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G. Gritsch:
"Error Performance of Multiple Antenna Systems";
Supervisor, Reviewer: H. Weinrichter, E. Bonek; Institut für Nachrichtentechnik und Hochfrequenztechnik, 2004.

In this thesis the error performance of multiple antenna systems has been investigated. Our focus lies on the analytical calculation of performance measures. Unfortunately, due to the difficult framework and the rather unpredictable behavior of the signal distances in randomly varying channels a closed form solution of the exact error performance could not be derived. However, tight performance bounds have been found that can be used to get important performance parameters.

This thesis consists of two main parts concerning the uncoded and the space-time block coded data transmission over spatially correlated, frequency flat Multiple Input / Multiple Output (MIMO) channels using Maximum Likelihood receivers. The spatial correlation is modelled by the so-called W-model, where measured data are used to determine the model parameters.

Uncoded MIMO-systems: Even for uncoded systems, the only simple to calculate performance measure is a union bound, which is simply the sum over all pairwise error probabilities. In this thesis it is shown that the error performance can be described by a few so called Error Types (ETs). The results of the corresponding union bound are compared with simulation results for different system parameters, i.e., number of transmit antennas, number of receive antennas, modulation formats, and for spatially uncorrelated and correlated MIMO-channels. The derived union bound is tight for Bit Error Ratio (BER) values below 10-3 for all systems investigated.

By means of this bound a high Signal to Noise Ratio (SNR) approximation for the BER vs. SNR performance is calculated. With this approximation the diversity order of the system and a so-called performance loss due to fading correlation can be figured out. Especially, the loss due to spatial correlation can be quantified. Using two parameters, the slope and the horizontal position of the BER vs. SNR curves, the error performance can be fully described in the high SNR range.

An optimal precoder, which minimizes the correlation induced power loss, is presented. For the example discussed in this thesis the error performance applying the optimal precoder in correlated fading is even better than the performance of the standard system in the low SNR range in uncorrelated fading channels.

Space-time block coded MIMO-systems: The second main part of this thesis is devoted to the calculation of performance measures for space-time block coded data transmission. In principle, we follow the same analysis as for uncoded systems. First, it is shown that for some channel types multiple instead of single errors dominate the error performance in MIMO systems (MIMO paradoxon). In deriving the union bound the ET concept is applied also. The calculated union bounds are compared with simulation results for several codes and several channel correlation types. It turns out that the union bound is tight for BER values of 10-3 and below.

Once again, a high SNR approximation of the union bound is calculated, to determine the diversity order and the power loss in case of correlated channels.

An optimal precoder for correlated fading is derived. Simulation results show that the precoder effectively mitigates the loss induced by correlated fading.

In addition, an extraordinarily tight lower bound of the BER is derived that allows for a two-sided bounding of the BER vs. SNR performance from below and from above. Several code examples assess the tightness of the lower bound, where, for uncorrelated channels, an almost exact performance approximation is achieved.

http://publik.tuwien.ac.at/files/pub-et_8799.pdf