An apparatus and method for compressive sensing tap identification for channel estimation comprising identifying a set of significant taps in the time domain; representing a time-flat channel response using a Taylor series expansion with the set of significant taps; converting the time-flat channel response to a vectorized channel response; transforming the vectorized channel response to a compressive sensing (CS) polynomial frequency response; aggregating the CS polynomial frequency response into a stacked frequency response; converting the stacked frequency response into a measured pilot frequency response; estimating a channel parameter vector based on the measured pilot frequency response; and generating a reconstructed channel response from the channel parameter vector.