An Efficient Soft-Output Fixed-Complexity Sphere Decoder for Large QAM Constellations

In this paper, an efficient soft-output fixedcomplexity sphere decoder (FSD), which is suitable for multipleinput multiple-output (MIMO) detection using large quadrature amplitude modulation (QAM) constellations, has been investigated. The sector-shaped enumeration algorithm, which stores the enumeration orders for both the real and the imaginary axes of the signal space, is designed for the first two layers of the proposed FSD. Meanwhile, the section-wise list candidate selection, employing a novel grouping strategy, is tailored for the leaf layer of the proposed FSD. Together, these techniques effectively lower computational complexity and substantially reduce time delays. In addition, the log-likelihood ratio (LLR) refinement is explored to address the overestimation caused by the bit-flipping algorithm, significantly improving error performance. Finally, several hardware designs are explored to further minimize both time and area complexity in hardware implementation. To the best of our knowledge, this is the first 8 × 8 1024-QAM MIMO detector implemented using an FSD-based algorithm. It is demonstrated that the proposed soft-output FSD achieves error performance comparable to that of the list sphere decoder, while also offering significantly reduced complexity compared to prior research in the literature.