Stochastic MV-PURE estimator: robust reduced-rank estimator for stochastic linear model

  • Authors:

  • Tomasz Piotrowski;Renato L. G. Cavalcante;Isao Yamada

  • Affiliations:

  • Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo;Department of Communications and Integrated System, Tokyo Institute of Technology, Tokyo, Japan and Institute for Digital Communications, Joint Research Institute Digital Signal and Image Processi ...;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2009

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Abstract

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 pseudounbiased 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 minimium 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 typiical 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.