AbstractIn this paper, we consider a time division multiple access (TDMA) transmission of coded symbols over a time and frequency selective channel. At the receiver, a turbo‐detector composed of a maximuma posteriori(MAP) equaliser and a MAP decoder is used. We give the expression of the MAP iterative burst‐by‐burst channel estimation algorithm using the Expectation‐Maximisation (EM) algorithm. Since the obtained algorithm is complex, we propose to simplify it by neglecting the inter‐symbol interference (ISI) term. In order to reduce the error caused by this simplification, we propose to use a candidate precoder at the transmitter chosen among a given set of precoders such that the selected precoded sequence leads to the minimum mean square value of the ISI neglected term. Simulations show that the performance of the approximate algorithm with precoding are almost similar to the performance of the exact algorithm. Copyright © 2010 John Wiley & Sons, Ltd.