IEEE Access (Jan 2021)
Multiple Complex Symbol Golden Space-Time Labeling Diversity
Abstract
The Golden code is a full-rate space-time block code (STBC), which achieves a diversity order of $2N_{r}$ , where $N_{r}$ is the number of receive antennas. The multiple complex symbol Golden code (MCS-Golden code) is a generalized Golden code. The MCS-Golden code not only achieves full-rate but also achieves a diversity order of $2^{n}{N_{r}}$ , $n$ , $n\ge {1}$ , is an integer, and $2^{n}$ is the number of multiple complex symbols in the MCS-Golden code system. In this paper, we apply the labelling diversity technique to the MCS-Golden code to form a new type of STBC, named as multiple complex symbol Golden space-time labelling diversity (MCS-GSTLD). The proposed MCS-GSTLD achieves a diversity order of $2\times {2^{n}}{N_{r}}$ , and further improves error performance compared to the MCS-Golden code. We also formulate the theoretical average bit error probability (ABEP) for the proposed MCS-GSTLD system. Furthermore, we apply sphere decoding with sorted detection subset (SD-SDS) to detect the transmitted symbols in the MCS-GSTLD system. Simulation results show that the SD-SDS scheme achieves the theoretical ABEP for $N_{r}>2$ . Both theoretical and simulation results demonstrate that with the same spectral efficiency and four receive antennas, the 2CS-GSTLD achieves at least 1.3 dB signal-to-noise ratio (SNR) gain compared to the 2CS-Golden code at a BER of $3\times {10^{-6}}$ , while the 4CS-GSTLD achieves at least 0.7 dB SNR gain compared to the 4CS-Golden code.
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