1. Power Efficient Communication ----Joint Routing, Scheduling and Power Control Design
Presenter: Rui Cao

2. Motivation Power is a critical issue in MANET;
Several layers affect energy consumption;
Cross-layer optimization design is a necessity.

3. An Example: 2 4 1 3 Routing: (2) (2) (1) (3) (3) Scheduling:
1) A node is not allowed to transmit
and receive at the same time;
2) A node cannot receive from more
than one node;
3) One transmitter should be D apart
from another receiver;
Power Control:

4. Common Steps Setup the system model and make assumptions;
Formulate the objective function: power consumption function;
Find the constraints: set of feasible solutions;
Simplify the formulas to work out the approximate solutions.

5. Assumptions: Formula : TDMA based Ad Hoc Network;
“Joint Scheduling and Power Control for Wireless Ad Hoc Networks”
---T. ElBatt and A. Ephremides,
IEEE Transactions on Wireless Communication, 2004
Assumptions:
TDMA based Ad Hoc Network;
Scheduling is determined at the beginning of each time slot;
Frame length fixed;
Each package is destined to a single node;
SINR can be known at the transmitter;
A central controller existed for executing the algorithm;
Formula :

6. Validity: Admissibility: Solution:
1) A node is not allowed to transmit
and receive at the same time;
2) A node cannot receive from more
than one node;
3) One transmitter should be D apart
from another receiver;
Admissibility:
Solution:
Exhaustive Search;
Suboptimal:
Examine the valid set sequentially;
Defer conflicted transmission;
Defer user with low SINR;
Power assignment:
(Iteration)

7. B. “On Power Efficient communication over Multi-hop Wireless Networks:
Joint Routing, Scheduling and Power Control”
---R. Bhatia and M. Kodialam, INFOCOM 2004.
Assumptions:
Routing: topology is known;
Single pair of source and destination;
Transmission: time-slotted TDMA/CDMA;
Interference: No interference between different neighboring transmission links in the same time slot;
No prime conflict: each node interact with one node;
Power (Physical Layer):
Pathloss function is known;
Shannon Capacity is achieved;

8. Problem Formulation Constraints: Routing: Scheduling:
Objective Function:
Solution:
Constraints:
Routing:
Scheduling:

9. Strategy:
Fix Flow problem;
End to end problem;
Whole Solution;

10. Fixed Flow Problem Providing a 2-approximation result:
Node Solution (Optimal Power)
Solving the optimum problem at each node; (Distributed)
Providing a 2-approximation result:

11. Solve mini-power problem at each node separately; Compute for all Set
Algorithm:
Solve mini-power problem at each node separately;
Compute for all
Set
Compute
Output is an approximate solution; e

12. form a 2-approximation solution for the whole problem:
The “local” optimal solution at each node can
form a 2-approximation solution for the whole problem:
: Optimal Power assignment and Data rate;
: Optimal Power consumption under fixed flow

13. Solve the node optimality problem :
Using Taylor expansion to simplify the “one node” problem

14. Now the node optimality solution:
Karush-Kuhn-Tucker conditions:
(Generalized Lagrange Multiplier)
Now the node optimality solution:

15. Feasible Solution: schedulable
Use the Sufficient Condition , instead of Necessary
Condition ;
R(e) is linear in ;
3-approximation result:

16. End to End Solution: Optimal flow
Optimal Solution:

17. Rewrite the last step: Convex Problem with linear constraints:
Quadratic Programming Problem;
Can be solved in polynomial time;
Frank-Wolfe method;

18. Whole Solution
Frank-Wolfe Method: Find the suboptimal flow
Fixed flow optimization:
Link coloring Problem: find the schedule;
Determine the Power:

19. Thank you!
Have a Nice Spring Break!