A general expression for a radiation signal received by a wave-guide antenna from an arbitrary inhomogeneous medium with the spatial dispersion is obtained using the electrodynamics reciprocity theorem. The radiation may be either a spontaneous noise emission or it may result from the scattering of the incident wave off fluctuations. The signal calculation is reduced to finding the electromagnetic field radiated by the receiving antenna into a physically realizable substance whose wave properties differ, to some extent from these of the real medium. This problem is usually much simpler than direct signal calculation with the use of the Green function. The reciprocity approach is especially useful in the presence of cut-offs and resonances or/and when the radiation source is located in the antenna near-field zone.