On time-invariant FDA beam-pattern design based on time-dependent frequency offsets

In the existing works on FDA beam-patterns produced by the traditional FDA are time variant, and this causes difficulties in target detecting and beam-pattern steering. For solving the problem, several time-dependent frequency offsets based time-invariant FDA beam-pattern design methods have been proposed, which, however, neglected the time-range relationship and led to erroneous conclusions. In this note, considering the practical constraint and the relationship between time and range, it is concluded that FDA beam-patterns are always time-variant and it is unable to form time-invariant beam-patterns.