Doctor's Theses (authored and supervised):

W. Weichselberger:
"Spatial Structure of Multiple Antenna Radio Channels";
Supervisor, Reviewer: E. Bonek, A. Molisch; Institut für Nachrichtentechnik und Hochfrequenztechnik, 2003.

English abstract:
The employment of multiple antennas at one side of a communications radio link (multiple-input single-output=MISO) allows for the utilization of the spatial domain by means of signal processing. Beamforming focuses the antenna array pattern into a specific direction and thereby enhances the signal strength. Multiple spatial replicas of the radio signal give rise to spatial diversity, which increases the reliability of the fading radio link. By applying an additional antenna array at the other link end (multiple-input multiple-output=MIMO), the radio channel supports multiple parallel signal streams in the spatial domain, i.e. the spatial multiplexing of data.

The first part of this thesis deals with MISO channels, which show a fundamental trade-off between beamforming and diversity. To which extent spatial diversity or beamforming can and should be utilized depends on the spatial properties of the radio channel, the knowledge about the channel state, and the requirements of the communications system. On one hand, I discuss the notions of array gain and diversity gain for the case of (i) no channel knowledge, (ii) knowledge of second-order statistics only, and (iii) full channel knowledge. On the other hand, I focus on the case of an antenna array at the transmit side, where only the second-order statistics of the channel are known. By allocating different fractions of transmit power on the diversity branches, a smooth trade-off between diversity and beamforming can be established. I investigate the optimum power allocation scheme, for the case of Rayleigh fading, and derive an approximate solution in closed form.

In the second part of this work, I extend the concept of spatial eigenmodes, which has been well understood for MISO systems, to the MIMO case. Due to the inherent matrix nature of MIMO channels, the second-order statistics of MIMO channels emerge naturally as fourth-order tensors. In contrast to the MISO case, the MIMO correlation tensor offers three different possiblities of decomposition: The MIMO eigendecomposition makes use of the Hermitian symmetry of the correlation tensor and is analogous to the eigendecomposition of Hermitian matrices. It yields matrix-valued eigenmodes which have the same physical interpretation as a MIMO channel matrix. The Kronecker mode decomposition decomposes the correlation tensor into separate receive and transmit components. It corresponds to the singular value decomposition of asymmetric matrices. The Kronecker modes are also matrix-valued but can be interpreted as spatial correlation matrices of the receive or transmit side, respectively. The vector mode decomposition is based on the tensor-valued nature of the second-order statistics of MIMO channels, and has no equivalent in matrix notation. It generalizes the concept of eigendecompositions and singular value decompositions to tensors, and decomposes the correlation tensor in vector-valued components. These components can be interpreted as link-end related excitation vectors of the MIMO channel.

After establishing the MIMO eigenstructure, I apply the corresponding mathematical tools to the spatial modeling of MIMO channels. I develop a nested hierarchy of channel models that are solely based on the eigenstructure of MIMO channels. Starting from an exact description of the MIMO correlation tensor, I gradually decrease the model complexity which, in turn, also decreases its accuracy. Furthermore, I present similar nested hierarchies for models based on steering vectors or random vectors. By combining the presented model hierarches and additional modeling approaches from literature, I establish a general framework for analytical MIMO channel models. The benefit of this framework is two-fold. On one hand it facilitates the understanding and classification of existing models. On the other hand, it allows for choosing the right model for a specific application by identifying the appropriate trade-off between accuracy and simplicity. The MIMO part of the thesis is wrapped up by comparing the performance of various analytical channel models. The ability of the models to reproduce the spatial power distribution and the mutual information of measured MIMO channels is evaluated and discussed.

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