Data estimation is performed in a wireless communication system using both oversampling and multiple reception antennas. A receive vector is produced for each antenna at a sampling interval which is a multiple of the chip rate of the received signal. A channel response matrix is produced for each antenna at a preferred multiple of the sampling rate. Each receive vector is processed using a sliding window based approach, where a plurality of successive windows are processed. For each window, a combined circulant channel response matrix is produced using the channel response matrices. Using the combined circulant channel response matrix and a combined received vector comprising each received vector in a discrete Fourier transform based approach to estimate a data vector corresponding to that window; and combining the data vector estimated in each window to form a combined data vector.