Optimal Channel Equalization for MIMO Time-Varying Channels
We consider optimal channel equalization for MIMO
(multi-input/multi-output) time-varying channels in the sense of
MMSE (minimum mean-squared-error), where the observation noise
can be non-stationary. We show that all ZF (zero-forcing) receivers
can be parameterized in an affine form which eliminates completely
the ISI (inter-symbol-interference), and optimal channel equalizers
can be designed through minimization of the MSE (mean-squarederror)
between the detected signals and the transmitted signals,
among all ZF receivers. We demonstrate that the optimal channel
equalizer is a modified Kalman filter, and show that under the AWGN
(additive white Gaussian noise) assumption, the proposed optimal
channel equalizer minimizes the BER (bit error rate) among all
possible ZF receivers. Our results are applicable to optimal channel
equalization for DWMT (discrete wavelet multitone), multirate transmultiplexers,
OFDM (orthogonal frequency division multiplexing),
and DS (direct sequence) CDMA (code division multiple access)
wireless data communication systems. A design algorithm for optimal
channel equalization is developed, and several simulation examples
are worked out to illustrate the proposed design algorithm.
[1] B.D. Anderson and J.B. Moore, Optimal Filtering, Prentice Hall, New
Jersey, 1979.
[2] E. F. Badran, Optimal Channel Equalization for Filterbank Transceivers
in Presence of White Noise, Ph.D Dissertation, Electrical and Computer
Eng. Dept., Louisiana State Univ., Baton Rouge, USA, May 2002.
[3] G. Gu and E.F. Badran, "Optimal design for channel equalization via
filterbank approach," IEEE Trans. Signal Processing, vol. 52, no. 2, pp.
536-545 Feb. 2004.
[4] S. Haykin, A.H. Sayed, J.R. Zeidler, P. Yee, and P.C. Wei, "Adaptive
tracking of linear time-variant systems by extended RLS algorithms,"
IEEE Trans. Signal Processing, vol. 45, pp. 1118-1128, 1997.
[5] C. Komninakis, C. Fragouli, A.H. Sayed, "MIMO fading channel tracking
and equalization using Kalman estimation," IEEE Trans. Signal Processing,
vol. 50, pp. 1065-1076, 2002.
[6] S.-Y. Kung, Y. Wu, and X. Zhang, "Bezout space-time precoders and
equalizers for MIMO channels," IEEE Trans. Signal Processing, vol. 50,
2499-2514, oct. 2002.
[7] T.J. Lim, L.K. Rasmussen, and H. Sugimoto, "An asynchronous multiuser
CDMA detector based on the Kalman filter," IEEE J. Select. Areas
Commun., vol. 16, no. 9, pp. 1711-1722, December 1998.
[8] E. Moulines, P. Duhamel, J. Cardoso, and S. Mayrargue, "Subspace
methods for the blind identification of multichannel FIR filters," IEEE
Trans. Signal Processing, vol. 43, pp. 516-525, Feb. 1995.
[9] A. Scaglione, G.B. Giannakis and S. Barbarossa "Redundant filterbank
precoders and equalizers, part I: Unification and optimal designs," IEEE
Trans. Signal Processing, vol. 47, pp. 1983-2006, July 1999.
[10] A. Scaglione, P. Stoica, S. Barbarossa, G.B. Giannakis, and H. Sampath,
"Optimal design for space-time linear precoders and decoders," IEEE
Trans. Signal Processing, vol. 50, pp. 1051-1064, May 2002.
[11] C. Tepedelenlioglu and G.B. Giannakis, "Transmitter redundancy for
blind estimation and equalization of time- and frequency-selective channels,"
IEEE Trans. on Signal Processing, vol. 48, No. 7, pp. 2029-2043,
July 2000.
[12] L. Tong and S. Perreau, "Multichannel blind identification: from subspace
to maximum likelihood methods," Proceedings of IEEE, vol. 86,
1951-1968, Oct. 1998.
[13] M.K. Tsatsanis and G.B. Giannakis, "Optimal decorrelating receivers
for DS-CDMA systems: A signal processing framework," IEEE Trans.
on Signal Processing, vol. 44, 3044-3055, 1996.
[1] B.D. Anderson and J.B. Moore, Optimal Filtering, Prentice Hall, New
Jersey, 1979.
