The analogy between the Butler matrix and the neural-network direction-finding array

Enhancing Tumor Detection in IR-UWB Breast Cancer System

“…The antenna consists of the feeding line and the transition and the radiating structures. In general, the radiated structure is exponentially or elliptically tapered, which means that they are composed of two layers structure [10, 17]. …”

Analysis, synthesis, and diagnostics of antenna arrays through complex-valued neural networks

“…Nevertheless, CVANNs have some advantages with respect to conventional ANNs, as the number of layers needed in each case: in real valued ANNs (RVANNs) it is often required the use of one or more hidden layers, mainly when the problem to solve is nonlinear [1] such as those related to radiation of antenna arrays [2][3][4]8], whereas CVANNs require a reduced number of layers (for example, no hidden layers are used in the examples presented here). Some features related to nonlinearity are avoided when using CVANNs [5,6].…”

“…A number of additional features were further simplified in the example presented in this work, such as the computational time of the training process, which was reduced to a matrix (pseudo) inversion. The simplification of the transfer functions was also advantageous: the ones used in RVANNs are related to exponential, hyperbolic tangential or sigmoid functions for hidden layers (that is, those layers inserted between the first and last layers of the neural network, often called input and output layers, respectively) [1][2][3][4]8], whose selections always imply additional computational effort; the CVANNs presented in this work use the identity as the only transfer function. Finally, the number of neurons in the CVANN presented here is equal to the number of outputs; therefore, no trial-and-error processes of selection of their architectures are needed, as is usually the case with RVANNs [1].…”

“…In antenna implementations, they have found several branches to deal with, such as, for example [1,2]: in antenna arrays, for signal-and power-control; in radar, for targets detection and recognition; in microwave devices, for design and optimization; and even in computational electromagnetics, for reducing the number of operations in some kind of calculations. In antenna array design, several works by Christodoulou, Southall, O'Donnell, and Mailloux (some of them with collaborators) are of concern [2,4]. The tools presented by those authors are based on real-valued ANNs, which, in principle, are the ones initially defined by the pioneers of that field (the first work about ANNs is attributed to McCullough and Pitts, in a paper dated 1943) [1].…”

“…This is an arbitrary angular range. The only limitation imposed on it is that it cannot be [0°, 180°], because 0°and 180°represent the same point 4. This is the minimum number of measurement points for the system of Eq.…”