bv_cvxbook_extra_exercises

# Bv_cvxbook_extra_exercises

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online