bv_cvxbook_extra_exercises

If your method relies on any convex functions that we

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
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