, no overlap with other Tx,
  go to step 4)
• Step 4) Choose the receiver as the node 2

7
Example
3
5
1
2
4

• Step 3) In this case, no overlap with other Tx,
  go to step 4)
• Step 4) Choose the receiver as the node 2

8
Example
3
2
5
1
1
2
4
Link 1-gt2 is Packed

• Step 5) If a feasible power exists using the
  linear program for power control in slide 9, then
  the link is packed
• And Repeat this process until no links can be
  further packed

9
Linear program for power control

• Px transmitting power
• ? SINR requirements
• X Set of transmitters, Yx Set of receivers
• Our objective is to minimize total transmit power
  while satisfying SINR requirements