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Carrier frequency offsets (CFO) greatly degrade the performance of orthogonal frequency-division multiplexing (OFDM) systems because they may violate the orthogonality of subcarriers and introduce intercarrier interferences. CFO effects of uplink of a spatial-diversity multiple-access (SDMA) OFDM system are first approximated by the CFO-vectors which are the fast Fourier transform (FFT) of complex exponential functions associated with the CFO. Then, the CFO-vectors are optimally estimated in a minimum mean square error sense by appropriately designing pilots which are in fact the δ-sequences subject to a specified distribution. In addition, the estimation is further improved by imposing a window function on the received signals to reduce the side-lobe leakages of the CFO-vectors. Through simulations, it is shown that the new estimators provide a satisfactory CFO estimation for fine tracking of uplink of OFDM/SDMA systems.