Abstract The response of an antenna with specified bandwidth characteristics to a complex, partially polarized, random process of arbitrary bandwidth is treated from the combined viewpoint of the theory of statistical communications, antenna theory, and the theory of optics. A stochastic spectral representation that accounts for the spatial variations of a random wave process is developed and used to determine the open circuit voltage excited in an antenna via the interaction of the incident process with the frequency varying far field pattern of the antenna. A general formula is derived for the autocorrelation function at the terminals of a receiving antenna in terms of the coherency matrix of the incident process and the antenna height function. This formulation applies for incoherent stochastic processes. The available power at the terminals of the antenna is related to this autocorrelation function.