M. Ghogho et al., Cramer-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals, IEEE SIGNAL, 47(11), 1999, pp. 2905-2916
The problem of estimating the phase parameters of a phase-modulated signal
in the presence of colored multiplicative noise (random amplitude modulatio
n) and additive white noise (both Gaussian) is addressed, Closed-form expre
ssions for the exact and large-sample Cramer-Rao Bounds (CRB) are derived,
It is shown that the CRB is significantly affected by the color of the modu
lating process when the signal-to-noise ratio (SNR) or the intrinsic SNR is
small. Maximum likelihood type estimators that ignore the noise color and
optimize a criterion with respect to only the phase parameters are proposed
, These estimators are shown to be equivalent to the nonlinear least square
s estimators, which consist of matching the squared observations with a con
stant amplitude phase-modulated signal when the mean of the multiplicative
noise is forced to zero. Closed-form expressions are derived for the effici
ency of these estimators and are verified via simulations.