In this work, we develop a new iterative turbo receiver for LDPC-coded multi-antenna systems based on semidefinite relaxation (SDR). For a classical turbo receiver, forward error correction (FEC) code is only used at decoder. Nonetheless, by taking advantage of FEC code in the detection stage, our proposed SDR detector can output extrinsic information with much improved reliability to the decoder. We also propose a simplified SDR turbo receiver that solves only one SDR problem per codeword instead of solving multiple SDR problems 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 in the sense that it is applicable to any list-based iterative receivers.