One of the uses of sensor arrays is for spatial filtering or beamforming. Current digital signal processing methods facilitate complex-weighted beamforming, providing flexibility in array design. Previous studies proposed the use of real-valued beamforming weights, which although reduce flexibility in design, may provide a range of benefits, e.g., simplified beamformer implementation or efficient beamforming algorithms. This paper presents a new method for the design of arrays with real-valued weights, that achieve maximum directivity, providing closed-form solution to array weights. The method is studied for linear and spherical arrays, where it is shown that rigid spherical arrays are particularly suitable for real-weight designs as they do not suffer from grating lobes, a dominant feature in linear arrays with real weights. A simulation study is presented for linear and spherical arrays, along with an experimental investigation, validating the theoretical developments.

翻译：传感器阵列的用途之一是实现空间滤波或波束形成。当前的数字信号处理方法支持复值加权波束形成，为阵列设计提供了灵活性。以往研究提出了实值波束形成权重的使用，尽管这降低了设计灵活性，但可能带来一系列优势，例如简化的波束形成器实现或高效的波束形成算法。本文提出了一种新的阵列设计方法，采用实值权重以实现最大指向性，并给出了阵列权重的闭式解。该方法针对线阵和球阵进行了研究，结果表明刚性球阵特别适合实值权重设计，因为它们不会产生栅瓣——这一现象在实值权重的线阵中尤为突出。本文通过线阵和球阵的仿真研究以及实验验证，证实了理论推导的正确性。