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In this paper, we present a low-complexity carrier frequency offset (CFO) compensation algorithm based on the minimum mean square error (MMSE) criterion for uplink orthogonal frequency division multiple access systems. CFO compensation with an MMSE filter generally requires an inverse operation on an interference matrix whose size equals the number of subcarriers. Thus, the computational complexity becomes prohibitively high when the number of subcarriers is large. To reduce the complexity, we employ the conjugate gradient (CG) method which iteratively finds the MMSE solution without the inverse operation. To demonstrate the efficacy of the CG method for our problem, we analyze the interference matrix and present several observations which provide insight on the iteration number required for convergence. The analysis indicates that for an interleaved carrier assignment scheme, the maximum iteration number for computing an exact solution is at most the same as the number of users. Moreover, for a general carrier assignment scheme, we show that the CG method can find a solution with far fewer iterations than the number of subcarriers. In addition, we propose a preconditioning technique which speeds up the convergence of the CG method at the expense of slightly increased complexity for each iteration. As a result, we show that the CFO can be compensated with substantially reduced computational complexity by applying the CG method.