Unformatted text preview: j does not need to transmit any message (directly)
to relay station i. The matrix of bit rates Rij is given. Although it doesn’t aﬀect the problem, R
would likely be sparse, i.e., each relay station needs to communicate with only a few others.
To guarantee accurate reception of the signal from relay station j to i, we must have
Sij ≥ βRij ,
where β > 0 is a known constant. (In other words, the minimum allowable received signal power
is proportional to the signal bit rate or bandwidth.)
The relay station positions xr+1 , . . . , xn are ﬁxed, i.e., problem parameters. The problem variables
are x1 , . . . , xr and p1 , . . . , pn . The goal is to choose the variables to minimize the total transmit
power, i.e., p1 + · · · + pn .
Explain how to solve this problem as a convex or quasiconvex optimization problem. If you introduce new variables, or transform the variables, explain. Clearly give the objective and inequality
constraint functions, explaining why they are convex. If your problem involves equality constraints,
express them using an aﬃne function. 95 12.5...
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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