In this paper, we present an efficient transmission scheme for multiple-input multiple-output (MIMO) systems, i.e.,\ncoded spatial modulation (SM) systems with soft-decision aided detector. To exploit the powerful error correction of\nchannel coding, the key challenge of coded SM systems is on designing a reliable but low-complexity soft-output\ndetector. Fighting against this problem, we first propose two soft-output detection algorithms by exploiting the\nfeatures of M-phase-shift keying (PSK) and M-quadrature amplitude modulation (QAM) constellations, namely,\nPSK-based soft-output detector (PBSD) and QAM-based soft-output detector (QBSD). Furthermore, to further enhance\nthe performance of the two algorithms, we propose another two soft-output detection algorithms taking into\naccount of counterpart maximum-likelihood (ML) estimate, namely, improved PSK-based soft-output detector (IPBSD)\nand improved QAM-based soft-output detector (IQBSD). The findings of this paper demonstrate that: (1) The\ncomputational complexity of PBSD and QBSD algorithms are much lower than that of Max-Log-LLR algorithm at the\nexpense of error performance. (2) Both the IPBSD and IQBSD algorithms achieve the same performance as\nMax-Log-LLR algorithm with reduced computational complexity. In addition, a comprehensive performance and\ncomputational complexity comparison between the proposed algorithms and the Max-Log-LLR algorithm is provided\nto verify our proposed low-complexity soft-output detectors.
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