Space-Time-Block-Codes (STBC) allow for an improved communication if multiple transmit- and receive antennas are available. In most practical applications certain properties of the communications channel can be assumed to be known at the receiver in order to simplify decoding. However, if one of the communication partners is moving at a high speed or if very many antennas are employed, that is not possible. This case is referred to as the noncoherent case and it is the main focus of this work. The best known codes for this situation are unitary code. Using these strongly restricts the amount of transmit antennas which can be used to enhance the communication. We investigate the general noncoherent case and develop a theoretical framework as well as criteria to construct and to decode noncoherent STBC. Notions of reduced and equivalent codebooks are introduced and used to conclude that it suffices to study codebooks built from positive semidefinite Hermitian matrices. Furthermore a suitable notion of a distance function between codebooks is introduced and studied. Building on the developed theory, specific constructions of codebooks are discussed. Particular one class of codebooks which can be decoded by means of the GLRT decoder is considered.A construction of codebooks within this class based on the matrix exponential map is presented and by its means optimal codebooks in the considered class are characterized. These optimal codes are shown to yield the same probability of error as optimal unitary codes.
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