Skip to main content
Log in

Convergence-Enhanced Subspace Channel Estimation for MIMO-OFDM Systems with Virtual Carriers

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. H. Ali, A. Doucet, Y. Hua, Blind SOS subspace channel estimation and equalization techniques exploiting spatial diversity in OFDM systems. Digital Signal Process. 14, 171–202 (2004)

    Article  Google Scholar 

  2. I. Barhumi, G. Leus, M. Moonen, Optimal training design for MIMO OFDM systems in mobile wireless channels. IEEE Trans. Signal Process. 51(6), 1615–1624 (2003)

    Article  Google Scholar 

  3. F. Boccardi, B. Clerckx, A. Ghosh, E. Hardouin, G. Jongren, K. Kusume, E. Onggosanusi, Y. Tang, Multiple antenna techniques in LTE-advanced. IEEE Commun. Mag. 50(3), 114–121 (2012)

    Article  Google Scholar 

  4. T. Cui, C. Tellambura, Joint frequency offset and channel estimation for OFDM systems using pilot symbols and virtual carriers. IEEE Trans. Wirel. Commun. 6(4), 1193–1202 (2007)

    Article  Google Scholar 

  5. F. Gao, Y. Zeng, A. Nallanathan, T.S. Ng, Robust subspace blind channel estimation for cyclic prefixed MIMO OFDM systems: algorithm, identifiability and performance analysis. IEEE J. Sel. Areas Commun. 26, 378–388 (2008)

    Article  Google Scholar 

  6. J.G. Kim, J.H. Oh, J.T. Lim, Subspace-based channel estimation for MIMO-OFDM systems with few received blocks. IEEE Signal Process. Lett. 19(7), 435–438 (2012)

    Article  Google Scholar 

  7. E.G. Larsson, F. Tufvesson, O. Edfors, T.L. Marzetta, Massive MIMO for next generation wireless systems. IEEE Commun. Mag. 52(2), 186–195 (2014)

    Article  Google Scholar 

  8. H. Li, C.K. Ho, J.W.M. Bergmans, F.M.J. Willems, Pilot-aided angle-domain channel estimation techniques for MIMO-OFDM systems. IEEE Trans. Veh. Technol. 57(2), 906–920 (2008)

    Article  Google Scholar 

  9. C. Li, S. Roy, Subspace-based blind channel estimation for OFDM by exploiting virtual carriers. IEEE Trans. Wirel. Commun. 2, 141–150 (2003)

    Article  Google Scholar 

  10. L. Lu, G.Y. Li, A.L. Swindlehurst, A. Ashikhin, R. Zhang, An overview of massive MIMO: benefits and challenges. IEEE J. Sel. Topics Signal Process. 8(5), 742–758 (2014)

    Article  Google Scholar 

  11. B. Muquet, M. de Courville, P. Duhamel, Subspace-based blind and semi-blind channel estimation for OFDM systems. IEEE Trans. Signal Process. 50(7), 1699–1712 (2002)

    Article  Google Scholar 

  12. Y.C. Pan, S.M. Phoong, An improved subspace-based algorithm for blind channel identification using few received blocks. IEEE Trans. Commun. 61(9), 3710–3720 (2013)

    Article  Google Scholar 

  13. S. Park, B. Shim, J.W. Choi, Iterative channel estimation using virtual pilot signals for MIMO-OFDM systems. IEEE Trans. Signal Process. 63(12), 3032–3045 (2015)

    Article  MathSciNet  Google Scholar 

  14. H. Rohling, OFDM Concepts for Future Communication Systems (Springer-Verlag, New York, 2011)

    MATH  Google Scholar 

  15. A. Sibille, C. Oestges, A. Zanella, MIMO from Theory to Implementation (Academic Press, New York, 2010)

    Google Scholar 

  16. B. Su, P.P. Vaidyanathan, Subspace-based blind channel identification for cyclic prefix systems using few received blocks. IEEE Trans. Signal Process. 55(10), 4979–4993 (2007)

