Open Access

An ML-Based Estimate and the Cramer-Rao Bound for Data-Aided Channel Estimation in KSP-OFDM

EURASIP Journal on Wireless Communications and Networking20072008:186809

https://doi.org/10.1155/2008/186809

Received: 3 May 2007

Accepted: 28 September 2007

Published: 23 October 2007

Abstract

We consider the Cramer-Rao bound (CRB) for data-aided channel estimation for OFDM with known symbol padding (KSP-OFDM). The pilot symbols used to estimate the channel are positioned not only in the guard interval but also on some of the OFDM carriers, in order to improve the estimation accuracy for a given guard interval length. As the true CRB is very hard to evaluate, we derive an approximate analytical expression for the CRB, that is, the Gaussian CRB (GCRB), which is accurate for large block sizes. This derivation involves an invertible linear transformation of the received samples, yielding an observation vector of which a number of components are (nearly) independent of the unknown information-bearing data symbols. The low SNR limit of the GCRB is obtained by ignoring the presence of the data symbols in the received signals. At high SNR, the GCRB is mainly determined by the observations that are (nearly) independent of the data symbols; the additional information provided by the other observations is negligible. Both SNR limits are inversely proportional to the SNR. The GCRB is essentially independent of the FFT size and the used pilot sequence, and inversely proportional to the number of pilots. For a given number of pilot symbols, the CRB slightly increases with the guard interval length. Further, a low complexity ML-based channel estimator is derived from the observation subset that is (nearly) independent of the data symbols. Although this estimator exploits only a part of the observation, its mean-squared error (MSE) performance is close the CRB for a large range of SNR. However, at high SNR, the MSE reaches an error floor caused by the residual presence of data symbols in the considered observation subset.

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Authors’ Affiliations

(1)
The Department of Telecommunications and Information Processing (TELIN), Ghent University

Copyright

© Heidi Steendam et al. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.