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The Cramer Rao bound (CRB) of the carrier frequency offset (CFO) estimation with virtual subcarriers in orthogonal frequency division multiplexing (OFDM) systems is derived. The obtained CRB gives a lower bound, which is much tighter than the modified CRB, for the variance of any unbiased CFO estimate. Also, the maximum likelihood estimator can achieve this tight CRB at high signal-to-noise ratio. Thus, the derived CRB is a good benchmark for evaluating whether a CFO estimator is good or not.
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Introduction: The OFDM technique has already been adopted by the 4th generation wireless standards. It has many good properties for data trans- mission over frequency selective fading channels, such as high spectral efficiency, simple equalisation, ease of adaptive resource allocation etc. However, it has the main disadvantage that it is sensitive to the carrier fre- quency offset (CFO). For CFO estimation in OFDM systems, several CFO estimators employing virtual subcarriers have been proposed [1- 4].The virtual subcarriers inserted in OFDM blocks carry no information data. In [1], the maximum likelihood (ML) estimator with virtual subcarriers is given and its equivalence to the MUSIC-like estimators is proved. As shown in [2] and [3], the complexity of the ML estimator can be reduced by using the root MUSIC-like polynomial rooting method and the deriva- tiverootingmethodseparately.Reference[4] studies how the virtual sub- carriers should be placed for consistent CFO estimation. For the evaluation of the performance of these estimators, a benchmark is needed. Although [4] derives the lower bound, modified CRB (MCRB), for the variance of any unbiased CFO estimate, it is too loose a lower bound to tell whether an estimator is good or not, since it does not depend on the data symbols deterministically. Thus, a much...