Golden Coded Multiple Beamforming

TL;DR

This paper introduces Golden Coded Multiple Beamforming (GCMB), a novel MIMO transmission scheme that combines the Golden Code with beamforming to achieve full diversity and reduced decoding complexity.

Contribution

The paper proposes GCMB, which transmits the Golden Code via 2x2 multiple beamforming, reducing worst-case decoding complexity to O(√M) while maintaining full diversity.

Findings

GCMB achieves full diversity order similar to traditional Golden Code systems.

Decoding complexity of GCMB is significantly lower at O(√M).

Performance of GCMB is comparable to existing MIMO schemes with Golden Code and FPMB.

Abstract

The Golden Code is a full-rate full-diversity space-time code, which achieves maximum coding gain for Multiple-Input Multiple-Output (MIMO) systems with two transmit and two receive antennas. Since four information symbols taken from an M-QAM constellation are selected to construct one Golden Code codeword, a maximum likelihood decoder using sphere decoding has the worst-case complexity of O(M^4), when the Channel State Information (CSI) is available at the receiver. Previously, this worst-case complexity was reduced to O(M^(2.5)) without performance degradation. When the CSI is known by the transmitter as well as the receiver, beamforming techniques that employ singular value decomposition are commonly used in MIMO systems. In the absence of channel coding, when a single symbol is transmitted, these systems achieve the full diversity order provided by the channel. Whereas this property is lost when multiple symbols are simultaneously transmitted. However, uncoded multiple beamforming can achieve the full diversity order by adding a properly designed constellation precoder. For 2 \times 2 Fully Precoded Multiple Beamforming (FPMB), the general worst-case decoding complexity is O(M). In this paper, Golden Coded Multiple Beamforming (GCMB) is proposed, which transmits the Golden Code through 2 \times 2 multiple beamforming. GCMB achieves the full diversity order and its performance is similar to general MIMO systems using the Golden Code and FPMB, whereas the worst-case decoding complexity of O(sqrt(M)) is much lower. The extension of GCMB to larger dimensions is also discussed.