Least-squares support vector machines for DOA estimation: a step-by-step description and sensitivity analysis

Adaptive beamforming in antenna arrays aims at adjusting the weighted linear combination of the output signals provided by the antennas so that the power of the received signals at dominant paths is maximized at the same time that the power of interference and noise signals is minimized. The weight vectors, each one associated with one received signal can be directly obtained if the direction of arrival (DOA) of the corresponding signal has already been estimated. The process of DOA estimation involves the prediction of the angle of arrival by means of monitoring the output produced by the antennas in the array, given that the number of antennas is higher than the number of signals to be detected. Even though signal subspace techniques have made a good job in DOA estimation, they present some important drawbacks that are alleviated here using a supervised learning approach, in the form of a multiclass LS-SVM classification problem. The main contribution of this paper is twofold: a step-by-step description of the complete set of algebraic manipulation for data preprocessing and for the synthesis of the classification device, and an analysis of the effect in performance when relevant parameters vary in a given operational interval.