Performance analysis of the MAP equalizer with a priori and distribution of the extrinsic LLRs

To combat the effects of intersymbol interference, the optimal equalizer to be used is based on maximum a posteriori (MAP) detection. We consider the case where the MAP equalizer is provided with a priori information on the transmitted data, as in a turbo equalizer. We propose to study analytically the impact of the a priori on the MAP equalizer performance. We distinguish two cases: the case of unreliable a priori and the case of reliable a priori. We show that when the a priori is reliable, it is better to perform the detection of the transmitted symbols based on the a posteriori outputs of the MAP equalizer rather than on the a priori only. In a turbo equalizer, the equalizer and the decoder exchange extrinsic log likelihood ratios (LLRs). We propose here to study analytically their distribution. The aim of this study is to perform in the future the analytical convergence analysis of turbo equalizers using the MAP equalization.