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Unformatted text preview: rates and time slot fractions. We consider a wireless system that uses timedomain
multiple access (TDMA) to support n communication ﬂows. The ﬂows have (nonnegative) rates
r1 , . . . , rn , given in bits/sec. To support a rate ri on ﬂow i requires transmitter power
p = ai (ebr − 1),
where b is a (known) positive constant, and ai are (known) positive constants related to the noise
power and gain of receiver i.
TDMA works like this. Time is divided up into periods of some ﬁxed duration T (seconds). Each
of these T long periods is divided into n timeslots, with durations t1 , . . . , tn , that must satisfy
t1 + · · · + tn = T , ti ≥ 0. In timeslot i, communications ﬂow i is transmitted at an instantaneous
rate r = T ri /ti , so that over each T long period, T ri bits from ﬂow i are transmitted. The power
required during timeslot i is ai (ebT ri /ti − 1), so the average transmitter power over each T long
period is
n P = (1/T )
i=1 ai ti (ebT ri /ti − 1). When ti i...
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 Fall '13
 F.Borrelli
 The Aeneid

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