Nonlinearities in digital manifold phased arrays

In digital beamforming (DBF), the phase shifter is functionally replaced with a receiver and digital phase rotation. A Taylor series expansion of mixer nonlinearities is used to generate receiver intermodulation spectrums respective of the element position and the iso-Doppler wavefront directions of signal arrival across the array. The dominant intermodulation distortion at each element experiences linear phase errors across the array proportional to the harmonic number and the desired steering direction phase gradient. The array distortion signals are reduced relative to the desired signal by the array factor sidelobe isolation when desired collimation directions exceed a few beamwidths of scan off the array normal vector. The result of the nonlinear down conversion analysis is extended to inphase and quadrature imbalances and batch manufacturing tolerances for element receivers.