A Low-Complexity Soft-Output wMD Decoding for Uplink MIMO Systems with One-Bit ADCs

This paper considers an uplink multiuser multiple-input-multiple-output (MU-MIMO) system with one-bit analog-to-digital converters (ADCs), in which $K$ users with a single transmit antenna communicate with one base station (BS) with $N_{\rm r}$ receive antennas. In this system, a novel MU-MIMO detection method, named weighted minimum distance (wMD) decoding, was recently proposed by introducing an equivalent coding problem. Despite of its attractive performance, the wMD decoding has the two limitations to be used in practice: i) the hard-decision outputs can degrade the performance of a channel code; ii) the computational complexity grows exponentially with the $K$. To address those problems, we first present a soft-output wMD decoding that efficiently computes soft metrics (i.e., log-likelihood ratios) from one-bit quantized observations. We then construct a low-complexity (soft-output) wMD decoding by introducing {\em hierarchical code partitioning}. This method can be regarded as a sphere decoding in Hamming space, in that a search-spare is considerably reduced. Finally, we demonstrate that the proposed method significantly performs the state-of-the-art methods with a comparable complexity.