Beam-Steering in Switched 4D Arrays Based on the Discrete Walsh Transform

4D arrays provide cost-effective beam steering capabilities considering radio-frequency switches (controlled by periodic sequences) instead of variable phase shifters. Their synthesis is based on the Fourier coefficients (which depend on configurable time parameters) of the corresponding periodic modulating sequences. Whereas Fourier series use trigonometric functions to synthesize any periodic continuous waveform, Walsh series relies on bipolar orthogonal sequences and, if such a series is truncated, the expanded function is approximated by a stairstep signal. In this paper we present a novel method to synthesize 4D arrays by means of a finite set of Walsh functions. The technique allows for implementing the analog time-modulated feeding network of an array employing single-pole double-throw switches and achieves excellent rejection levels of the undesired harmonics.