Research on Dynamic Beamforming Methods for Uniform Circular Frequency Diverse Array Sonar

Frequency diverse array (FDA) sonar achieves a range- and azimuth-dependent transmit beam by applying a small frequency increment to each transmitting element. However, beam position is difficult to control due to range–azimuth coupling and time-varying characteristics. While existing FDA research has primarily focused on uniform linear arrays, there remains a lack of analysis on the Uniform Circular Frequency Diverse Array (UCFDA). Moreover, studies on transmit beampatterns have largely concentrated on continuous waveforms, resulting in time-varying beam characteristics. In the field of sonar, however, pulse signals are commonly employed for target detection. Therefore, to more accurately characterize the behavior of the beampattern under such conditions, further investigation is warranted. This paper focuses on the UCFDA sonar, specifically studying the time-varying characteristics and “dot”-shaped beam synthesis under pulsed operation. First, the time-varying and spatial scanning characteristics of the UCFDA transmit beam under linear frequency offset are analyzed. Second, a nonlinear frequency offset model is constructed, and its characteristics of high range sidelobes and significant trailing are analyzed. Then, a time-modulated nonlinear frequency offset model is built, and the relationship between the time variable in the frequency offset term and the time variable in the signal propagation term is studied in detail. When the two are identical, cancellation can theoretically eliminate the beam’s time variance. However, their physical meanings differ: the time variable in the frequency offset term reflects the signal generation moment, while the signal propagation time variable reflects the propagation law of the signal in space; they cannot cancel each other out. Finally, a nonlinear multi-carrier frequency offset model is constructed. Simulation experiments on the transmit beams under these three models are conducted to synthesize dynamically propagating “dot”-shaped transmit beams. Comparative results verify that the multi-carrier frequency offset model yields the lowest range sidelobes.