Cramer-Rao bounds in the parametric estimation of fading radiotransmission channels

The context of this paper is parameter estimation for linearly modulated digital data signals observed on a frequency-flat time-selective fading channel affected by additive white Gaussian noise. The aim is the derivation of Cramer-Rao lower bounds for the joint estimation of all those channel parameters that impact signal detection, namely, carrier phase, carrier frequency offset (Doppler shift), frequency rate of change (Doppler rate), signal amplitude, fading power, and Gaussian noise power. Time-selective frequency-flat fading is modeled as a low-pass autoregressive multiplicative distortion process. In particular, the important case of "slow" fading, with the multiplicative process remaining constant over the whole data burst, is specifically discussed. Asymptotic expressions of the bounds, valid for a large observed sample or for high signal-to-noise ratio (SNR), are also derived in closed form. A few charts with numerical results are finally reported to highlight the dependence of the bounds on channel status (SNR, fading bandwidth, etc.).