Wireless Communication by Goldsmith_solution_to_ExercisesChapter 1 Solutions to Exercises1Chapter 2 Solutions to ExercisesExercise 2.1. 1. Let r(t) =2 r0 + (vt)2 + 2r0 vt cos(φ). Then,Er (f, t, r(t), θ, ψ )) =[α(θ, ψ, f ) exp{j 2πf (1 r(t)/c)}] . r(t)Moreover, if we assume that r0 vt, then we get that r(t) ≈ r0 + vt cos(φ). Thus, the doppler shift is f v cos(φ)/c. 2. Let (x, y, z ) be the position of the mobile in Cartesian coordinates, and (r, ψ, θ) the position in polar coordinates. Then (x, y, z ) = (r sin θ cos ψ, r sin θ sin ψ, r cos θ) (r, ψ, θ) = x2 + y 2 + z 2 , arctan(y/x), arccos(z/ x2 + y 2 + z 2 ) ……