Time-Variance Analysis for Frequency-Diverse Array Beampatterns

Frequency-diverse arrays (FDAs) have attracted great attention since being proposed due to their inherent range-angle-dependent characteristics. A variety of FDA schemes are proposed to focus the beam energy on the interested spot with a fixed range and angle, namely, the dot-shaped beampattern. However, the time-variance of the FDA beampattern makes it unavailable for practical engineering applications. Thus, some time-invariant techniques have then been analyzed and designed. Although the state-of-the-art publications have pointed out that the time-invariant FDA transmit beampattern is incorrect based on the range–time–frequency relationship, the newly designed joint transmit–receive FDA beampattern cannot be explained by the current theories. In this article, the time–range relationship is reviewed, and the traditional FDA, the time-modulated weighted FDA (TMW-FDA), and the transmit–receive FDA schemes are deeply analyzed. By properly designing the receiver with a signal processing technique, the corresponding beam information can be collected, but the beam energy will eventually pass every range cell. Thus, it demonstrates that the time-invariant range-dependent FDA beampattern is unachievable, whether using a transmit scheme or a joint transmit–receive scheme. Numerical simulations validate the related analyses and conclusions.