On the analysis of the MAP equalizer performance within an iterative receiver

We consider an iterative receiver composed of a maximum a posteriori (MAP) equalizer and a MAP decoder. During the iterations, the equalizer and the decoder exchange extrinsic information and use them as a priori in order to improve their performance. We propose here to study analytically the impact of the a priori information provided by the channel decoder on the equalizer performance. We show that it is equivalent to a gain in terms of signal-to-noise ratio (SNR) and we provide an analytical expression. Simulation results show that this expression approximates quite well the SNR gain.