Conformação de feixe em arranjos de antenas por meio de filtros adaptativos proporcionais linearmente restritos

Abstract

A minimum-disturbance description of adaptive beamforming algorithms opens up the derivation of novel methods for linearly constrained settings. Under this context, this paper proposes two algorithms, the IPCNLMS and the IPCNLMS-ℓ0, and discusses their application in adaptive beamforming applied to three different types of sensor arrays: SHA – Standard Hexagonal Array, URA – Uniform Rectangular Array, and ULA - Uniform Linear Array. These algorithms combine both proportionate and norm constraint strategies that are inserted in the traditional CNLMS algorithm in a smooth and rigorous way. The idea of jointly implementing CNLMS and IPNLMS algorithms is used to achieve faster convergence and the ability to attenuate interfering signals from multiple directions while using adaptive beamforming. The IPCNLMS updates each filter coefficient independently by adjusting the adaptation step size proportionally to the magnitude of the estimated filter coefficient. It is based on the ℓ1-norm penalty to exploit the convergence speed and sparsity of the system. To take this idea further, the ℓ0-norm penalty is also considered in the IPCNLMS-ℓ0 proposition. Simulations demonstrate that the proposed algorithms present faster convergence, under equivalent conditions of asymptotic performance.