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In this paper, an order recursive method is proposed to solve the joint estimation of channel impulse response (CIR) and carrier frequency offset (CFO) for orthogonal frequency-division multiplexing (OFDM) transmission. As long as one can obtain the solution for Qth-order Taylor expansion, the solution for (Q + 1)th order can also be obtained via a simple recursive relation. The proposed recursive algorithm actually provides a method to handle any Qth-order Taylor expansion, instead of just the second order adopted in the technical literature. Significant improvement can be observed by adopting higher order approximation. Analytical mean-square-error (MSE) performance results are given, demonstrating the efficiency of the proposed algorithm.