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This paper presents a novel turbo-detected multidimensional sphere packing (SP) modulation scheme using four transmit antennas combined with differentially encoded space-time spreading (DSTS). The DSTS scheme can be readily combined with PSK, QAM as well as SP modulation schemes. The SP-aided DSTS system advocated has low-complexity encoding and decoding algorithms that require no channel knowledge and it is capable of outperforming the DSTS system dispensing with sphere packing. Further system performance improvements can be attained by serially concatenated convolutional encoding combined with a unity-rate code (URC) referred to as a precoder. Then, at the receiver side, iterative decoding is invoked by exchanging extrinsic information between the precoder's decoder as well as the outer recursive systematic convolutional (RSC) code's decoder. Moreover, the convergence behaviour of the proposed system is evaluated with the aid of extrinsic information transfer (EXIT) charts. Explicitly, the turbo-detected precoded DSTS-SP system performs within 1.6 dB of the achievable multiple-input multiple output (MIMO) capacity. Finally, in contrast to an equivalent 0.5 bit/symbol throughput turbo- detected DSTS-SP scheme using no preceding, the turbo-detected precoded DSTS-SP scheme exhibits no error floor.