Multiple Beamforming with Constellation Precoding: Diversity Analysis and Sphere Decoding.

Multi-Input Multi-Output (MIMO) wireless communication systems commonly employ beamforming techniques with Singular Value Decomposition (SVD). In such systems, if no channel encoding is employed, the full diversity order provided by the channel is achieved when a single symbol is transmitted over multiple channels; however, this property is lost whenever multiple symbols are simultaneously transmitted. The full diversity order can be restored when channel coding is added to such a system. For example, when Bit-Interleaved Coded Modulation (BICM) is combined with this technique, the full diversity order of NM in an M ×N MIMO channel, transmitting S parallel streams is possible; provided SRc ≤ 1 where RC is the BICM convolutional code rate. In this paper, we present multiple beamforming with constellation precoding which can achieve the full diversity order with both uncoded and BICM-coded SVD systems. An analytical proof of this property is provided. In addition, to reduce the computational complexity of Maximum Likelihood (ML) decoding, we introduce a Sphere Decoding (SD) technique. This technique achieves several orders of magnitude reduction in computational complexity not only with respect to conventional ML decoding, but also, with respect to conventional SD.