This disclosure describes equalization techniques for spread spectrum wireless communication. The techniques may involve estimating a channel impulse response, estimating channel variance, and selecting filter coefficients for an equalizer based on the estimated channel impulse response and the estimated channel variance. Moreover, in accordance with this disclosure, the channel variance estimation involves estimation of two or more co-variances for different received samples. Importantly, the equalizer is “fractionally spaced,” which means that the equalizer defines fractional filtering coefficients (filter taps), unlike conventional equalizers that presume that filter coefficients are defined at integer chip spacing. The techniques can allow the equalizer to account for antenna diversity, such as receive diversity, transmit diversity, or possibly both.