Convergence analysis of the MAP turbo detector: New representation and convergence to the AWGN case

In this paper, we consider a coded transmission over a fre-quency selective channel. In [1, 2], we studied analytically the impact of a priori information on the MAP equalizer performance and gave the expression of the extrinsic Log Likelihood Ratios (LLRs) at its output. Based on these re-sults, we propose in this paper to study the convergence of the turbo equalizer using a Maximum a posteriori (MAP) equalizer and a MAP decoder. We give an analysis of the de-coder performance when it is provided with a priori. Then, we propose a new representation space for the convergence analysis of the turbo equalizer. This representation is inter-esting since for the equalizer it is independent of the signal to noise ratio (SNR). We also show that the performance of the turbo equalizer converges at high SNR to the Additive White Gaussian Noise (AWGN) channel performance under a certain condition on the channel and the code that we will derive. 1