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Two efficient list-based “soft”-output demodulators are developed for iterative receivers in multiple-input multiple-output (MIMO) communication systems with QPSK signaling. The proposed demodulators are based on the semidefinite relaxation (SDR) technique, and hence their computational costs are bounded by a low-order polynomial of the number of bits transmitted per channel use. The first demodulator applies the SDR technique once per demodulation-decoding iteration, and generates list members via the randomization procedure that is inherent in the SDR technique. The second demodulator is based on an approximation of that randomization procedure by a set of independent Bernoulli trials, and this approximation reduces the number of semidefinite programs that need to be solved to just one per channel use. List-free implementations that reduce the memory requirements of list demodulators with moderate to long lists are also developed. Analysis suggests that the proposed “Single-SDR” demodulator should offer good performance at moderate computational cost, especially for larger systems. This is quantified using simulations of a richly scattered environment, in which the performance of the Single-SDR demodulator is similar to that of the list sphere decoder with moderate sized lists and better than that of the minimum mean square error soft interference canceler. The average computational cost of a straightforward implementation of the Single-SDR demodulator is competitive with that of the list sphere decoder with moderate sized lists, and the distribution of its computational cost is quite concentrated around the average.