A recursive algorithm for estimating and updating the effective carrier frequency offset (CFO) vector in a multicarrier code-division multiple-access (MC-CDMA) system is proposed in this work. The recursive relation is derived based on the expectation maximization (EM) algorithm with a quadratic constraint. This new approach enables the use of linear estimation theory to tackle the CFO estimation problem with or without training data, which leads to an analytic CFO estimate in closed form.

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... ermore, the multiple access interference (MAI) is mitigated using the second order statistics of the interferenceplus-noise vector, which is updated in a recursive manner under the EM formulation, too. When reaching a converged estimate, a fixed-norm quadratic constraint is imposed so that the final CFO estimate is robust to an imprecise covariance matrix estimate caused by insufficient data samples. It is demonstrated by computer simulation that the performance of an MC-CDMA system without the CFO information can be restored by the proposed scheme in the sense that its bit error probability (BEP) performance is close to that with perfect CFO knowledge. Index Terms-Code division multiple access (CDMA), multicarrier CDMA, carrier frequency offset (CFO), recursive EM algorithm, quadratic constraint.