Diagonal loading is one of the most widely used and effective methods to improve robustness of adaptive beamformers. In this paper, we consider its application to the case of steering vector errors, i.e. when there exists a mismatch between the actual steering vector of interest and the presumed one. More precisely, we address the problem of optimally selecting the loading level with a view to maximise the signal to interference plus noise
ratio in the presence of random steering vector errors. First, we derive an expression for the optimal loading for a given steering vector error and we show that this loading is negative. Next, this optimal loading is averaged with respect to the probability density function of the steering vector errors, yielding a very simple expression for the average optimal loading. Numerical simulations attest to the validity of the analysis and show that diagonal loading with the optimal loading factor derived herein provides a performance close to optimum
