This paper treats channel estimation and signal detection in Laplacian noise. The received signal is assumed to be a transmitted signal which has been corrupted by an unknown channel, modeled as a FIR filter, the output being further disturbed by additive independent Laplacian noise. The transmitted signal is assumed to depend on an unknown parameter belonging to a known finite set. The simultaneous maximum likelihood (ML) estimator of the unknown parameter, as well as of the FIR filter coefficients, is derived. The ML estimate of the channel can be obtained by using a linear programming approach and the decision about the parameter is based on the output from a set of generalized matched filters. Simulation results are included in order to illustrate the performance of the proposed receivers.

This paper discusses parameter estimation and detection in laplace distributed noise. The received signal is modeled as r($DOT@) $EQ As($DOT@,$theta@) $PLU n($DOT@), where A is an unknown amplitude, $theta is the parameter vector to be estimated and n($DOT@) is independent laplace distributed noise. The simultaneous maximum likelihood estimator of (A,$theta@) is derived. The derived estimator is based on a combination of a weighted median filter$LB@1$RB and a generalized form of the ordinary matched filter$LB@2$RB@. Examples of performance for four different detectors are given for a case of binary detection, when the amplitude A or the signal shape s($DOT@,$theta@) are varied. Simulations indicate that the performance of detectors based on the generalized matched filter is not particularly dependent on either the estimate of the amplitude A or the signal shape.