  Semi-definite relaxation (SDR) detector has been demonstrated to be
successful in approaching maximum likelihood (ML) performance while the time
complexity is only polynomial. We propose a new receiver jointly utilizing the
forward error correction (FEC) code information in the SDR detection process.
Strengthened by code constraints, the joint SDR detector substantially improves
the overall receiver performance. For further performance boost, the ML-SDR
detector is adapted to MAP-SDR detector by incorporating a priori information
in the cost function. Under turbo principle, MAP-SDR detector takes in soft
information from decoder and outputs extrinsic information with much improved
reliability. We also propose a simplified SDR turbo receiver that solves only
one SDR per codeword instead of solving multiple SDRs in the iterative turbo
processing. This scheme significantly reduces the time complexity of SDR turbo
receiver, while the error performance remains similar as before. In fact, our
simplified scheme is generic and it can be applied to any list-based iterative
receivers.
