Using Bayesian Inference for Linear Antenna Array Design

Modified Bayesian Optimization Algorithm for Sparse Linear Antenna Design

“…To compare the results obtained by the M-BOA with those provided by other approaches, we have considered three examples of linear, broadside, sparse, symmetric arrays, already presented in [21][22][23][24]26]. In all the considered cases the array is symmetric, and the optimization goal is that of determining the array element excitation coefficients, a n , the position, normalized with respect to the wavelength λ, d n /λ, and the minimum number 2N of array elements that allows to satisfy the array radiation constraints.…”

“…However, the use of a not redundant number of elements is generally advantageous, since it allows to reduce the feeding network complexity and the antenna weight. For this reason, in the last years, several efforts have been made to propose techniques for the design of arrays, linear and planar, with a reduced number of elements not equally spaced [23][24][25][26]. Due to their probabilistic nature, BOA and M-BOA seem particularly suitable to determine, during the optimization process, also the proper number of array elements, and therefore the design of such kind of array seems a particularly suitable test case for comparing their performances.…”

“…6). Such requirements can be easily obtained with a uniformly spaced Chebyshev array with 2N = 20 elements (this is the reason why we named "Chebyshev-like" this type of radiation pattern) while in [23,26] the constraints have been satisfied with unequally spaced arrays with N = 6.…”

“…All these optimization approaches generally allow to obtain optimum solution using as free parameters the position and/or the excitation of the array elements, while their number is fixed "a priori". Recently, some published papers [23][24][25][26] proved the possibility to fulfill the design constraints while reducing the number of elements in non-uniformly spaced arrays. In [23,24] the number of elements in the array is achieved by the singular value decomposition (SDV) approach, while the proper excitation and location of the elements is obtained with the matrix pencil method (MPM); in [25] sparseness constrained optimization is adopted, and finally in [26] the "probability" of different values of the number of array elements is provided, by sampling the distribution using Bayesian Interference (BI); this method, however, has to take into account the information provided by thousands of samples in order to get the proper probability distribution.…”

“…Recently, some published papers [23][24][25][26] proved the possibility to fulfill the design constraints while reducing the number of elements in non-uniformly spaced arrays. In [23,24] the number of elements in the array is achieved by the singular value decomposition (SDV) approach, while the proper excitation and location of the elements is obtained with the matrix pencil method (MPM); in [25] sparseness constrained optimization is adopted, and finally in [26] the "probability" of different values of the number of array elements is provided, by sampling the distribution using Bayesian Interference (BI); this method, however, has to take into account the information provided by thousands of samples in order to get the proper probability distribution. Moreover, the distribution inferred by the BI approach is usually heavily affected by the initial assumptions, e.g., by the probability distribution assignment to all the parameters; therefore this approach could not guarantee that the obtained value is the absolute optimum one, but only the optimum of a solution subspace defined by the first guess choice, and this can dramatically affect not only the efficiency but even the robustness of all the procedure.…”