A method and apparatus are disclosed for equalizing a channel using improved channel estimates. The present invention assumes that fading will follow a statistical model and obtains an improved channel estimate using one or more basis functions to describe the channel based on known channel statistics. A Karhunen-Loeve expansion can be used for channel estimation to describe the channel. Waveforms are selected that are matched to characteristics of the channel, such as transmission waveforms whose energy is largely restricted to a bandwidth assigned to the channel. Coefficients are estimated for the basis functions using real-time data.