# Constant-Beamwidth LCMV Beamformer with Rectangular Arrays
###### Abstract  
This paper presents a novel approach utilizing uniform rectangular arrays to design a constant-beamwidth (CB) linearly constrained minimum variance (LCMV) beamformer, which also improves white noise gain and directivity. By employing a generalization of the convolutional Kronecker product beamforming technique, we decompose a physical array into virtual subarrays, each tailored to achieve a specific desired feature, and we subsequently synthesize the original array's beamformer. Through simulations, we demonstrate that the proposed approach successfully achieves the desired beamforming characteristics while maintaining favorable levels of white noise gain and directivity. A comparative analysis against existing methods from the literature reveals that the proposed method performs better than the existing methods.  
LCMV beamformer; constant-beamwidth beamforming; Kronecker product beamformer; array signal processing; rectangular sensor arrays +
Footnote †: journal: _arxiv  
0000-000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-0000-00000-00000-00000-0000  
linear convolutional Kronecker product (LCKP) method [23]. The LCKP method is valid only for linear arrays, however it allows for the virtual utilization of more sensors than are physically available [23]. Meanwhile, the KP method can be used in linear or rectangular arrays, but it does not increase the number of sensors available for beamforming. For both combination methods (the KP and LCKP), beampattern features and distortionless constraints are preserved in the combined beamformers. Therefore, by using beamformers with desired beampattern characteristics that respect the distortionless constraint, these are maintained in the end result.  
In this paper, we propose a novel approach to constructing a CB-LCMV beamformer for rectangular arrays. To this end, we generalize the LCKP beamforming technique to the case of rectangular arrays. We synthesize beamformers for virtual subarrays and, with our proposed generalized technique, apply them to a full array to achieve the desired beamwidth and null placement. This is achieved without sacrificing white noise gain or the directivity factor. The performance of the proposed method is compared against that of beamformers obtained through the KP and LCKP methods. Our results demonstrate superior performance in terms of the beamwidth, white noise gain, and directivity of the beamformers obtained using the proposed method when compared to the performance of the beamformers obtained using the methods in the literature.  
This paper is organized as follows: Section 2 presents the array and signal model considered for the problem; Section 3 shows the traditional beamforming techniques and methods that are used further. In Section 4, the newly proposed method for an array analysis for rectangular arrays is introduced and detailed, as well as its proposed usage for solving the problem at hand. In Section 5, we present the conducted simulations and discuss the results, comparing them to those in the literature. Finally, Section 6 concludes this paper, presenting an overview of the main contributions.