Detection of signals corrupted by non-gaussian disturbances
Abstract: The detection of signals in additive, non-Gaussian disturbances is the main theme of this thesis. The disturbances are modeled either by non-Gaussian noise or by Gaussian noise in combination with intersymbol or co-channel interference. The maximum likelihood (ML) approach is adopted in the design of receivers, which leads to a generalized form of the conventional matched filter. The most prominent feature of the resulting ML receivers is that the multipliers of the conventional matched filter are replaced by non-linearities. Receiver performance is found to be mainly governed by the characteristics of the non-linearities and the amount of impulsive noise in the observed signal. The performance is not very sensitive to mismatch in the receiver design parameters, although the choice of these parameter values becomes more critical as the noise becomes more impulsive. Furthermore, receiver performance appears to be strongly dependent on the signal shape, especially in impulsive noise. A simultaneous ML detector and channel estimator is derived for noise characterized by the Laplacian or the uniform distributions. For uniform noise it is found that the ML receiver is not unique due to the special character of this noise distribution. Therefore, the effect of different channel estimators and decision rules are studied and it is found that the performance is sensitive to how these are chosen. A novel ML receiver structure is presented for the case when the disturbance consists of Gaussian noise in combination with either co-channel interference (CCI) in multiuser systems or intersymbol interference (ISI) in time-dispersive communication systems. The relation of detection problems in CCI systems to detection problems in ISI systems is considered, as is the relation of their corresponding receivers. Moreover, this new receiver structure illustrates the relationship between the ML receiver and three other commonly recognized receivers. The final part ot the thesis deals with the problem of arrival time estimation of narrowband signals in Gaussian noise. The minimum-mean square eror (MMSE) estimator is investigated and its performance is compared to that of the maximum a posteriori (MAP) estimator. The performance of the estimators is demonstrated by some examples of three-dimensional ultrasonic imaging.
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