Analysis of range-angle coupled beamforming with frequency-diverse chirps

Recently range-dependent (or time-varying) beamforming has been presented as a method to spread transmit energy over a desired spatial extent via a linear frequency shift across the waveforms transmitted at each element of an array. This element-level waveform diversity yields additional degrees of freedom relative to traditional beamforming techniques for which some sensing benefits have been suggested. In this paper, chirp waveforms with slightly different starting frequencies are analyzed to characterize the associated range-dependent beampattern. Specifically, it is determined that by utilizing this particular waveform structure, the energy transmitted over a pulse duration can be spread in a practically linear manner within the spatial extent specified by two angles despite the nonlinear relationship between spatial and electrical angles if the set of frequency-diverse chirps are appropriately parameterized. Additionally, a space-range ambiguity diagram is formulated. The ambiguity is discussed for the traditional and frequency-diverse array scenarios.