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 gener...
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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 2nN(r), n, n >= 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 x 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 3x10(-6) while the 4CS-GSTLD achieves at least 0.7 dB SNr gain compared to the 4CS-Golden code.
The Golden code is a full-rate full-diversity (FRFD) space-time block code (STBC). The conventional Golden code takes four complex symbols and generates two pairs of Golden codewords. Each pair of Golden codewords con...
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The Golden code is a full-rate full-diversity (FRFD) space-time block code (STBC). The conventional Golden code takes four complex symbols and generates two pairs of Golden codewords. Each pair of Golden codewords contains two complex symbols. In this paper, a new type of Golden code is proposed, where we extend the two complex symbols in each pair of Golden codewords into multiple complex symbols. The scheme hereinafter referred to as the multiple complex symbol Golden code (MCS-Golden code) preserves the FRFD property but achieves a diversity order of compared to the conventional Golden code, where is the number of receive antennas,, is an integer, and is the number of multiple complex symbols in the MCS-Golden code system. An equivalent model of the MCS-Golden code is constructed, then used to derive a closed-form bound on the average bit error probability (ABEP) for the MCS-Golden code system. We further propose a low complexity detection scheme, sphere decoding with sorted detection subset (SD-SDS) for the MCS-Golden code. Finally, we discuss the detection complexity for the proposed SD-SDS. Both simulation and theoretical results show that the MCS-Golden code significantly improves error performance compared to the conventional Golden code. For example, at an average bit error rate of , a four complex symbol Golden code system with three receive antennas achieves approximately 2.5 dB signal-to-noise ratio (SNR) gain compared to the conventional Golden code.
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