The signal () in a pulse-doppler radar is conveniently represented as being complex-valued, () = ₁() + _Q() = ()e^j() where ₁() and _Q() represent the in-phase and quadrature-phase components of (), respectively. Let () and () represent the amplitude and phase of (). A(t) = sqrt(x²₁(t) + x²_Q(t)) and ()=actan(x_Q(t)/x₁(t))

(t)=max(|x (t)|,|x (t)|) + a*min(|x (t)|,|x (t)|) for some fixed R

Question 2a: Assume that () is uniformly distributed on the interval [0, 2]. Derive the value for that yields [=()] = A.

Question 2b: Assume that () is uniformly distributed on the interval [0, 2]. What is the variance of the estimator for the -value obtained in (2a.)?