Design and implementation of M-BCJR algorithm based turbo equalizer

Turbo equalizers have been shown to be successful in mitigating the effects of inter-symbol interference introduced by partial response modems and by dispersive channels for code rates of R > 1/2. We analyze the performance of iterative equalization and decoding (IED) using an M-BCJR equalizer. We use bit error rate (BER), frame error rate simulations and extrinsic information transfer (EXIT) charts to study and compare the performances of M-BCJR and BCJR equalizers on precoded and non-precoded channels. Using EXIT charts, the achievable channel capacities with IED using the BCJR, M-BCJR and MMSE LE equalizers are also compared. We predict the BER performance of IED using the M-BCJR equalizer from EXIT charts and explain the discrepancy between the observed and predicted performances by showing that the extrinsic outputs of the M-BCJR algorithm are not true logarithmic-likelihood ratios (LLR´s). We show that the true LLR´s can be estimated if the conditional distributions of the extrinsic outputs are known and finally we design a practical estimator for computing the true LLR´s from the extrinsic outputs of the MBCJR equalizer.