Minimum BER block precoders for zero-forcing equalization

Yanwu Ding, Timothy N. Davidson, Zhi Quan Luo, Kon Max Wong

Research output: Contribution to journalArticlepeer-review

143 Scopus citations


In this paper, we determine the linear precoder that minimizes the bit error rate (BER) at moderate-to-high signal-to-noise ratios (SNRs) for block transmission systems with zero-forcing (ZF) equalization and threshold detection. The design is developed for the two standard schemes for eliminating inter-block interference, viz, zero padding (ZP) and cyclic prefix (CP). We show that both the ZP minimum BER precoder and the CP minimum BER precoder provide substantially lower error rates than standard block transmission schemes, such as orthogonal frequency division multiplexing (OFDM). The corresponding SNR gains can be on the order of several decibels. We also show that the CP minimum BER precoder can be obtained by a two-stage modification of the water-filling discrete multitone modulation (DMT) scheme in which the diagonal water-filling power loading is replaced by a full matrix consisting of a diagonal minimum mean square error power loading matrix post multiplied by a discrete Fourier transform (DFT) matrix.

Original languageEnglish (US)
Pages (from-to)2410-2423
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - Sep 2003

Bibliographical note

Funding Information:
Manuscript received April 12, 2002; revised February 21, 2003. This work was supported in part by the National Science and Engineering Research Council of Canada. The work of the third author is also supported by the Canada Research Chairs Program. The associate editor coordinating the review of this paper and approving it for publication was Dr. Helmut Boelcskei.

Copyright 2008 Elsevier B.V., All rights reserved.


  • Block precoding
  • Cyclic prefix
  • Discrete multitone modulation (DMT)
  • Minimum bit error rate
  • Orthogonal frequency division multiplexing (OFDM)

Fingerprint Dive into the research topics of 'Minimum BER block precoders for zero-forcing equalization'. Together they form a unique fingerprint.

Cite this