An extended correlation function of two random variables applied to mobile radio transmission

The definition, properties, and application of an extended correlation function of two random variables involving two common parameters are described and applied to mobile radio systems. The correlation functions of a predetection diversity combined signal (using a scheme of phase equalizing by multiple heterodyning) and of a directional antenna array signal are derived with the help of the extended correlation function. These correlation functions can be used to determine parameter values giving minimum correlation between two signals desirable for diversity systems. One can also obtain the power spectra by taking the Fourier transform of these correlation functions. Thus extended correlation functions promise to be useful.