  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.
