The fundamental input/output structure of a linear, time-varying array receiver

A single-output array receiver based on static antenna elements of arbitrary geometry that drive linear, time-invariant signal processing is well known to be fully characterized by a frequency response dependent on direction-of-arrival (DOA). This paper develops the generalized characterization that results when the time-invariance requirement is removed. The special case based on periodically varying signal processing is further derived and shows such a system to be fundamentally, structurally incapable of realizing a long-sought goal in navigation engineering: a frequency shift smoothly dependent on DOA. Self-contained developments of time-varying continuous-time linear systems and of a 4D Fourier-transform view of propagating electromagnetic waves are given in the appendices.