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This paper addresses the problem of joint maximum-likelihood estimation of carrier frequency offsets, and channel responses in an orthogonal frequency division multiple access (OFDMA) uplink, which is a computationally-intensive, multiparameter, multidimensional problem. We propose to apply a recently-developed meta-heuristic algorithm called the firefly algorithm (FA) for the estimation of required parameters. We also introduce a new initialization procedure for the FA algorithm based on the separability of cost functions, which drastically reduces its computational complexity. A separate pilot OFDMA symbol is transmitted prior to the data symbols to estimate the parameters. The proposed technique is shown to achieve excellent performance at reduced computational complexity, especially at low signal-to-noise ratio. Also, it can be applied to OFDMA systems with any type of carrier assignment …