Modified Cramér-Rao Bound for $M$-FSK Signal Parameter Estimation in Cauchy and Gaussian Noise

The Cramér-Rao bound (CRB) provides an efficient standard for evaluating the quality of standard parameter estimators. In this paper, a modified Cramér-Rao bounds (MCRB) for modulation parameter estimations of M-ary frequency-shift-keying (M-FSK) signals is proposed under the condition of the Gaussian and non-Gaussian additive interference. We extend the MCRB to the estimation of a vector of non-random parameters in the presence of nuisance parameters. Moreover, the MCRB is applied to the joint estimation of phase offset, frequency offsets, frequency deviation, and symbol period of M-FSK signal with two important special cases of alpha stable distributions, namely, the Cauchy and the Gaussian. The extensive simulation studies are conducted to contrast the MCRB for the modulation parameter vector in different noise environments.