Skip to content


  • Research Article
  • Open Access

MMSE Beamforming for SC-FDMA Transmission over MIMO ISI Channels

  • 1,
  • 1,
  • 2 and
  • 1Email author
EURASIP Journal on Advances in Signal Processing20102011:614571

  • Received: 12 May 2010
  • Accepted: 9 November 2010
  • Published:


We consider transmit beamforming for single-carrier frequency-division multiple access (SC-FDMA) transmission over frequency-selective multiple-input multiple-output (MIMO) channels. The beamforming filters are optimized for minimization of the sum of the mean-squared errors (MSEs) of the transmitted data streams after MIMO minimum mean-squared error linear equalization (MMSE-LE), and for minimization of the product of the MSEs after MIMO MMSE decision-feedback equalization (MMSE-DFE), respectively. We prove that for SC-FDMA transmission in both cases eigenbeamforming, diagonalizing the overall channel, together with a nonuniform power distribution is the optimum beamforming strategy. The optimum power allocation derived for MMSE-LE is similar in spirit to classical results for the optimum continuous-time transmit filter for linear modulation formats obtained by Berger/Tufts and Yang/Roy, whereas for MMSE-DFE the capacity achieving waterfilling strategy well known from conventional single-carrier transmission schemes is obtained. Moreover, we present a modification of the beamformer design to mitigate an increase of the peak-to-average power ratio (PAPR) which is in general associated with beamforming. Simulation results demonstrate the high performance of the proposed beamforming algorithms.


  • Power Allocation
  • Optimum Power Allocation
  • Beamforming Algorithm
  • Beamformer Design
  • Transmitted Data Stream

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

Institute of Mobile Communications, University of Erlangen-Nürnberg, Cauerstraβe 7, 91058 Erlangen, Germany
Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada, V6T1Z4


© Uyen Ly Dang et al. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.