空间宽带天线阵列因子的分析与近似
Analysis and Approximation of a Spatially Wideband Antenna Array Factor
AI总结：
该研究针对均匀线阵的空间宽带天线阵列因子，推导了窄带、宽带信号及通用的近似式，可抑制旁瓣与稀疏阵列栅瓣，适用于宽范围带宽和单元间距。
AI中文摘要：
本研究探讨均匀线阵的空间宽带（SWB）天线阵列因子（AF）。首先，针对窄带（NB）信号及满足奈奎斯特准则的大孔径、单元间距，推导SWB AF近似式，推导过程考虑不同的空间窗与频谱窗。接着，在均匀空间加权和频谱加权条件下，推导宽带（WB）信号的SWB AF近似式，分析表明对于全填充阵列，增大带宽可有效抑制AF的旁瓣。最后，提出一种通用SWB AF近似式，其核心是将SWB AF视为空间变卷积，将其表示为空间窄带（SNB）AF与SWB核的卷积，借此可理解带宽和频谱加权对SWB AF的影响。该近似式在宽范围带宽和单元间距（包括稀疏阵列）下均表现出良好精度；对于稀疏阵列，带宽可将栅瓣能量分散到更宽角域，从而抑制栅瓣幅度，同时给出了栅瓣包络关于带宽-孔径乘积的近似式。
英文摘要：
This work investigates the spatially wideband (SWB) antenna array factor (AF) of uniform linear arrays. First, the SWB AF approximation is derived for narrowband (NB) signals and a large aperture with element spacing satisfying the Nyquist criterion. The derivation accounts for different spatial and spectral windows. Next, an approximation of the SWB AF for a wideband (WB) signal is developed under uniform spatial and spectral weighting. The analysis shows that for fully populated arrays, increasing the bandwidth effectively suppresses the AF sidelobes. Finally, a universal SWB AF approximation is introduced, which is based on recognizing the SWB AF as a spatially variant convolution. In this formulation, the SWB AF is expressed as a convolution of the spatially narrowband (SNB) AF and the SWB kernel, providing insight into how the bandwidth and the spectral weighting affect the resulting SWB AF. The proposed approximation is shown to be accurate for a wide range of bandwidths and element spacings, including sparse arrays. In particular, for sparse arrays, the bandwidth enables suppression of grating-lobe amplitudes by spreading their energy over a wider angular range. An approximation of the grating lobe envelope as a function of the bandwidth-aperture product is provided.
