The fisher information matrix and the CRLB in a non-AWGN model for the phase retrieval problem

In this paper we derive the Fisher information matrix and the Cramer-Rao lower bound for the non-additive white Gaussian noise model yk = |{x, f_k) + μk|², 1 ≤ k ≤ m, where {f₁, · · ·, f_m} is a spanning set for Cⁿ and (μ₁, ..., μ_m) are i.i.d. realizations of the Gaussian complex process CN(0, ρ²). We obtain closed form expressions that include quadrature integration of elementary functions.