Optimal SP Training and Precoding Designs for Channel Estimation and Symbol Detection in MIMO-OFDM Systems
Based on convex programming for optimization, a closed-from solution of superimposed (SP) training on linearly precoded data for jointly optimal channel estimation and symbol detection is proposed in this paper for MIMO-OFDM systems. The newly designed method not only efficiently identifies the frequency-selective fading channel but also effectively enhances the symbol detection. Although linearly precoding technique is employed and protects the transmitted data over the multi-path MIMO wireless channels, the precoded data is always arithmetically added to the training sequence to prevail transmission bandwidth. Analytical and numerical results confirm that the proposed design efficiently estimates the wireless fading channel and effectively recovers the source data symbols.
 I. E. Telatar, “Capacity of multi-antenna gaussian channels,”European Trans. on Tele., vol. 10, Nov./Dec. 1999.
 B. Hassibi and B. M. Hochwald, “How much training is needed in multiple-antenna wireless links?,” IEEE Trans. Inform. Theory, vol. 49, pp. 951–963, April 2003.
 D. D. Lin, R. Pacheco, T. J. Lim, and D. Hatzinakos, “Joint estimation of channel response, frequency offset, and phase noise in OFDM,” IEEE Trans. Signal Process., vol. 54, pp. 3542–3554, Sept. 2006.
 X. Ma, L. Yang, and G. B. Giannakis, “Optimal training for MIMO frequency-selective fading channels,” IEEE Trans. on Wireless Commun., vol. 4, pp. 453–466, March 2005.
 J. K. Tugnait and X. Meng, “On superimposed training for channel estimation: performance analysis, training power allocation, and frame synchronization,” IEEE Trans. Signal Process., vol. 54, pp. 752–765, Feb. 2006.
 I. Barhumi, G. Leus, and M. Moonen, “Optimal training design for MIMO OFDM systems in mobile wireless channels,”IEEE Trans. Signal Process., vol. 51, pp. 1615–1624, Jun. 2003.
 O. Edfors, M. Sandell, J. V. D. Beek, S. K. Wilson, and P. O. Borjesson, “OFDM channel estimation by singular value decomposition,” IEEE Trans. Commun., vol. 46, pp. 931–939, July 1998.
 J. H. Manton, “Optimal training sequences and pilot tones for OFDM systems,” IEEE Commun. Letter, vol. 5, pp. 151–153, April 2001.
 H. Minn and N. Al-Dhahir, “Optimal training signals for MIMO OFDM channel estimation,” IEEE Trans. Wireless Commun., vol. 5, pp. 1158–1168, May 2006.
 R. Negi and J. Cioffi, “Pilot tone selection for channel estimation in a mobile OFDM system,” IEEE Trans. Consumer Electronics, vol. 44, pp. 1122–1128, Aug. 1998.
 G. D. Forney and M. V. Eyuboglu, “Combined equalization and coding using precoding,” IEEE Comm. Magazine, Dec. 1991.
 G. B. Giannakis, “Filterbanks for blind channel identification and equalization,” IEEE Sig. Proc. Lett., vol. 4, pp. 184–187, Jun. 1997.
 J. H. Manton, “Design and analysis of linear precoders under a mean square error crition, Part I: foundations and worst case design,” Systems and Control Lett., vol. 49, pp. 121–130, 2003.
 J. H. Manton, “Design and analysis of linear precoders under a mean square error crition, Part II: MMSE design and conclusions,” Systems and Control Lett., vol. 49, pp. 131–140, 2003.
 D. P. Palomar, M. A. Lagunas, and J. M. Cioffi, “Optimum linear joint transmit-receive processing for MIMO channels with qos constraints,” IEEE Trans. on Sig. Proc., vol. 52, pp. 1179–1197, May 2004.
 I. M. J.H. Manton and Y. Hua, “Affine precoders for reliable communications,” pp. 2749–2752, in Proc. of IEEE Inter. Conf. on Acoustics, Speech and Sig. Proc., Jun. 2000.
 S. Ohno and G. B. Giannakis, “Optimal training and redundant precoding for block transmissions with application to wireless OFDM,” IEEE Trans. Commun., vol. 50, pp. 2113–2123, Dec. 2002.
 A. Vosoughi and A. Scaglione, “Everything you always wanted to know about training: guidelines derived using the affine precoding framework and CRB,” IEEE Trans. on Signal Process., vol. 54, pp. 940–954, Mar. 2006.
 D. Pham and J. Manton, “Orthogonal superimposed training on linear precoding : a new affine precoder design,” pp. 445–449, IEEE 6-th Workshop of Sig. Proc. Advance in Wireless Comm., Jun. 2005.
 N. N. Tran, D. H. Pham, and H. D. Tuan, “Affine precoding and decoding MIMO frequency-selective fading channel for estimation and source detection,” in Proc. IEEE ISSPIT’06, pp. 749–754., Aug. 2006.
 C. Pirak, Z. Wang, K. Liu, and S. Jitapunkul, “Adaptive channel estimation using pilot-embedded data-bearing approach for MIMO-OFDM systems,” IEEE Trans. on Sig. Proc., vol. 54, pp. 4706–4715,, Dec. 2006.
 N. N. Tran, D. H. Pham, H. D. Tuan, and H. H. Nguyen, “Orthogonal affine precoding and decoding for channel estimation and source detection in MIMO frequency-selective fading channels,” IEEE Trans. Signal Process., vol. 57, pp. 1151–1162, Mar. 2009.
 S. M. Kay, Fundamentals of statistical signal processing, vol. I - estimation theory. Prentice Hall PTR, New Jersey 07458, 1993.