Low-complexity coherent frequency-difference beamforming for broadband signals

To address the high background sidelobe level in the bearing spectrum of conventional frequency-difference beamforming for broadband signals, a coherent frequency-difference beamforming method and a phase-only coherent frequency-difference beamforming method are proposed by exploiting the phase information of the auto-product terms in the frequency-difference process. First, auto-products are constructed by conjugate multiplication of broadband signals at different frequencies, such that the resulting processing frequencies satisfy the spatial Nyquist sampling requirement of the array. Then, spatial filtering is applied to the auto-product terms to extract phase information, based on which different coherent corrections are performed on the auto-product components. Finally, coherent averaging is carried out in the frequency domain and the difference-frequency domain to obtain the broadband bearing estimation spectrum. Simulation results demonstrate that the proposed methods can effectively suppress the additional interference introduced by the frequency-difference process, improve weak target detection capability, and enhance target resolution in multi-target scenarios. Moreover, the proposed methods maintain relatively low computational complexity, making real-time implementation feasible in practical engineering applications. Experimental results using horizontal array data from sea trials further compare the bearing-time records obtained by conventional methods and the proposed coherent approaches, verifying the superior performance of the proposed coherent processing methods.