Constant-Beamwidth Kronecker Product Beamforming With Nonuniform Planar Arrays

In this paper, we address the problem of constant-beamwidth beamforming using nonuniform planar arrays. We propose two techniques for designing planar beamformers that can maintain different beamwidths in the XZ and YZ planes based on constant-beamwidth linear arrays. In the first technique, we utilize Kronecker product beamforming to find the weights, thus eliminating matrix inversion. The second technique provides a closed-form solution that allows for a tradeoff between white noise gain and directivity factor. The second technique is applicable even when only a subset of the sensors is used. Since our techniques are based on linear arrays, we also consider symmetric linear arrays. We present a method that determines where sensors should be placed to maximize the directivity and increase the frequency range over which the beamwidth remains constant, with a minimal number of sensors. Simulations demonstrate the advantages of the proposed design methods compared to the state-of-the-art. Specifically, our method yields a 1000-fold faster runtime than the competing method, while improving the wideband directivity factor by over 8 dB without compromising the wideband white noise gain in the simulated scenario.