Efficient and Accurate Frequency-Invariant Beam Pattern Synthesis Utilizing Iterative Spatiotemporal Fourier Transform

An iterative spatiotemporal Fourier transform (STFT) method is presented to efficiently design finite-impulse-response (FIR) filter coefficients for generating a desired frequency-invariant (FI) beam pattern of an antenna array. In this method, by introducing the concepts of normalized temporal angular frequency and spatial angular frequency, the broadband pattern is treated as a spatiotemporal spectral distribution. The relationship between the FIR coefficient distribution and the spatiotemporal spectral distribution can be built as an STFT, and consequently the 2-D fast Fourier transform (2D-FFT) and inverse 2D-FFT (2D-IFFT) can be utilized to efficiently accomplish the transformation between the FIR coefficient distribution and the spatiotemporal spectral distribution. Thus, the proposed synthesis method starts from an initial spatiotemporal spectral distribution and then adopt an iterative modification-and-transformation strategy to successively update the obtained spatiotemporal spectral distribution and the corresponding FIR coefficients. Two kinds of pattern modification techniques including the mainlobe FI modification and broadband sidelobe control are adopted in each iteration. Several examples for synthesizing different FI patterns are conducted. Synthesis results show that the proposed method can obtain much better FI pattern performance in terms of both mainlobe FI property and sidelobe control than the original FT method whilst costing less CPU time than the convex optimization method especially for the case of large FI arrays.