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EE263 Autumn 2007-08 Prof. S. Boyd EE263 homework problems Lecture 2 – Linear functions and examples 2.1 A simple power control algorithm for a wireless network. First some background. We consider a network of n transmitter/receiver pairs. Transmitter i transmits at power level pi (which is positive). The path gain from transmitter j to receiver i is Gij (which are all nonnegative, and Gii are positive). The signal power at receiver i is given by si = Gii pi . The noise plus interference power at receiver i is given by qi = σ + X Gij pj j6=i where σ > 0 is the self-noise power of the receivers (assumed to be the same for all receivers). The signal to interference plus noise ratio (SINR) at receiver i is defined as Si = si /qi . For signal reception to occur, the SINR must exceed some threshold value γ (which is often in the range 3 – 10). Various power control algorithms are used to adjust the powers pi to ensure that Si ≥ γ (so that each receiver can receive the signal transmitted by its associated transmitter). In this problem, we consider a simple power control update algorithm. The powers are all updated synchronously at a fixed time interval, denoted by t = 0, 1, 2, . . .. Thus the quantities p, q, and S are discrete-time signals, so for example p3 (5) denotes the transmit power of transmitter 3 at time epoch t = 5. What we’d like is Si (t) = si (t)/qi (t) = αγ where α > 1 is an SINR safety margin (of, for example, one or two dB). Note that increasin ...
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