Data-Aided SNR Estimation in Time-Variant Rayleigh Fading Channels

This paper addresses the data-aided (DA) signal-to-noise ratio (SNR) estimation for constant modulus modulations over time-variant flat Rayleigh fading channels. The time-variant fading channel is modeled by considering the Jakes' model and the first order autoregressive (AR1) model. Closed-form expressions of the Cramér-Rao bound (CRB) for DA SNR estimation are derived for known and unknown fast fading Rayleigh channels parameters cases. As special cases, the CRBs over slow and uncorrelated fading Rayleigh channels are derived. Analytical approximate expressions for the CRBs are derived for low and high SNR. These expressions that enable the derivation of a number of properties that describe the bound's dependence on key parameters such as SNR, channel correlation and sample number. Since the exact maximum likelihood (ML) estimator is computationally intensive in the case of fast-fading channels, two approximate ML estimator solutions are proposed for high and low SNR cases in the case of known channel parameters. The performances of theses estimators are examined analytically in terms of means and variances. In the presence of unknown channel parameters, a high SNR ML estimator based on the AR1 correlation model is derived. It is shown that the ML estimates of the SNR parameter and unknown channel parameters may be obtained in a separable form. Finally, simulation results illustrate the performance of the estimator and confirm the validity of the theoretical analysis.