bv_cvxbook_extra_exercises

Show how to construct a feasible power allocation x

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Unformatted text preview: ze i=1 n n 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 nonsingular and B −1 = I − C with Cij ≥ 0. Express the problem above as a convex optimization problem. Hint. Use y = Bp as variables. 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.

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