bv_cvxbook_extra_exercises

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Unformatted text preview: rates and time slot fractions. We consider a wireless system that uses time-domain 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 time-slots, with durations t1 , . . . , tn , that must satisfy t1 + · · · + tn = T , ti ≥ 0. In time-slot 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 time-slot 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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