The thinned and sparse beamforming for semicircular FDAs were investigated, where the excitation amplitudes were also considered in thinned semicircular FDAs, and only the elements’ positions were incorporated into the sparse semicircular FDA. Firstly, the transmit–receive model was introduced to handle the inherent time-varying issue of FDA, followed by the thinned and sparse implementations successively. Note that three types of non-linearly varying frequency offsets (FO), i.e., log-FO, sin-FO, and tanh-FO, were adopted during the investigations. Under the same assumption that 50% of the elements should be saved, the sidelobe levels (SLLs) of the thinned semicircular -FDAs were reduced by 5.8 dB, 4.4 dB, and 4.4 dB, and the widths of the mainlobes were all widened by 3° in their angle dimension. Compared with the thinned semicircular FDAs, the phenomenon of mainlobe widening was alleviated in the sparse semicircular FDAs where the SLLs were reduced by 2.2 dB, 3.7 dB and 3.5 dB, and the mainlobes’ widths in the angle dimension were widened by 1°, 0° and 1°, respectively. It should be highlighted that the sparse semicircular FDA with sin-FO did not broaden the mainlobe in the angle dimension. Therefore, it can be concluded that a sparse semicircular FDA is superior over a thinned semicircular FDA, since it can reduce the same cost with a higher array resolution.

To address the range-angle coupling issue of frequency diverse array (FDA), a beamforming method based on subarray partitioning is proposed, with a focus on analyzing uniform continuous and nonuniform discontinuous subarray structures. Based on the transmit–receive signal model established to solve the time-varying issue of FDA, two subarray partitioning methods under the same array aperture are investigated. In the case of uniform continuous subarray structure, when different linear frequency offsets (FOs) are applied to each subarray, the mainlobe width in range dimension is 4.35 km, and the peak sidelobe level (PSLL) is −7.25 dB. When nonlinear FOs are applied, the mainlobe width is reduced to 2.76 km, and the PSLL is decreased to −9.64 dB. Furthermore, by adopting a nonuniform discontinuous subarray structure combined with nonlinear FOs, the mainlobe width is further narrowed to 1.29 km, and the PSLL is reduced to −11.75 dB. The simulation results demonstrate that under the same conditions, the nonuniform discontinuous subarray structure significantly improves range resolution and effectively suppresses sidelobe. Based on above results, a joint optimization combining the bat algorithm (BA) and K-means++ clustering algorithm is proposed to optimize the subarray structure and element amplitudes simultaneously. Finally, the mainlobe width of the optimized FDA is 1.18 km and the PSLL is −12.32 dB. Simulation results confirm the effectiveness and potential of the proposed method in enhancing range resolution and achieving a focused beampattern.