Statistical analysis of the eigenvector projection method for adaptive spatial filtering of interference

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Abstract
Adaptive beamforming based on eigenanalysis of the covariance matrix of the outputs of an array of sensors has been shown to be most effective for removing directional interference. The author provides an analytical performance evaluation of the signal-to-noise-plus-interference ratio (SNIR) of the adaptive beamformer obtained by the eigenvector projection (EVP) method. The approach presented to derive the statistical properties is based only on the statistics of the sensor outputs, rather than on the asymptotical distribution of the eigenvectors of the sample covariance matrix. The expression for the probability density function can be used to predict the achievable rate of convergence and the resulting loss of performance for arbitrary sample sizes and interference environments, particularly when compared to the classical Wiener filter solutions or other suboptimum projection methods. In the case of an infinite interference-to-noise ratio (INR), it is shown that the SNIR is exactly beta-distributed and independent of the number of sensor elements. Furthermore, the case of finite INR is discussed and it is shown that the distribution is valid for nearly all practical cases. Finally, some relevant numerical examples are presented to illustrate the agreement with the theoretical results.

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