Generalized Consistent Estimation in Arbitrarily High Dimensional Signal Processing

The theory of statistical signal processing Þnds a wide variety of applications in the Þelds of data communications, such as in channel estimation, equalization and symbol detection, and sensor array processing, as in beamforming, and radar systems. Indeed, a large number of these applications can be interpreted in terms of a parametric estimation problem, typically approached by a linear Þltering operation acting upon a set of multidimensional observations. Moreover, in many cases, the underlying structure of the observable signals is linear in the parameter to be inferred. This dissertation is devoted to the design and evaluation of statistical signal processing methods under realistic implementation conditions encountered in practice. Traditional statistical signal processing techniques intrinsically provide a good performance under the availability of a particularly high number of observations of Þxed dimension. Indeed, the original optimality conditions cannot be theoretically guaranteed unless the number of samples increases asymptotically to inÞnity. Under this assumption, a statistical characterization can be often afforded by using the large-sample theory of sample covariance matrices. In practice, though, the application of these methods to the implementation of, for instance, training schemes in communication systems and adaptive procedures for radar detection problems, must rely on an observation window of Þnite length. Moreover, the dimension of the received signal samples (e.g. number of array sensors in multi-antenna systems) and the observation window size are most often comparable in magnitude. Under these situations, approaches based on the classical multivariate statistical analysis signiÞcantly lose efficiency or cannot even be applied. As a consequence, the performance of practical solutions in some real situations might turn out to be unacceptable. In this dissertation, a theoretical framework for characterizing the efficiency loss incurred by classical multivariate statistical approaches in conventional signal processing applications under the practical conditions mentioned above is provided. Based on the theory of the spectral analysis of large-dimensional random matrices, or random matrix theory (RMT), a family of new statistical inference methods overcoming the limitations of traditional inferential schemes under comparably large sample-size and observation dimension is derived. SpeciÞcally, the new class of consistent estimators generalizes conventional implementations by proving to be consistent even