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Unformatted text preview: ility function, we cannot have ri = 0, and therefore we cannot have ti = 0;
therefore the constraints ri ≥ 0 and ti ≥ 0 cannot be active or tight. This will allow you to simplify
the optimality conditions.
12.9 Optimal jamming power allocation. A set of n jammers transmit with (nonnegative) powers
p1 , . . . , pn , which are to be chosen subject to the constraints
p 0, Fp g. The jammers produce interference power at m receivers, given by
n Gij pj , di =
j =1 99 i = 1, . . . , m, where Gij is the (nonnegative) channel gain from jammer j to receiver i.
Receiver i has capacity (in bits/s) given by
2
Ci = α log(1 + βi /(σi + di )), i = 1, . . . , m, where α, βi , and σi are positive constants. (Here βi is proportional to the signal power at receiver
2
i and σi is the receiver i selfnoise, but you won’t need to know this to solve the problem.)
Explain how to choose p to minimize the sum channel capacity, C = C1 + · · · + Cm , using convex
optimization. (This corresponds to the most eﬀective jamming, given the power...
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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 University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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