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In this paper, the design of iterative detection and decoding (IDD) schemes relying on a low-complexity probabilistic data association (PDA) aided method is conceived for turbo-coded multiple-input multiple-output (MIMO) systems communicating over Nakagami-m fading channels. The known PDA based MIMO detectors typically operate purely in the probability-domain. We show that the classic relationship where the extrinsic LLRs are given by subtracting the a priori LLRs from the a posteriori LLRs does not hold for the existing PDA based MIMO detectors. Therefore, the PDA method is not readily applicable to the IDD receiver. To overcome this predicament, we propose an approximate Bayesian theorem based log-domain PDA (AB-Log-PDA) detector, as well as a novel simple approach of calculating the bit-wise extrinsic LLRs for the AB-Log-PDA, which makes the AB-Log-PDA well-suited for employment in IDD receivers. It is shown that the proposed AB-Log-PDA based IDD scheme is capable of achieving a comparable performance to that of the optimal maximum a posteriori (MAP) detector based IDD receiver, while imposing a much lower computational complexity in the scenarios considered.

Iterative detection and decoding using approximate bayesian theorem based PDA method over MIMO Nakagami-m fading channels