Abstract
To maximize the throughput of frequency-selective multicast channel, the minimum-phase Finite Impulse Response (FIR) precoder design is investigated in this paper. This problem can be solved in two steps. Firstly, we focus on designing a nonminimum-phase FIR precoder under the criterion of maximizing the throughput, and develop two efficient algorithms for the FIR precoder design from perspectives of frequency domain and time domain. In the second step, based on the theory of spectral factorization, the nonminimum-phase FIR precoder is transformed into the corresponding minimum-phase FIR precoder by a classic iterative algorithm without affecting the throughput. Numerical results indicate that the achievable rate of the proposed design has remarkable improvement over that of existing schemes, moreover, the group delay introduced by the FIR precoder is minimized.
Similar content being viewed by others
References
H. Sari, G. Karam, and I. Jeanclaude. Transmission techniques for digital terrestrial TV broadcasting. IEEE Communications Magazine, 33(1995)2, 100–109.
N. D. Sidiropoulos, T. N. Davidson, and Z. Q. Luo. Transmit beamforming for physical-layer multicasting. IEEE Transactions on Signal Processing, 54(2006)6, 2239–2251.
A. Abdelkader, A. B. Gershman, and N. D. Sidiropoulos. Multiple-antenna multicasting using channel orthogonalization and local refinement. IEEE Transactions on Signal Processing, 58(2010)7, 3922–3927.
S. Shi, M. Schubert, and H. Boche. Physical layer multicasting with linear MIMO transceivers. Conference on Information Sciences and Systems, Princeton University, USA, March 2008, 884–889.
Yi Jiang and Mahesh K. Varanasi. Extended uniform channel decomposition for MIMO communications with intersymbol interference. Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA, November 2007, 1549–1553.
C. Y. Chen and P. P. Vaidyanathan. Precoded FIR and redundant V-BLAST systems for frequency-selective MIMO channels. IEEE Transactions on Signal Proceesing, 55(2007)7, 3390–3404.
Y. Guo and B. C. Levy. Design of FIR precoders and equalizers for broadband MIMO wireless channels with power constraints. EURASIP Journal on Wireless Communications and Networking, 2004(2004)2, 344–356.
S. Kung, Y. Wu, and X. Zhang. Bezout space-time precoders and equalizers for MIMO channels. IEEE Transactions on Signal Processing, 50(2002)10, 2499–2514.
Ching-Chih Weng and P. P. Vaidyanathan. Block diagonal GMD for zero-padded MIMO frequency selective channels. IEEE Transactions on Signal Proceesing, 59(2011)2, 713–727.
T. M. Cover and J. A. Thomas. Elements of Information Theory. Hoboken, NJ, USA, John Wiley & Sons, Inc., 2006, 277–280.
S. Boyd and L. Vandenberghe. Convex Optimization, Cambridge, U.K., Cambridge University Press, 2004, 599–600.
Gu Qiang and Xu Xiaodong. FIR precoder for MIMO frequency-selective fading channel. Communications Technology, 45(2012)8, 1–4 (in Chinese). 古强, 许小东. 适合频率选择性MIMO信道的FIR预编码器. 通信技术, 45(2012)8, 1–4.
Z. Q. Luo, W. K. Ma, A. M. C. So, et al. Semidefininite relaxation of quadratic optimization problems. IEEE Signal Processing Magazine, 27(2010)3, 20–34.
A. Oppenheim and R. Schafer. Discrete-time Signal Processing. Englewood Cliffs, NJ, USA, Prentice-Hall, 1989, 311–322.
Vladimir Kucera. Factorization of rational matrices: A survey of methods. IEEE International Conference on Control, Edinburgh, U. K., 1991, 1074–1078.
A. H. Sayed and T. Kailath. A survey of spectral factorization methods. Numerical Linear Algebra with Applications, 8(2001)7, 467–496.
Gigla Janashia, Edem Lagvilava, and Lasha Ephremidze. A new method of matrix spectral factorization. IEEE Transactions on Information Theory, 57(2011)4, 2318–2326.
Robert F. H. Fischer. Sorted spectral factorization of matrix polynomials in MIMO communications. IEEE Transactions on Communications, 53(2005)6, 945–951.
Michael Grant and Stephen Boyd. CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx, September 2012.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (No. 61271272), the National Science and Technology Special Projects of China (No. 2012ZX03001007-002), and the National High Technology Research and Development Program of China (863 Program) (No. 2012-AA01A502).
About this article
Cite this article
Du, B., Xu, X. & Dai, X. Minimum-phase fir precoder design for multicasting over MIMO frequency-selective channels. J. Electron.(China) 30, 319–327 (2013). https://doi.org/10.1007/s11767-013-3045-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11767-013-3045-y
Key words
- Finite Impulse Response (FIR) precoder
- Physical layer multicasting
- Frequency-selective channel
- Minimum-phase filter