On imaginary-valued diagonal loading levels with application to hyperparameter-free robust adaptive beamforming

Robust adaptive beamforming algorithms with fully automatic diagonal level computation are desired but scarce in the literature. We note that the an imaginary-valued diagonal loading level well approximates but differs from its real-valued counterpart in terms of output signal-to-interference-plus-noise ratio (SINR), and an estimate of the optimal diagonal loading level can be found by the highest double-sided peak of the cross-correlation-coefficient curve of the two outputs using realand imaginary-valued diagonal loading levels with the same absolute values. The performance of the resulting beamformer is illustrated via numerical examples, compared with several other hyperparameter-free algorithms.