In the field of radar remote sensing of the Earth, the problem of detecting and / or identifying spatially distributed targets against the background of a homogeneous surface is becoming increasingly important, for example, the tasks of the coast guard, monitoring of unauthorized forest logging, assessing the consequences of natural disasters, and others. This study is devoted to solving the problem of developing the optimal algorithm for making a decision on the class of a spatially distributed target based on data from side-scan radar systems with a synthetic aperture. A detailed description of the signal formation process in the fixed range channel is given, taking into account possible interference factors. Based on the statistical criterion by the method of maximum likelihood, the recognition algorithm is proposed, expressions for the formation of a feature vector are obtained, and the nonparametric decision rule is proposed. The algorithm has been tested on the example of recognizing three classes of spatially distributed targets that differ in size.