The existing research on frequency diverse arrays (FDAs) predominantly concentrates on narrowband uniform linear frequency diverse arrays (ULFDAs). The uniform circular array presents advantages, such as a small aperture and omnidirectional scanning. In practical underwater acoustic environments, multi-carrier narrowband signals are commonly utilized. Nevertheless, current studies lack theoretical analysis and exploration of the performance of narrowband uniform circular frequency diverse arrays (UCFDAs). This paper, utilizing a UCFDA sonar transmit and single-element receive model, introduces narrowband signals employing a multi-carrier design. Through the time-domain convolution of signals output from matched filters, we deduce the general expression of the ambiguity function and its properties for UCFDA sonar within the narrowband framework. Simulations employing rectangular pulses are executed to validate the accuracy of the derived analytical expression of the ambiguity function. Moreover, we conduct a comparative analysis of the ambiguity function shapes for UCFDA sonar with linear frequency offset models, natural logarithmic frequency offset models, and multi-carrier UCFDA sonar. This analysis reveals that the nonlinear characteristics of the natural logarithmic frequency offset model effectively eliminate the periodically appearing ambiguity peaks in the ambiguity function of traditional linear frequency offset UCFDA sonar. Furthermore, the multi-carrier design significantly diminishes the sidelobe level in the zero-Doppler cut and has higher robustness under noise conditions.
Liu et al. (2026) studied this question.