bv_cvxbook_extra_exercises

We consider a wireless system that uses time domain

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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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