Low-complexity soft-output detectors for LDPC coded spatial modulation systems

In this paper, we present an efficient transmission scheme for multiple-input multiple-output (MIMO) systems, i.e., low density parity check (LDPC) coded spatial modulation (SM) systems. To exploit the powerful error correction of LDPC code, the key challenge of LDPC coded SM systems is on designing a reliable but low complexity soft-output detector. To tackle this problem, we propose two soft-output detection algorithms based on hard-decision detectors by exploiting the features of M-PSK and M-QAM constellations, namely, PSK-based soft-output detector (PBSOD) and QAM-based soft-output detector (QBSOD). The analytical results show that the number of the searched signal candidates is reduced from N_tM to N_t, where N_t is the number of transmit antennas, M is the modulation order. Furthermore, we propose a more general simpler detector, that is, using the absolute value instead of the Frobenius norm to calculate the soft bit metrics. The findings of this paper suggest that the proposed three soft-output detectors for LDPC coded SM systems exhibit lower complexity compared to optimal maximum a posteriori (MAP) log likelihood ratio (LLR) detector and Max-Log detector while imposing only marginal performance degradation. In addition, a comprehensive performance and computational complexity comparison between the proposed detectors and the state-of-the-art detectors is provided to validate the proposed low-complexity detectors. The achieved performance and complexity of the proposed detectors make them suitable candidates for practical coded SM-MIMO systems.