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.