On the use of tracking loops for low-complexity multi-path channel estimation in OFDM systems

• Algorithms for tracking the complex amplitudes of a multi-path channel in OFDM systems.
• The tracking algorithms are inspired by digital PLLs, with low-complexity.
• Asymptotic MSE is almost the same as a Kalman filter-based estimator.
• Analytic formulae of the sub-optimal parameters and the performance are provided.
• The given formulae are adaptable to any Doppler spectrum models of a WSS channel.
• Generalization to the second and third order loop of the link between the maximum frequencies of the Jakes and 3D model Doppler spectra that give the same asymptotic performance.

This paper treats pilot aided multi-path channel estimation with tracking loops for OFDM systems under slow to moderate fading conditions. Recent works have presented theoretical results for the tuning of second-order and third-order tracking loops in the particular context of Jakes׳s Doppler spectrum channel. The method for getting the loop coefficients resorted either to the use of a given constraint, which made the obtained coefficients sub-optimal, or was obtained in part by simulations. Here, we perform a global optimization of the coefficients without constraints to get the optimal coefficients, and analytical formulas are provided. One remarkable result of this optimization is that only the natural frequency depends on the transmission parameters, i.e., the channel Doppler spectrum, the power delay profile, and the noise variance. Consequently, only one parameter has to be tuned. Moreover, asymptotic performance is formulated in a more general way as a function of the 2rth moments of the Doppler spectrum (r is the loop order). Hence, all our derivations are usable for any Doppler spectrum and are not specific to Jakes׳s Doppler spectrum. A complete table sums up for the three orders of the theoretical results of the optimal coefficients together with the asymptotic performance. The performance is also compared with that of the asymptotic Kalman filter.