[2] E. F. Badran, Optimal Channel Equalization for Filterbank Transceivers
in Presence of White Noise, Ph.D Dissertation, Electrical and Computer
Eng. Dept., Louisiana State Univ., Baton Rouge, USA, May 2002.
[3] G. Gu and E.F. Badran, "Optimal design for channel equalization via
filterbank approach," IEEE Trans. Signal Processing, vol. 52, no. 2, pp.
536-545 Feb. 2004.
[4] S. Haykin, A.H. Sayed, J.R. Zeidler, P. Yee, and P.C. Wei, "Adaptive
tracking of linear time-variant systems by extended RLS algorithms,"
IEEE Trans. Signal Processing, vol. 45, pp. 1118-1128, 1997.
[5] C. Komninakis, C. Fragouli, A.H. Sayed, "MIMO fading channel tracking
and equalization using Kalman estimation," IEEE Trans. Signal Processing,
vol. 50, pp. 1065-1076, 2002.
[6] S.-Y. Kung, Y. Wu, and X. Zhang, "Bezout space-time precoders and
equalizers for MIMO channels," IEEE Trans. Signal Processing, vol. 50,
2499-2514, oct. 2002.
[7] T.J. Lim, L.K. Rasmussen, and H. Sugimoto, "An asynchronous multiuser
CDMA detector based on the Kalman filter," IEEE J. Select. Areas
Commun., vol. 16, no. 9, pp. 1711-1722, December 1998.
[8] E. Moulines, P. Duhamel, J. Cardoso, and S. Mayrargue, "Subspace
methods for the blind identification of multichannel FIR filters," IEEE
Trans. Signal Processing, vol. 43, pp. 516-525, Feb. 1995.
[9] A. Scaglione, G.B. Giannakis and S. Barbarossa "Redundant filterbank
precoders and equalizers, part I: Unification and optimal designs," IEEE
Trans. Signal Processing, vol. 47, pp. 1983-2006, July 1999.
[10] A. Scaglione, P. Stoica, S. Barbarossa, G.B. Giannakis, and H. Sampath,
"Optimal design for space-time linear precoders and decoders," IEEE
Trans. Signal Processing, vol. 50, pp. 1051-1064, May 2002.
[11] C. Tepedelenlioglu and G.B. Giannakis, "Transmitter redundancy for
blind estimation and equalization of time- and frequency-selective channels,"
IEEE Trans. on Signal Processing, vol. 48, No. 7, pp. 2029-2043,
July 2000.
[12] L. Tong and S. Perreau, "Multichannel blind identification: from subspace
to maximum likelihood methods," Proceedings of IEEE, vol. 86,
1951-1968, Oct. 1998.
[13] M.K. Tsatsanis and G.B. Giannakis, "Optimal decorrelating receivers
for DS-CDMA systems: A signal processing framework," IEEE Trans.
on Signal Processing, vol. 44, 3044-3055, 1996.
@article{"International Journal of Electrical, Electronic and Communication Sciences:52791", author = "Ehab F. Badran and Guoxiang Gu", title = "Optimal Channel Equalization for MIMO Time-Varying Channels", abstract = "We consider optimal channel equalization for MIMO
(multi-input/multi-output) time-varying channels in the sense of
MMSE (minimum mean-squared-error), where the observation noise
can be non-stationary. We show that all ZF (zero-forcing) receivers
can be parameterized in an affine form which eliminates completely
the ISI (inter-symbol-interference), and optimal channel equalizers
can be designed through minimization of the MSE (mean-squarederror)
between the detected signals and the transmitted signals,
among all ZF receivers. We demonstrate that the optimal channel
equalizer is a modified Kalman filter, and show that under the AWGN
(additive white Gaussian noise) assumption, the proposed optimal
channel equalizer minimizes the BER (bit error rate) among all
possible ZF receivers. Our results are applicable to optimal channel
equalization for DWMT (discrete wavelet multitone), multirate transmultiplexers,
OFDM (orthogonal frequency division multiplexing),
and DS (direct sequence) CDMA (code division multiple access)
wireless data communication systems. A design algorithm for optimal
channel equalization is developed, and several simulation examples
are worked out to illustrate the proposed design algorithm.", keywords = "Channel equalization, Kalman filtering, Time-varying
systems.", volume = "2", number = "11", pages = "2488-8", }