Robust beamforming using sensors with nonidentical directivity patterns

Abstract

The optimal weights for a beamformer that provide maximum directivity, are often found to be severely lacking in terms of robustness. Although an ideal implementation of the beamformer with these weights provides high directivity, minor perturbations of the weights or of sensor placement cause severe degradation. Therefore, a robustness constraint is often imposed during the beamformer's design stage. The classical method of diagonal loading is commonly used for this purpose. There are known results in this field which pertain to an array consisting of sensors with identical directivity-patterns and orientations. We extend these results to account for sensors with nonidentical directivity patterns, and sensors which share placement errors. We show that in such cases, modification of the classical loading scheme to incorporate nonidentical diagonal elements and off-diagonal elements is beneficial.Index Terms-robust beamforming, maximum directivity

Robust beamforming under uncertainties in the loudspeakers directivity pattern

“…With respect to the Tikhonov regularization, however, the loading is not diagonal, as P and Π may have non-diagonal elements different from zero. A similar result was attained in [24] in the context of data-dependent beamformers. We also notice from (16) that P and Π are related through B.…”

“…Even if developed following a different strategy, the method in [24] attains similar conclusions for what concerns the loading of the least-squares solution. We remark, however, that the beamforming in [24] is data-dependent, whereas the technique presented in this paper is data-independent.…”

“…The first embeds the probability density functions of the steering vectors, whereas the second optimizes the worst-case performance through the minimax criterion. In [24] Levin et al propose a technique that modifies the classical loading scheme incorporating a non-diagonal elements to attenuate the effect of sensor uncertainties. The method in [24], however, is data-dependent, i.e.…”

“…In [24] Levin et al propose a technique that modifies the classical loading scheme incorporating a non-diagonal elements to attenuate the effect of sensor uncertainties. The method in [24], however, is data-dependent, i.e. the filters depend on the signal to be rendered, thus making its use for rendering purposes quite cumbersome.…”

Near-field signal acquisition for smartglasses using two acoustic vector-sensors

“…It should be noted that(21) is fairly rudimentary. Other regularization methods which are more advanced exist such as diagonal loading[15,14], alternative loading schemes[16], and eigenvalue thresholding[17]. We decided to use (21) due to its computational simplicity: no weighting coefficient must be determined, nor is eigenvalue decomposition called for.…”