Flexible Complexity Fast Decoding of Multiplexed Alamouti Codes in Space-Time-Polarization Systems

Space-time codes built with multiplexed Alamouti components provide multiplexing as well as diversity gain. Their orthogonal structure also leads to simpler decoding algorithms. We consider a 4 × 2 system with multiplexed Alamouti codes. An exhaustive search maximum likelihood (ML) decoding for a 4×2 system is of order M⁴, for a modulation scheme with constellation size M. For multiplexed orthogonal designs, an exact fast ML decoding algorithm has recently been reported whose complexity order is M² for a 4 × 2 system with QAM constellations. Nevertheless, the quadratic complexity of this fast ML algorithm may still be infeasible in practice for large constellations (e.g. M ≥ 64 QAM). In this paper, we present a method for designing low complexity sub-optimal decoders based on a combination of search based ML decoding and linear decoding. Our formulation facilitates a direct investigation of the trade-off between performance and complexity. The complexity of our hybrid decoder is flexible and it can be fixed based on the desired performance for a hardware implementation. Although extendable to more general multiplexed Alamouti systems, we focus here on a 4 × 2 space-time-polarization system comprising of two dual-polarized transmit antennas and one dual-polarized receive antenna.