A wireless communication method, comprising: receiving, by a first wireless device during a training phase, reference tones using a first number of resource elements from a transmitter of a second wireless device, wherein the first wireless device comprises multiple receiving antennas; estimating, by the first wireless device, from the receiving the reference tones, a second order statistics of wireless channels between the multiple receiving antennas and the transmitter of the second wireless device, wherein the second order statistics comprises K dominant eigenvalues and corresponding eigenvectors of a covariance matrix representation of a channel response, wherein the K dominant eigenvalues correspond to K dominant reflectors in the wireless channels, wherein K is an integer, wherein the covariance matrix representation comprises an N×N matrix, wherein N is an integer that is a product of a number of the reference tones and a number of the multiple receiving antennas, and wherein the N×N matrix is approximated using an N×K matrix comprising the corresponding eigenvectors and a K×K diagonal matrix comprising the K dominant eigenvalues; and estimating the channel response, during an operational phase subsequent to the training phase, using the second order statistics and reference tones received on a second number of resource elements, wherein the second number is less than the first number, wherein the first number of resource elements comprises a first frequency band and the second number of resource elements comprises a second frequency band that is non-overlapping with the first frequency band. receiving, by a first wireless device during a training phase, reference tones using a first number of resource elements from a transmitter of a second wireless device, wherein the first wireless device comprises multiple receiving antennas; estimating, by the first wireless device, from the receiving the reference tones, a second order statistics of wireless channels between the multiple receiving antennas and the transmitter of the second wireless device, wherein the second order statistics comprises K dominant eigenvalues and corresponding eigenvectors of a covariance matrix representation of a channel response, wherein the K dominant eigenvalues correspond to K dominant reflectors in the wireless channels, wherein K is an integer, wherein the covariance matrix representation comprises an N×N matrix, wherein N is an integer that is a product of a number of the reference tones and a number of the multiple receiving antennas, and wherein the N×N matrix is approximated using an N×K matrix comprising the corresponding eigenvectors and a K×K diagonal matrix comprising the K dominant eigenvalues; and estimating the channel response, during an operational phase subsequent to the training phase, using the second order statistics and reference tones received on a second number of resource elements, wherein the second number is less than the first number, wherein the first number of resource elements comprises a first frequency band and the second number of resource elements comprises a second frequency band that is non-overlapping with the first frequency band.