  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.
