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The statistics of the matched filter output are examined for the case of a nonfluctuating target in K-type clutter. The resulting "homodyned-K" backscatter model is a generalization of the classic Rayleigh-Rice model and has applications in radar, sonar, optics, and ultrasonic medical imaging. This paper presents exact and asymptotic equations for the probability density function, survival function, moments, and parameter estimation. The exact equations are expressed as infinite series. Also provided are proof of the series' convergence and guidance for their numerical computation. Examples illustrating the model's application to radar and sonar are presented using electromagnetic and acoustic backscatter data.