Principles of Modern Radar - Volume 2 1891121537

13.9 Problems 62915. A left-circularly polarized wave from a radar is scattered from a target, with itsscattering matrix given by[ ] 2 j1S =j1 4Diagonalize S and determine the two eigenvalues λ 1 and λ 2 in (13.36). Find thetransmit and receive polarization ratios of a monostatic radar antenna to (a) maximizeand (b) minimize the copolarized received power. Find the polarization states (complexunit vectors) corresponding to the polarization ratios, and show that the state vectorsare orthonormal (see Chapter 6 in [3]).16. Assume that the scattering matrix of a target is given by[ ] 2 j 0.5S =0.5 jDiagonalize S and determine the two eigenvalues λ 1 and λ 2 in (13.36). Using thethree-step procedure proposed in [19], determine the optimal transmit and receivepolarization states for maximum backscattered power.17. A dihedral corner has the monostatic scattering matrix given by[ ] 1 0S =0 −1Find the Kennaugh matrix. Show the optimal polarization states by locating the verticesof the polarization fork on the Poincaré sphere.18. Determine the Kennaugh matrix for the spherical target, whose scattering matrix isderived in Problem 12.19. Determine the Kennaugh matrices for the right- and left-handed helices, whose scatteringmatrices are derived in Problem 14.