A method and apparatus for calibrating a phased antenna array. The antennas are excited using several excitation patterns, each changing the state of the antennas by a specific amplitude and phase. The phases correspond to phase values of a basis function of a two-dimensional discrete Fourier transform, and each excitation pattern corresponds to a different basis function. Using a calibration antenna, e.g. at a fixed point inside the system, the phase and amplitude of the radiated field due to each excitation patterns is measured sequentially. From this data, the phase and amplitude of the radiated field for each element at the location of the calibration antenna is obtained and used to adjust the phase shifters and amplifiers. For calibrated systems, the spectral domain representation of radiated fields can be sparse. Taking advantage of this property and a spectrally compressed sensing technique, recalibration can involve fewer measurements to mitigate service interruptions.