In this paper, we describe a patent pending, fine carrier frequency synchronization algorithm based on a minimum mean-squared error (MMSE) approach for OFDM systems which is insensitive to symbol timing offsets. In order to obtain these attributes, the proposed algorithm adopts a cost function similar to the CMA (constant modulus algorithm) used for blind channel equalization. Another advantage of the algorithm is that the transmission of a known training pattern is unnecessary, thus, improving the transmission efficiency. A hardware efficient version of the proposed algorithm is also developed. Computer simulations are performed to evaluate the performance with QPSK and 64-QAM modulations under a frequency selective multipath channel.