A new generic maximum-likelihood metric expression for space-time block codes with applications to decoding
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Space-time block coding is a technique used to exploit diversity in a multiple-input multiple-output (MIMO) environment. Orthogonal space-time block codes (OSTBCs) are desirable because they can achieve full transmit diversity while maintaining a simple low-complexity maximum-likelihood (ML) decoding algorithm. However, OSTBCs are limited in their error performance. This has led to the development of more general linear space-time block codes, such as quasi-orthogonal space-time block codes (QOSTBCs). QOSTBCs offer better error performance, but their decoding complexity is a concern since it is no longer a linear function of the number of transmitted symbols. In this thesis, a new vectorization for linear STBCs is proposed that explicitly maintains the redundancy in the STBC transmission matrix. By expressing the ML metric using the new vectorization, a new generic representation of the ML metric expression for a linear STBC is derived. One immediate application of this new metric expression is the convenient partial decoupling and simplification of the detection metric for linear STBCs. The new metric expression can also be used as a design tool to help in the construction of new STBCs with low decoding complexity. As an example, a new QOSTBC is constructed that has lower decoding complexity than one previously proposed in the literature of equal rate and diversity. A comparison is conducted to answer the following question: for the family of QOSTBCs, when is it best to perform an exhaustive search using a metric expression that is simplified and decoupled as much as possible, and when should an efficient implementation of the sphere decoding algorithm be applied? Determining this boundary is an important and practical issue not yet directly addressed in the literature. The new metric expression can also be used as the framework for a new family of sub-optimal decoding algorithms for STBCs that trade-off error performance for a reduction in decoding complexity. A practical example of such an algorithm is given as an example.