Power control infeasibility consider a three link

2. Power control infeasibility ??
Consider a three-link cell with the link gains G
ij
shown below. The receivers
request γ
1
= 1 , γ
2
= 2, and γ
3
= 1. The noise n
i
= 0 . 1 for all i .
G =


1 0 . 5 0 . 5
0 . 5 1 0 . 5
0 . 5 0 . 5 1


.
Prove this set of target SIRs is infeasible.
4

Solving this system of linear equations, we find that p
1
≤ − 0 . 4 , p
2
≤ − 0 . 6 , p
3
≤
− 0 . 4, which is infeasible since the powers are negative. This problem can also be
solved using the Perron-Frobenius theorem discussed in the Advanced Material.

Problem 2.1
Three advertisers (1 , 2 , 3) bid for two ad spaces ( A, B ). The average revenues per click are $6,
$4, $3 for the bidders, respectively, and the clickthrough rate of the ad spaces are 500, 300 clicks
per hour respectively.
(a) Draw the bipartite graph with nodes indicating advertisers/ad spaces and edges indicating
values per hour. Indicate the maximum matching with bold lines.
(b) Assume a GSP auction with truthful bidding, what is the result of the auction in terms of
the allocation, the prices charged, and the payoffs received?
Solution: