bv_cvxbook_extra_exercises

# The received signal power for link i is gii pi the

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Unformatted text preview: ay, uniformly spaced) θ1 , . . . , θN over the interval [−π, π ], and replacing the objective with max{|G(θk )| | |θk − θtar | ≥ ∆} (a) Formulate the antenna array weight design problem as an SOCP. (b) Solve an instance using CVX, with n = 40, θtar = 15◦ , ∆ = 15◦ , N = 400, and antenna positions generated using rand(’state’,0); n = 40; x = 30 * rand(n,1); y = 30 * rand(n,1); 97 Compute the optimal weights and make a plot of |G(θ)| (on a logarithmic scale) versus θ. Hint. CVX can directly handle complex variables, and recognizes the modulus abs(x) of a complex number as a convex function of its real and imaginary parts, so you do not need to explicitly form the SOCP from part (a). Even more compactly, you can use norm(x,Inf) with complex argument. 12.7 Power allocation problem with analytic solution. Consider a system of n transmitters and n receivers. The ith transmitter transmits with power xi , i = 1, . . . , n. The vector x will be the variable in this problem....
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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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