In order to overcome the overhigh complexity of MAP- based soft demodulation strategy for Turbo- MIMO system,this paper introduces the concepts of quasi- maximum- likelihood phase- shift- keying (QML- PSK) detection and bit- level multi- stream coded layered space- time (LST) transmitter,and proposes a low- complexity soft demo-dulation algorithm and the corresponding receiver,which are suitable for all kinds of quadrature amplitude modula-tion (QAM) constellations and can approach the MIMO channel capacity.In this algorithm,the MAP problem of solving the extrinsic information of bits is converted into maximum likelihood demodulation problems that are then efficiently solved by using the QML- PSK detector.Moreover,as the QML- PSK detector is suitable only for the soft demodulation of PSK signals,a QAM- PSK soft demodulation algorithm is further proposed,which introduces the bit- level multi- stream coded LST transmitter to convert the QAM signal into PSK signals.Theoretical analysis and simulation results show that the proposed QAM- PSK soft demodulation algorithm achieves almost the same BER per-formance with a complexity less than half of that of the existing optimal sphere decoding- based soft demodulation algorithms,and that the advantage of low complexity of the algorithm is more obvious in larger problem dimensions.