Statistical Analysis for Time Modulation-Based Frequency Diverse Array Beampattern

Frequency diverse array (FDA) has received much attention due to its both range- and angle-dependent beampatterns. However, the range-angle coupling and time-variant beampattern in FDA may affect its applicability. In order to address the beampattern range-angle coupling problem and time variance, many existing algorithms, by using the time-modulated optimized frequency offset (TMOFO) scheme, are presented to obtain the spatial-focusing time-invariant transmit beampattern synthesis for the FDA. To discuss their irrationality, we first give a time-modulated optimized weight vector (TMOWV) scheme with frequency offset optimization, which is a more general time-modulated scheme for the FDA beampattern synthesis and more convenient for the statistical analysis of the designed FDA transmit beampattern characteristics. Then, the statistical analysis of the designed FDA transmit beampattern is investigated through both theoretical derivations and numerical examples. The extensive simulation results demonstrate that the time-modulated approach for the time-invariant FDA transmit beampattern is invalid.