Arbitrary-Order Output Intercept Points of an Analog Receive Beamforming System

We derive a general expression for the mth-order intercept point (IPm) of an analog RF receive beamforming system comprising multiple inputs, an array of nonlinear elements, and a single output. Given parallel inputs, the general IPm expression includes the gain and nonlinearity of each element in the array as well as both intrinsic and extrinsic loss factors and phase shifts. We then impose constraints on the calculation of IPm by making certain assumptions about the statistical relationship between the phases of the distortion signals at the output to obtain the coherent and incoherent mth-order output intercept points (OIPm), which determine lower and upper bounds, respectively, on an actual measured output intercept point. Finally, we present the results of a series of experiments and show that the OIP2 and OIP3 obtained from 36 independent measurements all fall between the theoretical calculated bounds. These results will be of utility in the design, analysis, and testing of analog phased-arrays, multi-channel receivers, and receive-mode beamformers.