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Unformatted text preview: ility in a wireless system with interference. Consider a wireless network consisting
of n data links, labeled 1, . . . , n. Link i transmits with power Pi > 0, and supports a data rate
Ri = log(1 + γi ), where γi is the signaltointerferenceplusnoise ratio (SINR). These SINR ratios
depend on the transmit powers, as described below.
n×
The system is characterized by the link gain matrix G ∈ R++n , where Gij is the gain from the
transmitter on link j to the receiver for link i. The received signal power for link i is Gii Pi ; the
noise plus interference power for link i is given by
2
σi + Gij Pj ,
j =i 2
where σi > 0 is the receiver noise power for link i. The SINR is the ratio γi = 2
σi Gii Pi
.
+ j =i Gij Pj The problem is to choose the transmit powers P1 , . . . , Pn , subject to 0 < Pi ≤ Pimax , in order to
maximize the log utility function
n U (P ) = log Ri .
i=1 2
(This utility function can be argued to yield a fair distribution of rates.) The data are G, σi , and
max .
Pi Formulate this problem as a conv...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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