Skip to main content
  • Research Article
  • Open access
  • Published:

Optimal Design of Noisy Transmultiplexer Systems

Abstract

An optimal design method for noisy transmultiplexer systems is presented. For a transmultiplexer system with given transmitters and desired crosstalk attenuation, we address the problem of minimizing the reconstruction error while ensuring that the crosstalk of each band is below a prescribed level. By employing the mixed optimization, we will ensure that the system with suboptimal reconstruction error is more robust and less sensitive to the changes of input signals and channel noises. Due to the overlapping of adjacent subchannels, crosstalk between adjacent channels is expected. And the problem of crosstalk attenuation is formulated as an optimization problem, solved in terms of linear matrix inequalities (LMIs). The simulation examples demonstrate that the proposed design performs better than existing design methods.

References

  1. Bellanger M, Daguet JL: TDM-FDM transmultiplexer: digital polyphase and FFT. IEEE Transactions on Communications 1974, 22(9):1199–1205. 10.1109/TCOM.1974.1092391

    Article  Google Scholar 

  2. Lin Y-P, Phoong S-M: ISI-free FIR filterbank transceivers for frequency-selective channels. IEEE Transactions on Signal Processing 2001, 49(11):2648–2658. 10.1109/78.960412

    Article  Google Scholar 

  3. Vetterli M: A theory of multirate filter banks. IEEE Transactions on Acoustics, Speech, and Signal Processing 1987, 35(3):356–372. 10.1109/TASSP.1987.1165137

    Article  Google Scholar 

  4. Scheuermann H, Göckler H: A comprehensive survey of digital transmultiplexing methods. Proceedings of the IEEE 1981, 69(11):1419–1450.

    Article  Google Scholar 

  5. Vaidyanathan PP: Multirate Systems and Filter Banks. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.

    MATH  Google Scholar 

  6. Vetterli M: Perfect transmultiplexers. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '86), April 1986, Tokyo, Japan 11: 2567–2570.

    Article  Google Scholar 

  7. Koilpillai RD, Nguyen TQ, Vaidyanathan PP: Some results in the theory of crosstalk-free transmultiplexers. IEEE Transactions on Signal Processing 1991, 39(10):2174–2183. 10.1109/78.91174

    Article  Google Scholar 

  8. Critchley J, Rayner PJW: Design methods for periodically time varying digital filters. IEEE Transactions on Acoustics, Speech, and Signal Processing 1988, 36(5):661–673. 10.1109/29.1576

    Article  Google Scholar 

  9. Prater JS, Loeffler CM: Analysis and design of periodically time-varying IIR filters, with applications to transmultiplexing. IEEE Transactions on Signal Processing 1992, 40(11):2715–2725. 10.1109/78.165658

    Article  Google Scholar 

  10. Liu T, Chen T: optimization applied to general transmultiplexer design. Proceedings of the 39th IEEE Conference on Decision and Control, December 2000, Sydney, NSW, Australia 5: 4314–4319.

    Google Scholar 

  11. Lin Y-P, Phoong S-M: Perfect discrete multitone modulation with optimal transceivers. IEEE Transactions on Signal Processing 2000, 48(6):1702–1711. 10.1109/78.845928

    Article  Google Scholar 

  12. Chen B-S, Chen L-M: Optimal reconstruction in multirate transmultiplexer systems under channel noise: Wiener separation filtering approach. Signal Processing 2000, 80(4):637–657. 10.1016/S0165-1684(99)00158-9

    Article  Google Scholar 

  13. Chen B-S, Lin C-W, Chen Y-L: Optimal signal reconstruction in noisy filter bank systems: multirate Kalman synthesis filtering approach. IEEE Transactions on Signal Processing 1995, 43(11):2496–2504. 10.1109/78.482101

    Article  Google Scholar 

  14. Chen B-S, Lin C-W: Optimal design of deconvolution filters for stochastic multirate signal systems. Signal Processing 1995, 47(3):287–305. 10.1016/0165-1684(95)00116-6

    Article  MathSciNet  Google Scholar 

  15. Lin C-W, Chen B-S: State space model and noise filtering design in transmultiplexer systems. Signal Processing 1995, 43(1):65–78. 10.1016/0165-1684(94)00144-O

    Article  Google Scholar 

  16. Cheng Y-M, Chen B-S, Chen L-M: Minimax deconvolution design of multirate systems with channel noises: a unified approach. IEEE Transactions on Signal Processing 1999, 47(11):3145–3149. 10.1109/78.796451

    Article  Google Scholar 

  17. Chen B-S, Tsai C-L, Chen Y-F: Mixedfiltering design in multirate transmultiplexer systems: LMI approach. IEEE Transactions on Signal Processing 2001, 49(11):2693–2701. 10.1109/78.960416

    Article  Google Scholar 

  18. Gahinet P, Nemirovski A, Laub AJ, Chilali M: LMI Control Toolbox—for Use with MATLAB. The MathWorks, Natick, Mass, USA, 1995

    Google Scholar 

  19. Al-Dhahir N, Cioffi JM: Optimum finite-length equalization for multicarrier transceivers. IEEE Transactions on Communications 1996, 44(1):56–64. 10.1109/26.476097

    Article  Google Scholar 

  20. Boyd S, El Ghaoui L, Feron E, Balakrishnan V: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, Pa, USA; 1994.

    Book  Google Scholar 

  21. Chu LC, Brooke M: A study on multiuser DSL channel capacity with crosstalk environment. Proceedings of the IEEE Pacific Rim Conference on Communications, Computers and signal Processing (PACRIM '01), August 2001, Victoria, BC, Canada 1: 176–179.

    Google Scholar 

  22. Zhang C, Liao Y: A sequentially operated periodic FIR filter for perfect reconstruction. Circuits, Systems, and Signal Processing 1997, 16(4):475–486. 10.1007/BF01198063

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Huan Zhou.

Rights and permissions

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

Reprints and permissions

About this article

Cite this article

Zhou, H., Xie, L. Optimal Design of Noisy Transmultiplexer Systems. EURASIP J. Adv. Signal Process. 2006, 064645 (2006). https://doi.org/10.1155/ASP/2006/64645

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/ASP/2006/64645

Keywords