From Nominal to True A Posteriori Probabilities: An Exact Bayesian Theorem Based Probabilistic Data Association Approach for Iterative MIMO Detection and Decoding

It was conventionally regarded that the approximate Bayesian theorem based existing probabilistic data association (PDA) algorithms output the estimated symbol-wise a posteriori probabilities (APPs) as soft information. In our recent work, however, we demonstrated that these probabilities are not the true APPs in the rigorous mathematical sense, but a type of nominal APPs, which are unsuitable for the classic architecture of iterative detection and decoding (IDD) aided receivers. To circumvent this predicament, in this paper we propose an exact Bayesian theorem based logarithmic domain PDA (EB-Log-PDA) method, whose output has similar characteristics to the true APPs, and hence it is readily applicable to the classic IDD architecture of multiple-input-multiple-output (MIMO) systems using the general M-ary modulation. Furthermore, we investigate the impact of the EB-Log-PDA algorithm´s inner iteration on the design of EB-Log-PDA aided IDD receiver. We demonstrate that introducing inner iterations into EB-Log-PDA, which is common practice in conventional-PDA aided uncoded MIMO systems, would actually degrade the IDD receiver´s performance, despite significantly increasing the overall computational complexity of the IDD receiver. Finally, we investigate the relationship between the extrinsic log-likelihood ratios (LLRs) of the proposed EB-Log-PDA and of the approximate Bayesian theorem based logarithmic domain PDA (AB-Log-PDA) reported in our previous work. Despite their difference in extrinsic LLRs, we also show that the IDD schemes employing the EB-Log-PDA and the AB-Log-PDA without incorporating any inner PDA iterations have a similar achievable performance close to that of the optimal maximum a posteriori (MAP) detector based IDD receiver, while imposing a significantly lower computational complexity in the scenarios considered.