Likelihood-based metric for Gibbs sampling turbo MIMO detection

In a multiple-input multiple-output (MIMO) system, maximum likelihood detection (MLD) is the best demodulation scheme if no a priori information is available. However, the complexity of MLD increases exponentially with the number of signal streams. Therefore, various demodulation schemes with less complexity have been proposed and some of those schemes show performance close to that of MLD. One kind of those schemes uses a Gibbs sampling (GS) algorithm. GS MIMO detection that combines feedback from turbo decoding has been proposed. In this scheme, the accuracy of GS MIMO detection is improved by feeding back loglikelihood ratios (LLRs) from a turbo decoder. In this paper, GS MIMO detection using only feedback LLRs from a turbo decoder is proposed. Through extrinsic information transfer (EXIT) chart analysis, it is shown that the EXIT curves with and without metrics calculated from received signals overlap as the feedback LLR values increase. Therefore, the proposed scheme calculates the metrics from received signals only for the first GS MIMO detection and the selection probabilities of GS MIMO detection in the following iterations are calculated based only on the LLRs from turbo decoders. Numerical results obtained through computer simulation show that the performance of proposed GS turbo MIMO detection is worse than that of conventional GS turbo MIMO detection when the number of GS iterations is small. However the performance improves as the number of GS iterations increases. When the number of GS iterations is 30 or more, the bit error rate (BER) performance of the proposed scheme is equivalent to that of the conventional scheme. Therefore, the proposed scheme can reduce the computational complexity of selection probability calculation in GS turbo MIMO detection.