Investigation into the characteristics and behaviours of Laplace noise is of crucial importance for evaluating the performance of communication systems operating in impulsive noise, as well as for ultra-wideband wireless systems operating in the presence of multi-user interference. The bit error rate performances of a binary data communication system operating in the presence of additive bandlimited white Laplace noise is analyzed theoretically. A theoretical expression for the average bit error rate is derived using the Beaulieu series for the optimal soft-limiting detector and the matched-filter detector when arbitrary pulse shapes are used. The bit error rate performance of a reduced complexity version of the optimal detector, the hard-limiting detector, and a reduced complexity version of the matched-filter detector, the sum-of-samples detector, are also analyzed. The analytical expressions for the bit error rate are validated by numerical examples.

Estimation of the received signal amplitude is critical to the optimization of the performance of detectors for data communication systems operating in the presence of impulse-like interference. A binary data communication system in the presence of Laplace noise is considered. Maximum likelihood estimators are derived for both data-aided and non- data-aided cases. A ML-based non-data-aided absolute median estimator with simpler implementation is also proposed. The performances of the proposed estimators are examined and compared to the well-known mean estimator and absolute moment estimator in terms of their mean- squared errors. Numerical results quantify the superiority of the optimal ML estimators over the conventional estimators.

The estimation of signal amplitude for a binary data communication system in the presence of Laplace noise is considered. Maximum likelihood estimators are derived for both data-aided and non-data-aided cases. An absolute median estimator with a simple implementation is also proposed. The performances of the proposed estimators are examined and compared to well-known previous estimators in terms of mean-squared error. Numerical results quantify the superiority of the proposed estimators over the conventional estimators.