bv_cvxbook_extra_exercises

# If your method relies on any convex functions that we

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Unformatted text preview: c. 12.6 Antenna array weight design. We consider an array of n omnidirectional antennas in a plane, at positions (xk , yk ), k = 1, . . . , n. ( x k , yk ) θ 96 A unit plane wave with frequency ω is incident from an angle θ. This incident wave √ induces in the k th antenna element a (complex) signal exp(i(xk cos θ + yk sin θ − ωt)), where i = −1. (For simplicity we assume that the spatial units are normalized so that the wave number is one, i.e., the wavelength is λ = 2π .) This signal is demodulated, i.e., multiplied by eiωt , to obtain the baseband signal (complex number) exp(i(xk cos θ + yk sin θ)). The baseband signals of the n antennas are combined linearly to form the output of the antenna array n wk ei(xk cos θ+yk sin θ) G( θ ) = k=1 n = k=1 (wre,k cos γk (θ) − wim,k sin γk (θ)) + i (wre,k sin γk (θ) + wim,k cos γk (θ)) , if we deﬁne γk (θ) = xk cos θ + yk sin θ. The complex weights in the linear combination, wk = wre,k + iwim,k , k = 1, . . . , n, are called the antenna array coeﬃcients or...
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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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