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j =1 Bij pj − pi pi = 1 subject to (38) i=1 pi ≥ 0, i = 1, . . . , n,
where B ∈ Rn×n is deﬁned as B = A + v 1T , i.e., Bij = Aij + vi , i, j = 1, . . . , n. Suppose B is
B −1 = I − C
with Cij ≥ 0. Express the problem above as a convex optimization problem. Hint. Use y = Bp as
12.4 Radio-relay station placement and power allocation. Radio relay stations are to be located at positions x1 , . . . , xn ∈ R2 , and transmit at power p1 , . . . , pn ≥ 0. In this problem we will consider the
problem of simultaneously deciding on good locations and operating powers for the relay stations.
The received signal power Sij at relay station i from relay station j is proportional to the transmit
power and inversely proportional to the distance, i.e.,
Sij = αpj
xi − xj 2 , where α > 0 is a known constant.
Relay station j must transmit a signal to relay station i at the rate (or bandwidth) Rij ≥ 0 bits
per second; Rij = 0 means that relay station...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
- Fall '13
- The Aeneid