Stochastic MV-PURE Estimator- Robust Reduced-Rank Estimator for Stochastic Linear Model

• Published in: IEEE transactions on signal processing Vol. 57; no. 4; pp. 1293 - 1303
• Main Authors: Piotrowski, T., Cavalcante, R., Yamada, I.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Criteria; Detection, estimation, filtering, equalization, prediction; Distortion; Error analysis; Errors; Estimates; Estimators; Exact sciences and technology; Information, signal and communications theory; Linear regression; Mathematical analysis; Mathematical model; Mathematical models; Mean square error methods; Mean square errors; Miscellaneous; Model uncertainties; reduced-rank estimation; robust linear estimation; Robustness; Signal and communications theory; Signal processing; Signal, noise; Stochastic linear model; Stochastic MV-PURE estimator; Stochastic processes; Stochastic resonance; Stochasticity; Studies; Telecommunications and information theory; Terminology; Vectors; Wiener filter; Performance evaluation; Stochastic model; Second order; Terminology; Robust estimation; Random vector; Linear model; Mean square error; Wiener filter; Selection criterion; Robustness; Linear estimation; MIMO system; Stochastic MV-PURE estimator; Linear regression; Order statistic; Regression analysis; reduced-rank estimation; Statistical method; Stochastic linear model; Minimal variance; Unbiased estimation; Regression model; Model uncertainties; Numerical simulation; robust linear estimation
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.2011839

This paper proposes a novel linear estimator named stochastic MV-PURE estimator, developed for the stochastic linear model, and designed to provide improved performance over the linear minimum mean square error (MMSE) Wiener estimator in cases prevailing in practical, real-world settings, where at least some of the second-order statistics of the random vectors under consideration are only imperfectly known. The proposed estimator shares its main mathematical idea and terminology with the recently introduced minimum-variance pseudo-unbiased reduced-rank estimator (MV-PURE), developed for the linear regression model. The proposed stochastic MV-PURE estimator minimizes the mean square error (MSE) of its estimates subject to rank constraint and inducing minimum distortion to the target random vector. Therefore, the stochastic MV-PURE combines the techniques of the reduced rank Wiener filter (named in this paper RR-MMSE) and the distortionless-constrained estimator (named in this paper C-MMSE), in order to achieve greater robustness against noise or model errors than RR-MMSE and C-MMSE. Furthermore, to ensure that the stochastic MV-PURE estimator combines the reduced-rank and minimum-distortion approaches in the MSE-optimal way, we propose a rank selection criterion which minimizes the MSE of the estimates obtained by the stochastic MV-PURE. As a numerical example, we employ the stochastic MV-PURE, RR-MMSE, C-MMSE, and MMSE estimators as linear receivers in a MIMO wireless communication system. This example is chosen as a typical signal processing scenario, where the statistical information on the data, on which the estimates are built, is only imperfectly known. We verify that the stochastic MV-PURE achieves the lowest MSE and symbol error rate (SER) in such settings by employing the proposed rank selection criterion.