Antenna complex radiation pattern

A basic question regarding the interpretation of measured antenna radiation pattern data.
Usually the measured antenna radiation pattern data includes the Phi , Theta angles and Ephi_amplitude, Etheta_amplitude and their corresponding phases for each Phi and Theta angles.

When refer to complex antenna pattern ( that we usually plot in 3D spherical coordinates) are we meaning the Etotal = Ephi(complex) + Etheta(complex), where Ephi(complex) = Ephi_amplitude*exp(j*Ephi_phase)? or something else?

I am planning to use the measured antenna pattern data in a channel emulator that try totake the effect of the antenna into account, so I want to use the given data regarding the pattern correctly.

Thank you for your guidance