We propose a method for direct diagnostics of a stochastic ionospheric radio channel. This method can recalculate probe signal characteristics into transmitted signal characteristics. We derive analytical equations of second-order statistical moments for trajectory characteristics of the main and probe signals propagating in a three-dimensional randomly inhomogeneous ionosphere. We take into account boundary conditions at signal transmission and reception points. As a model of random irregularities of permittivity of the ionosphere, we utilize the concept of a changing space-time correlation ellipsoid, which is self-consistent with spatial changes in the average ionosphere. Time fluctuations of random irregularities are taken into account by the hypothesis of frozen transfer. We use analytical relationships to calculate the expected statistical characteristics of decameter signals along oblique probing paths of the ionosphere. An operational numerical algorithmization of the formulas derived is proposed. We report results of numerical experiments to determine the expected phase variances, group delay, and Doppler frequency shift of the main signal on a given single-hop path, based on measurements of these characteristics of a probe signal on a secondary path. We demonstrate the efficiency of the proposed method for diagnosing statistical trajectory characteristics of a decameter signal along single-hop paths under conditions when ground points of transmission and reception of the main and probe signals are outside the vicinity of focusing points of the wave field.