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EE263 homework problems Lecture 2 – Linear functions and ...

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EE263 Autumn 2007-08Prof. S. BoydEE263 homework problemsLecture 2 Linear functions and simple power control algorithm for a wireless some background. We considera network ofntransmitter/receiver pairs. Transmitteritransmits at power levelpi(whichis positive). The path gain from transmitterjto receiveriisGij(which are all nonnegative,andGiiare positive). The signal power at receiveriis given bysi=Giipi. The noise plusinterference power at receiveriis given byqi= +Xj6=iGijpjwhere >0 is the self-noise power of the receivers (assumed to be the same for all receivers).Thesignal to interference plus noise ratio(SINR) at receiveriis defined asSi=si/qi. Forsignal reception to occur, the SINR must exceed some threshold value (which is often inthe range 3 10). Variouspower control algorithmsare used to adjust the powerspitoensure thatSi (so that each receiver can receive the signal transmitted byits associatedtransmitter).

usage if the force comes from a thruster.) There might be more than one minimizer; we just want one. If you can solve these optimiza-tion problems exactly, that’s fine; but you are free to solve the problems numerically (and even approximately). We don’t need an analysis verifying that your solution is indeed the best one.

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