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The technique of orthogonal frequency division multiplexing is very sensitive to the carrier frequency offset (CFO). The requirement for high estimation accuracy when we acquire the CFO value is demanding. An efficient high-order approximation algorithm for jointly estimating the CFO and the channel impulse response (CIR) has been presented in the literature. From their simulation results, it is found that the estimator mean-square error (MSE) values are very close to the Cramer-Rao bound values, indicating that the highest estimation accuracy is achieved. However, no theoretical analysis is provided to confirm this assertion. In this article, we derive the theoretical formulas for the CFO MSE and the average CIR MSE for the estimators. It is found that the theoretical MSE for a joint CFO and CIR estimation problem approximates the Cramer-Rao bound when the signal-to-noise ratio (SNR) is high and the generalized CAZA sequence is used as the preamble. From our simulations, the theoretical results still hold true even for an SNR as low as 5 dB. Consequently, the range of SNR for which the theoretical analysis is valid is quite large.

MSE analysis for the finite order joint frequency tracking and channel estimation in OFDM systems