Maximally Robust 2-D Channel Estimation for OFDM Systems

Two-dimensional minimum mean square error (MMSE) channel estimation for orthogonal frequency division multiplexing (OFDM) systems is known to perform better than the least squares, as well as the conventional 1-D MMSE estimation, owing to its ability of exploiting both, the time and the frequency correlations among the channel frequency response (CFR) coefficients. Its superior performance comes however at the price of increased requirements-the knowledge of observation noise power and that of the channel frequency, as well as time correlation functions. In practical transmission scenarios, where channel correlation functions are not known or cannot be easily estimated, it is desirable to have an estimator that is robust to mismatches between the assumed and the actual channel correlation function. While such a robust estimator, for the case of an infinite number of observations, is well known for various uncertainty classes, not much attention has been paid to the practical case of a finite number of observations. We derive in this paper, the maximally robust (MR) 2-D channel estimator for the case of a finite number of pilot observations under some realistic constraints on the uncertainty class to which the 2-D channel correlation sequence belongs. We demonstrate that the correlation sequence associated with the MR estimator can be obtained by a simple semi-definite optimization procedure and is interestingly different from the well-known heuristic proposals. Simulation results establish the superiority of the proposed MR estimator over commonly employed heuristic robust estimator by as much as 3 dB in terms of the worst-case estimation MSE and around 1 dB in terms of the average BER performance under different practical transmission scenarios of interest.