Steering vector errors and diagonal loading

Abstract

Diagonal loading is one of the most widely used and effective methods to improve robustness of adaptive beamformers. The authors 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, the problem addressed is that of optimally selecting the loading level with a view to maximising the signal-to-interference-plus-noise ratio in the presence of steering vector errors. First, an expression is derived for the optimal loading for a given steering vector error and it is shown that this loading is negative. Next, random steering errors are considered and the 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 derived optimal loading factor provides a performance close to optimum.

Iterative robust adaptive beamforming

“…Using the fact that multiplying the weight vector by any arbitrary constant does not change the output SINR, we can transform (9) to…”

“…The solve idea takes reference to [9,23], and [24]. Using Woodbury formula of matrix inverse, we have…”

“…For example, the class of diagonal loading technology [9,10] augment the data covariance with a constant improves the robustness; the worst-case performance optimizationbased beamformer (WCB) [11,12] restrains the gain in signal uncertainty range that is larger than one; the covariance fitting-based beamformer [13,14] solves a new steering vector which is fitting for the sample covariance matrix to avoid desired signal cancellation; the magnitude response constraints method [15,16] improves the robustness by restraining the main beam pattern; the covariance matrix reconstruction approach [17,18] eliminates the signal component from the data covariance matrix to prevent desired signal cancellation.…”

Robust Adaptive Beamforming Using a Fully Data-Dependent Loading Technique

“…Diagonal loading (DL) is one of the widely used techniques to improve robustness of the SMI against the errors [4,[8][9][10][11][12], where a scaled identity matrix is added to the sample correlation matrix. Although the DL is effective, the main drawback is that choosing the required loading factor is not an easy task.…”

“…However, the loading factors of those methods cannot be obtained analytically and have to be solved numerically. Furthermore, in [12], an analytical expression of the optimal loading factor is derived by maximizing the output SINR in the presence of random steering vector error, the main disadvantage is that the obtained negative loading factor may lead to a rank-deficient problem if it equals an eigenvalue of the correlation matrix. On the other hand, it follows from [13][14][15] that the loading factor can be calculated based on the uncertainty set of the steering vector.…”