bv_cvxbook_extra_exercises

134 bounding portfolio risk with incomplete

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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 signal-to-interference-plus-noise 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.

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