An arrangement (300) and method, for iterative channel impulse response estimation in a system such as a GSM/EDGE system employing a transmission channel, by: producing (310) from a received signal (y) a channel impulse response estimate signal (p); and producing (320) from the received signal (y) a noise estimate signal (w) which is iteratively fed back to improve the channel impulse response estimate signal (p). The noise estimate signal comprises a matrix (w) respresenting the inverse of noise covariance; the matrix may be calculated at each iteration or may be selected from predetermined values corresponding to statistics of expected noise. This provides the advantages of reduced complexity, independence of the equalization method used to produce the channel impulse response estimate signal, and consequent performance improvement.