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  • 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

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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