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Phase Noise in MIMO Systems: Bayesian Cramér-Rao Bounds and Soft-Input Estimation
IEEE Transactions on Signal Processing (2013)
  • Ali A. Nasir, Australian National University
  • Hani Mehrpouyan, California State University
  • Robert Schober, University of British Columbia
  • Yingbo Hua, University of California, Riverside
Abstract

This paper addresses the problem of estimating time varying phase noise caused by imperfect oscillators in multi-input multi-output (MIMO) systems. The estimation problem is parameterized in detail and based on an equivalent signal model its dimensionality is reduced to minimize the overhead associated with phase noise estimation. New exact and closed-form expressions for the Bayesian Cram´er-Rao lower bounds (BCRLBs) and soft-input maximum a posteriori (MAP) estimators for online, i.e., filtering, and offline, i.e., smoothing, estimation of phase noise over the length of a frame are derived. Simulations demonstrate that the proposed MAP estimators’ mean-square error (MSE) performances are very close to the derived BCRLBs at moderate-to-high signal-to-noise ratios. To reduce the overhead and complexity associated with tracking the phase noise processes over the length of a frame, a novel soft-input extended Kalman filter (EKF) and extended Kalman smoother (EKS) that use soft statistics of the transmitted symbols given the current observations are proposed. Numerical results indicate that by employing the proposed phase tracking approach, the bit-error rate performance of a MIMO system affected by phase noise can be significantly improved. In addition, simulation results indicate that the proposed phase noise estimation scheme allows for application of higher order modulations and larger numbers of antennas in MIMO systems that employ imperfect oscillators.

Keywords
  • Bayesian Cramér Rao lower bound (BCRLB),
  • extended Kalman smoother (EKS),
  • maximum-a-posteriori (MAP),
  • multiple-input multiple-output (MIMO),
  • soft-decision extended Kalman filter (EKF),
  • Wiener phase noise
Publication Date
May 15, 2013
Publisher Statement
© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. doi: 10.1109/TSP.2013.2243444
Citation Information
Ali A. Nasir, Hani Mehrpouyan, Robert Schober and Yingbo Hua. "Phase Noise in MIMO Systems: Bayesian Cramér-Rao Bounds and Soft-Input Estimation" IEEE Transactions on Signal Processing Vol. 61 Iss. 10 (2013)
Available at: http://works.bepress.com/hani_mehrpouyan/11/