Dr.-Ing. Christian Pietsch

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PhD Thesis


Coherent Space Time Block Codes




Multiple input multiple output (MIMO) systems are an attractive option for wireless communications due to their capability of providing extra capacity and/or diversity in comparison with single antenna schemes. This book contributes to the analysis and the construction of space time constellations that allow for a reliable transmission in fading environments where the transmitter does not have any knowledge about the channel state information. Initiated by new findings on the structure of orthogonal space time block codes (OSTBCs), we establish two mappings that link these constellations to unique sets of subspaces, which are termed Grassmannian packings in the mathematical literature. We derive the packing properties that result from OSTBCs. In the first place, this gives us new insight into the structure of OSTBCs. Moreover, since Grassmannian packings have been previously applied for the construction of non-coherent constellations, we identify similarities and differences between a variety of coherent and non-coherent constellations. The packings that are related to OSTBCs are severely constrained. Allowing for more general packings, this lets us construct space time constellations that support higher data rates. It provides a new powerful framework that links the design of general coherent space time constellations with the search for good Grassmannian packings. We derive packing properties that yield space time constellations with excellent performance in terms of mutual information and diversity. We propose two methods that enable the design of these packings. Constructing space time constellations from the resulting packings, we obtain full rate coherent space time block codes (STBCs) that turn out to be superior to the best known coherent STBCs that we are aware of. While the emphasis of this work is on the analysis and the construction of space time constellations, a well defined transmission model eases many derivations. In particular, the relationship between models that include spreading matrices, dispersion matrices, real-valued and complex-valued notation turns out to be important.

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Research Interests

Many aspects of multiple-input multiple-output (MIMO) systems like:

  • Space-time signal processing
  • Space-time coding
  • Information theoretic aspect
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Dr.-Ing. Christian Pietsch

Christian Pietsch
Dr.-Ing. Christian Pietsch