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  • Research Article
  • Open Access

Constrained Optimization of MIMO Training Sequences

EURASIP Journal on Advances in Signal Processing20072007:080857

  • Received: 30 May 2006
  • Accepted: 11 January 2007
  • Published:


Multiple-input multiple-output (MIMO) systems have shown a huge potential for increased spectral efficiency and throughput. With an increasing number of transmitting antennas comes the burden of providing training for channel estimation for coherent detection. In some special cases optimal, in the sense of mean-squared error (MSE), training sequences have been designed. However, in many practical systems it is not feasible to analytically find optimal solutions and numerical techniques must be used. In this paper, two systems (unique word (UW) single carrier and OFDM with nulled subcarriers) are considered and a method of designing near-optimal training sequences using nonlinear optimization techniques is proposed. In particular, interior-point (IP) algorithms such as the barrier method are discussed. Although the two systems seem unrelated, the cost function, which is the MSE of the channel estimate, is shown to be effectively the same for each scenario. Also, additional constraints, such as peak-to-average power ratio (PAPR), are considered and shown to be easily included in the optimization process. Numerical examples illustrate the effectiveness of the designed training sequences, both in terms of MSE and bit-error rate (BER).


  • Cost Function
  • Quantum Information
  • Nonlinear Optimization
  • Channel Estimate
  • Numerical Technique

Authors’ Affiliations

Toshiba Telecommunications Research Laboratory, 32 Queen Square, Bristol, BS1 4ND, UK


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© J. P. Coon and M. Sandell. 2007

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.