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An algorithm to detect and estimate a linear mixture of deterministic signals corrupted by white Gaussian noise is presented. The number of signals is assumed to be unknown, and the noise power can be either known or unknown. The algorithm is based on an information-theoretic criterion in which the probability of false alarm can be adjusted; typical information criteria, such as the Akaike (AIC) and the minimum description length (MDL) criteria, can be regarded as particular cases of it for given probabilities of false alarm. The proposed approach includes the use of the atomic decomposition and the expectation maximization (EM) algorithms to efficiently approximate the signal maximum likelihood estimate. For the first time, upper-bounds for the probabilities of underestimation and overestimation of the number of signals are obtained. In addition, the constant false-alarm rate (CFAR) characteristic is shown, and the statistical efficiency of the signal parameter estimation is discussed and illustrated by simulation. Numerical experiments show the suitability of the algorithm for signal interception by using synthetic and real-life radar signals.