On Reduced Complexity Soft-Output MIMO ML detection
  In multiple-input multiple-output (MIMO) fading channels maximum likelihood (ML) detection is desirable to achieve high performance, but its complexity grows exponentially with the spectral efficiency. The current state of the art in MIMO detection is list decoding and lattice decoding. This paper proposes a new class of lattice detectors that combines some of the principles of both list and lattice decoding, thus resulting in an efficient parallelizable implementation and near optimal soft-ouput ML performance. The novel detector is called layered orthogonal lattice detector (LORD), because it adopts a new lattice formulation and relies on a channel orthogonalization process. It should be noted that the algorithm achieves optimal hard-output ML performance in case of two transmit antennas. For two transmit antennas max-log bit soft-output information can be generated and for greater than two antennas approximate max-log detection is achieved. Simulation results show that LORD, in MIMO system employing orthogonal frequency division multiplexing (OFDM) and bit interleaved coded modulation (BICM) is able to achieve very high signal-to-noise ratio (SNR) gains compared to practical soft-output detectors such as minimum-mean square error (MMSE), in either linear or nonlinear iterative scheme. Besides, the performance comparison with hard-output decoded algebraic space time codes shows the fundamental importance of soft-output generation capability for practical wireless applications. 
Massimiliano Siti, Michael P. Fitz