In this thesis, we first study the complex version of Amicable Orthogonal Design (AOD) called Amicable Complex Orthogonal Design (ACOD), and use it to construct O-STBCs with practical implementation advantages, such as balanced power distribution properties and rational-number code coefficients. Next, we study the decoding of QO-STBC with noise-whitening pre-filter and propose Group-Constrained Linear Transformation (GCLT) as an alternative means to optimse the QO-STBC performance without increasing its decoding complexity. We also propose a new class of QO-STBC called QO-STBC with Minimum Decoding Complexity (MDC-QOSTBC). The decoding complexity of MDC-QOSTBC is only next to O-STBC, as MDC-QOSTBC requires a joint detection of only two real symbols. In the thesis, we examine the relationship between the mathematical structures of MDC-QOSTBC and AOD, and found out that MDC-QOSTBC can be constructed from two AODs that form a Preferred AOD Pair, which is a new concept introduced in this thesis. We derive the theoretical maximum achievable code rate of MDC-QOSTBC. Finally, we also propose for the first time differential space-time modulation (DSTM) schemes based on QO-STBC and MDC-QOSTBC to provide blind transmit diversity. The DSTM scheme based on QO-STBC is double-symbol decodable, while the DSTM scheme based on MDC-QOSTBC is single-symbol decodable, hence both have very low decoding complexity.