  Current literature show that frequency diverse arrays (FDAs) are able of
producing range-angle-dependent and time-variant transmit beampatterns, but the
resulting time and range dependencies and their characteristics are still not
well understood. This paper examines the FDA transmission model and the model
for the FDA array factor, considering their time-range relationship. We develop
two FDA transmit beampatterns, both yielding the auto-scanning capability of
the FDA transmit beams. The scan speed, scan volume, and initial mainlobe
direction of the beams are also analyzed. In addition, the equivalent
conditions for the FDA integral transmit beampattern and the multiple-input
multiple-output (MIMO) beampattern are investigated. Various numerical
simulations illustrate the auto-scanning property of the FDA beampattern and
the proposed equivalent relationship with the MIMO beampattern, providing the
basis for an improved understanding and design of the FDA transmit beampattern.
