bv_cvxbook_extra_exercises

Bv_cvxbook_extra_exercises

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Unformatted text preview: The path gain from each transmitter j to each receiver i will be denoted Aij and is assumed to be known (obviously, Aij ≥ 0, so the matrix A is elementwise nonnegative, and Aii > 0). The signal received by each receiver i consists of three parts: the desired signal, arriving from transmitter i with power Aii xi , the interfering signal, arriving from the other receivers with power j =i Aij xj , and noise βi (which are positive and known). We are interested in allocating the powers xi in such a way that the signal to noise plus interference ratio at each of the receivers exceeds a level α. (Thus α is the minimum acceptable SNIR for the receivers; a typical value might be around α = 3, i.e., around 10dB). In other words, we want to find x 0 such that for i = 1, . . . , n Aii xi ≥ α Equivalently, the vector x has to satisfy x j =i Aij xj + βi . 0, Bx αβ (39) where B ∈ Rn×n is defined as Bii = Aii , Bij = −αAij , j = i. (a) Show that (39) is feasible if and only if B is invertible and z = B −1 1 0 (1...
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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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