X-Codes: A low complexity full-rate high-diversity achieving precoder for TDD MIMO systems

We consider a time division duplex multiple-input multiple-output (n(t) x n(r) MIMO). Using channel state information (CSI) at the transmitter, singular value decomposition (SVD) of the channel matrix is performed. This transforms the MIMO channel into parallel subchannels, but has a low overall diversity order. Hence, we propose X-Codes which achieve a higher diversity order by pairing the subchannels, prior to SVD precoding. In particular, each pair of information symbols is encoded by a fixed 2 x 2 real rotation matrix. X-Codes can be decoded using n(r) very low complexity two-dimensional real sphere decoders. Error probability analysis for X-Codes enables us to choose the optimal pairing and the optimal rotation angle for each pair. Finally, we show that our new scheme outperforms other low complexity precoding schemes.