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

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Abstract
The context of this paper is parameter estima- tion 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 Cram´ er-Rao lower bounds for the joint estimation of all those channel pa- rameters 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 mul- tiplicative 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.).