    Article  MathSciNet  Google Scholar 

  17. J.R. Vershynin, How close is the sample covariance matrix to the actual covariance matrix? J. Theor. Probab. 25(3), 655–686 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. F. Wan, W.-P. Zhu, M.N.S. Swamy, Semiblind sparse channel estimation for MIMO-OFDM systems. IEEE Trans. Veh. Technol. 60(6), 2569–2582 (2011)

    Article  Google Scholar 

  19. J.L. Yu, D.Y. Hong, A novel subspace channel estimation with fast convergence for ZP-OFDM systems. IEEE Trans. Wirel. Commun. 10(10), 3168–3173 (2011)

    Article  Google Scholar 

  20. Y. Zeng, T.S. Ng, A semi-blind channel estimation method for multiuser multiantenna OFDM systems. IEEE Trans. Signal Process. 52, 1419–1429 (2004)

    Article  MathSciNet  Google Scholar 

  21. B. Zhang, J.L. Yu, W.R. Kuo, Fast convergence on blind and semi-blind channel estimation for MIMO-OFDM systems. Circuits Syst. Signal Process. 34(6), 1993–2013 (2015)

    Article  MathSciNet  MATH  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jung-Lang Yu.

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

$$\begin{aligned}&\varvec{\alpha }_i (\mathbf{F}_\mathrm{VC}^H \otimes \mathbf{I}_P )= \sum _{n=0}^{N-1} {\varvec{\alpha }_i (n)(\mathbf{g}_n \otimes \mathbf{I}_P )}\nonumber \\&\quad =\sum _{n=0}^{N-1} {(1/\sqrt{N})\left[ {e^{j2\pi ni_1 /N}\varvec{\alpha }_i (n)\ldots e^{j2\pi ni_D /N}\varvec{\alpha }_i (n)} \right] } =\mathbf{0} \end{aligned}$$
(31)

The homogeneous system in (31) is reformulated in an alternative way

$$\begin{aligned} \left( {{\begin{array}{c} {\sum \limits _{n=0}^{N-1} {(1/\sqrt{N})e^{j2\pi ni_1 /N}\varvec{\alpha }_i (n)} } \\ \vdots \\ {\sum \limits _{n=0}^{N-1} {(1/\sqrt{N})e^{j2\pi ni_D /N}\varvec{\alpha }_i (n)} } \\ \end{array} }} \right) \hbox {=}\left( {{\begin{array}{c} {\mathbf{f}_{i_1 }^\mathrm{T} } \\ \vdots \\ {\mathbf{f}_{i_D }^\mathrm{T} } \\ \end{array} }} \right) \underbrace{\left( {{\begin{array}{c} {\varvec{\alpha }_i (0)} \\ \vdots \\ {\varvec{\alpha }_i (N-1)} \\ \end{array} }} \right) }_{{\varvec{\beta }} }=\mathbf{F}_\mathrm{VC}^*{{\varvec{\beta }}}=\mathbf{0}, \end{aligned}$$
(32)

where \({\varvec{\beta }}\) is a \(N \times P\) matrix. Since \(\varvec{\alpha }_i =\mathbf{u}_i^H \mathbf{H}_\mathrm{cir}\), we have

$$\begin{aligned} \varvec{\alpha }_i (n)=\sum _{l=0}^L {\mathbf{u}_i^H ((n+l))_N \mathbf{H}(l)} \end{aligned}$$
(33)

From the definition of \({{\varvec{\beta }}}\), we obtain

$$\begin{aligned} {{\varvec{\beta }}}=\mathbf{V}_i^H \mathbf{H} \end{aligned}$$
(34)

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

$$\begin{aligned} \mathbf{F}_\mathrm{VC}^*\mathbf{V}_i^H \mathbf{H}=\mathbf{0} \end{aligned}$$
(35)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-016-0415-3

Keywords

Navigation