Fixed Beamforming
Jacob Benesty, Israel Cohen, Jingdong Chen · 2017
This chapter details a large class of fixed beamformers in tandem with uniform linear arrays (ULAs), where the sensors are located along a line with uniform spacing. It aims to design beamformers, independent of the statistics of the signals, which are able to form a main beam in the direction of the desired signal, θ d, in order to extract it undistorted while attenuating signals coming from other directions. Usually, the array processing or beamforming is performed by applying a temporal filter to each sensor signal and summing the filtered signals. The chapter discusses the spatial aliasing problem encountered in array processing; it is similar to the temporal aliasing that occurs when a continuous-time signal is sampled at a rate lower than twice its highest frequency. Several useful fixed beamformers are derived from the white noise gain (WNG) and the directivity factor (DF), which can be viewed as meaningful criteria as the MSE criterion.