This thesis focuses on the concept of uniquely factorable constellations (UFCs) in the design of space-time block codes (STBCs) for wireless communication systems using three different approaches. Based on intelligent constellation collaboration, UFCs can provide the systematic design of a full diversity code with improved coding gain. Firstly, motivated by the energy-efficient hexagonal lattice carved from the Eisenstein integer domain, hexagonal UFCs and hexagonal uniquely factorable constellation pairs (UFCPs), of various sizes, are constructed for a noncoherent single-input multiple-output (SIMO) system. It is proved that these designs assure the blind unique identification of channel coefficients and transmitted signals in a noise-free case and full diversity for the noncoherent maximum likelihood (ML) receiver in a noisy case. In addition, an optimal energy scale is found to maximize the coding gain. Secondly, using a matrix similar to the Alamouti matrix and the UFCP concept based on the quadrature amplitude modulation (QAM) constellation, a novel energy-efficient unitary STBC is designed for a noncoherent multiple-input single-output (MISO) system with two transmitter antennas and one receiver antenna by using the QR decomposition. It is shown that the proposed UFCP-STBC design also allows for the blind unique identification of both the transmitted signals and channel coefficients as well as full diversity. In addition, an optimal unitary UFCP-STBC is devised to maximize the coding gain subject to a transmission bit rate constraint. The last approach is to demonstrate how the UFCP concept is applied to the systematic design of a coherent relay network coding system. A class of uniquely factorable Alamouti matrix pairs is proposed for the design of a novel amplify-forward relay network coding scheme, which allows the relay node to transmit its own information. By carefully making use of the Alamouti coding structure and strategically encoding the signals from the two antennas at the relay node, the resulting coding scheme enables the optimal full diversity gain and better coding gain for the ML detector. Comprehensive computer simulations show that the three uniquely factorable designs presented in this thesis have the best error performance compared to the current designs in literature. / Thesis / Candidate in Philosophy

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