Recently, Multiple Input and Multiple Output (MIMO) systems have shown a tremendous potential to increase the spectral efficiency and the reliability of wireless communication. These aspects are quantified in terms of the spatial multiplexing gain and the diversity gain respectively. It was shown that there is a trade-off between diversity and multiplexing gains. Bit Interleaved Coded Modulation with Iterative Decoding (BICM-ID) for Multiple Input and Multiple Output channels has recently been addressed as an effective mean to achieve high data rates while maintaining high diversity.  It has been shown that, when signal constellation, interleaver and error control code are fixed, signal mapping has a crucial influence on the error performance of a BICM-ID system. The role of signal mapping applies to the error performance of MIMO-BICM-ID system.  In this thesis, the design of constellation mapping for MIMO-BICM-ID system is studied. Based on minimizing pair-wise error probability, a design criterion is proposed to find the optimal constellation mapping for MIMO-BICM-ID. To reduce computational complexity of exhaustive search, Binary Switching Algorithm is improved to find the optimal solution. Using the design criterion and employing the Binary Switching Algorithm, some optimal constellation mappings are found for 2-dimensional and 3-dimensional cases.  A measurement based on mutual information is developed to evaluate the proposed constellation mappings. It is shown that proposed mappings sacrifice bit-wise mutual information without a priori information but improve significantly when perfect a priori knowledge is available. At the receiver, to avoid the computational complexity of the optimal Maximum-Likelihood (NIL) detector, List Sphere Decoder (LSD) is used as the inner detector.  Simulation results demonstrate that proposed schemes outperform conventional ones significantly at high signal to noise ratio (SNR) over fading channels. System simulations are carried out specifically for 2-dimensional QPSK, 2-dimensional 8QAM and 3-dimensional QPSK constellations/mappings. Results show an improvement of 1.3 dB, 1.6 dB and 1.8 dB compared to conventional constellation mappings over slow fading channels, respectively. This improvement increase to 3.5 dB, 2.7 dB and 2.4 dB for fast fading channels