Multiple Complex Symbol Golden Code

Abstract

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 2nNr compared to the conventional Golden code, where Nr is the number of receive antennas, n, n ≥ 1, is an integer, and 2n 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 3 × 10-6, 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.

Keywords

• Golden code
• golden codeword
• maximum likelihood detection
• multiple complex symbol golden code
• sphere decoding
• sphere decoding with sorted detection subset