**7. References**


82 Fourier Transform Applications

Results are in good agreement with the results from literature for various ground electrical parameters, heights of vertical dipoles above ground, in the near and far field. Based on these results, it can be concluded that the effects of lossy ground are greater on horizontal than on vertical electric field, and that specific conductivity influences more than electrical permittivity. Fourier transform application has to be further investigated in terms of optimal choice of FFT parameters in order to reduce computing time which can be important in antenna modeling of lightning discharge channels and in analysis of lightning

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**4** 

Liu Congfeng

*China* 

**Robust Beamforming and DOA Estimation** 

*Electronic Countermeasure Research Institute, Xidian University, Xian Shaanxi,* 

Beamforming is a ubiquitous task in array signal processing with applications, among others, in radar, sonar, acoustics, astronomy, seismology, communications, and medical imaging. Without loss of generality, we consider herein beamforming in array processing applications.

The traditional approach to the design of adaptive beamformers assumes that the desired signal components are not present in training data, and the robustness of beamformer is known to depend essentially on the availability of signal-free training data. However, in many important applications such as mobile communications, passive location, microphone array speech processing, medical imaging, and radio astronomy, the signal-free training data cells are unavailable. In such scenarios, the desired signal is always present in the training snapshots, and the adaptive beamforming methods become very sensitive to any violation of underlying assumptions on the environment, sources, or sensor array. In fact, the performances of the existing adaptive array algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal [10]-[12]. Similar types of degradation can take place when the array response is known precisely but the training sample size is small, namely the mismatch between the actual and the estimated covariance matrix [13]-[15]. Therefore, robust approaches to adaptive beamforming appear to be of primary importance in these

Many approaches have been proposed to improve the robustness of the adaptive beamformer during the past three decades. Indeed, the literatures on the robust adaptive beamformer are quite extensive. We provide a brief review as fellows. For more recent

For the specific case of the signal direction mismatch, there are several efficient methods have been developed. Representative examples of such techniques are the linearly constrained minimum variance (LCMV) beamformer [26], which is also denoted as the linearly constrained minimum power (LCMP) beamformer in other references [27] and this chapter, signal blocking-based algorithms [10][28], and Bayesian beamformer [29]. Although

The introduction to beamforming can be found in [1]-[9] and the references herein.

**1. Introduction** 

cases [16][17].

detailed critical reviews, see [18] and [19]-[25].

**1.1.1 Robust approaches for signal direction mismatch** 

**1.1 Robust beamforming overview** 

