Abstract
This paper investigates the convergence-enhanced subspace channel estimation technique for multiple-input–multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems with or without virtual carriers (VCs). Since the perturbations of the correlation matrix and the noise subspace are inversely proportional to the number of OFDM symbols, the subspace channel estimation involves much computational complexity to improve the convergence speed when computing the noise subspace from the correlation matrix of the received signals. Using the block circular property of the channel matrix, the circular repetition method (CRM) is proposed to generate a group of equivalent signals for each OFDM symbol. The subspace estimation of the channel coefficients performs very well within a few OFDM symbols using these equivalent symbols for both the CP-OFDM and ZP-OFDM systems with or without VCs. The computational complexity is analyzed for the CRM-based channel estimation, which reveals that it has an almost identical complexity to the traditional method. Computer simulations demonstrate that the proposed CRM-based blind/semi-blind channel estimation achieves a lower MSE than the other methods.
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Acknowledgments
This work was supported by the Ministry of Science and Technology, Taiwan under Grant MOST 103-2221-E-030-002, the National Natural Science Foundation of China under Grants No. 61501041, the Open Foundation of State Key Laboratory under Grants No. ISN16-08, the Special Foundation for Young Scientists of Quanzhou Normal University of China under Grants No. 201330 and Fujian Province Education Department under Grant JA13267.
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Appendix 1
Appendix 1
We denote \(\mathbf{F}_\mathrm{VC}^H =[\mathbf{f}_{i_1 } \ldots \mathbf{f}_{i_D } ]=[\mathbf{g}_0^H \ldots \mathbf{g}_{N-1}^H ]^{H}\) where \(\mathbf{f}_{i_d } =(1/\sqrt{N})[1 e^{j2\pi i_d /N}\ldots e^{j2\pi (N-1)i_d /N}]^{T}\)and \(\mathbf{g}_n =(1/\sqrt{N})[e^{j2\pi ni_1 /N}\ldots e^{j2\pi ni_D /N}]\), and define \(\varvec{\alpha }_i =[\varvec{\alpha }_i (0)\ldots \varvec{\alpha }_i (N-1)]=\mathbf{u}_i^H \mathbf{H}_\mathrm{cir}\) where \(\varvec{\alpha }_i (n)\in C^{1\times P}\). Then, the linear homogeneous system \(\mathbf{u}_i^H \mathbf{H}_\mathrm{cir} (\mathbf{F}_\mathrm{VC}^H \otimes \mathbf{I}_P ) = \mathbf{0}\) is rewritten as
The homogeneous system in (31) is reformulated in an alternative way
where \({\varvec{\beta }}\) is a \(N \times P\) matrix. Since \(\varvec{\alpha }_i =\mathbf{u}_i^H \mathbf{H}_\mathrm{cir}\), we have
From the definition of \({{\varvec{\beta }}}\), we obtain
where \(\mathbf{H}=\left[ {\mathbf{H}^\mathrm{T}(0),\ldots ,\mathbf{H}^\mathrm{T}\left( L \right) } \right] ^\mathrm{T}\in C^{Q\left( {L+1} \right) \times P}\) and \(\mathbf{V}_i \) is a block Hankel matrix in (24). Substituting (34) into (32), the homogeneous system becomes
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Zhang, B., Yu, JL., Yuan, Y. et al. Convergence-Enhanced Subspace Channel Estimation for MIMO-OFDM Systems with Virtual Carriers. Circuits Syst Signal Process 36, 2384–2401 (2017). https://doi.org/10.1007/s00034-016-0415-3
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DOI: https://doi.org/10.1007/s00034-016-0415-3