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In direct-conversion orthogonal frequency division multiplexing receivers, the compensation of carrier frequency offset (CFO) and I/Q imbalance is critical. In the existing modified periodic pilot based scheme, I/Q imbalance compensation completely depends on CFO estimation, which however needs a computational expensive one-dimensional search and correct timing synchronization. In this paper, we propose a novel periodic pilot and an associated compensation method. Taking advantage of the pilot's periodicity, the proposed scheme simultaneously estimates the CFO and coefficients of I/Q imbalance compensation, in closed forms based on the linear least squares algorithm. The proposed scheme not only has significantly reduced complexity, but also is inherently robust to timing error. Simulations confirm the validity and superiority of the proposed scheme.