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Channel Frequency Response Estimation for MIMO Systems with Frequency-Domain Equalization


Since its recent adoption for the uplink transmissions in the next-generation cellular systems 3GPP long-term evolution (LTE) and LTE advanced, single-carrier frequency-domain equalization (SC-FDE), an effective technique to mitigate the distortion induced by long-spanning intersymbol interference has seen a surge of interest in the research community. Implementation of SC-FDE in multiple-input multiple-output (MIMO) systems usually requires, in advance, the channel information in terms of the channel frequency response (CFR). In this paper, we present a training-based CFR estimation scheme, which is hardware efficient when integrated with SC-FDE and space-time coding (STC) in MIMO systems. A thorough mean square error (MSE) analysis of this CFR estimation scheme is provided, where we consider linear estimators based on both least squares (LS) and minimum MSE (MMSE) criteria by assuming different knowledge of the channel statistics. More specifically, for the LS-based approach, we assume no a priori knowledge of the channel statistics is given other than the noise statistics, while for the MMSE-based method, we assume both the channel covariance matrix and the noise statistics are known. Given a constraint which effectively limits the transmit power of training signals, we also investigate the optimal design of training signals under both criteria. For the special case when the number of transmit antennas is equal to 2, we further demonstrate that the CFR estimation could be implemented in an adaptive manner by means of certain block-wise recursive algorithms. Extensive simulation results are provided, which demonstrate the efficacy of this CFR estimation scheme.

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Correspondence to Yang Yang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yang, Y., Shi, Z., Chew, Y.H. et al. Channel Frequency Response Estimation for MIMO Systems with Frequency-Domain Equalization. EURASIP J. Adv. Signal Process. 2011, 501703 (2011).

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  • Mean Square Error
  • Channel Statistic
  • Minimum Mean Square Error
  • Noise Statistic
  • MIMO System