Pilot Placement for Time-Varying MIMO OFDM Channels with Virtual Subcarriers

Alieh Moradi, Hamidreza Bakhshi, Vahid Najafpoor

.

DOI: 10.4236/cn.2011.31005                

Abstract

The rapid time-variation of a fading multipath environment can impair the performance of multiple-input multiple-output orthogonal frequency division multiplexing (MIMO OFDM). This paper proposes a pilot placement method for MIMO OFDM systems under time-varying channels with the guard band. The time-varying channel is described by complex exponential basis expansion model (BEM). We discuss the least square (LS) channel estimation to obtain the minimum mean square error (MSE) and derive the pilot allocation that can satisfy the minimum MSE with regard to guard band in time-varying channels. It is shown that optimal pilot clusters can distribute non-uniformly in frequency domain and minimize the MSE. We generalize our scheme over G OFDM symbols and compare it with comb pilots. It is demonstrated that the proposed approach is more effective than previous work. Simulation results validate our theoretical analysis.

Keywords

Guard Band, MIMO OFDM, Pilot, Time-Varying Channel, Virtual Subcarriers

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. Jankiraman, “Space-Time Codes and MIMO Systems,” Artech House, London, 2004.
[2]	I. Barhumi, G. Leus and M. Moonen, “Optimal Training Design for MIMO OFDM Systems in Mobile Wireless Channels,” IEEE Transactions on Signal Processing, Vol. 51, No. 6, June 2003, pp. 1615-1624. doi:10.1109/TSP. 2003.811243
[3]	J. Manton, “Optimal Training Sequences and Pilot Tones for OFDM Systems,” IEEE Communications Letters, Vol. 5, No. 4, April 2001, pp. 151-153. doi:10.1109/4234.9170 97
[4]	S. Adireddy, L. Tong and H. Viswanathan, “Optimal Placement of Training for Frequency-Selective Block- Fading Channels,” IEEE Transactions on Information Theory, Vol. 48, No. 8, August 2002, pp. 2338-2353. doi:10.1109/TIT.2002.800466
[5]	M. Dong, and L. Tong, “Optimal Design and Placement of Pilot Symbols for Channel Estimation,” IEEE Tran- sactions on Signal Processing, Vol. 50, No. 12, 2002, pp. 3055-3069. doi:10.1109/TSP.2002.805504
[6]	S. Adireddy, L. Tong and H. Viswanathan, “Optimal Embedding of Known Symbols for OFDM,” Proceedings of ICASSP’01, Vol. 4, 2001, pp. 2393-2396.
[7]	R. Negi and J. Cioffi, “Pilot Tone Selection for Channel Estimation in a Mobile OFDM System,” IEEE Transac- tions on Consumer Electronics, Vol. 44, No. 3, August 1998, pp. 1122-1128. doi:10.1109/30.713244
[8]	Hu, L. Yang, Y. Shi and L. He, “Optimal Pilot Sequence Design for Channel Estimation in MIMO OFDM Systems,” IEEE Communications Letters, Vol. 10, No. 1, January 2006, pp. 1-3. doi:10.1109/LCOMM.2006.1576 550
[9]	D. L. Xinming and W. Fang, “A New Algorithm for Solving Systems of Linear Inequalities,” ACTA Mathe- maticae Applicatae sinica, Vol. 18, July 1995, pp. 340- 343.
[10]	Z. Lu, and J. H. Ge, “Time-Domain Training Sequences Design for MIMO OFDM Channel Estimation,” Journal of Zhejiang University SCIENCE A, Vol. 9, No. 4, December 2007, pp .464-469.
[11]	H. Minn and N. Al-Dhahir, “Optimal Training Signals for MIMO OFDM Channel Estimation,” IEEE Transactions on Wireless Communications, Vol. 5, No. 5, May 2006, pp. 1158-1168.
[12]	X. Ma, L. Yang, and G. Giannakis, “Optimal Training for MIMO Frequency-Selective Fading Channels,” IEEE Transactions on Wireless Communications, Vol. 4, No. 2, March 2005, pp. 453-466. doi:10.1109/TWC.2004.8429 98
[13]	M. K. Tsatsanis and Z. Xu, “Pilot Symbol Assisted Modulated in Frequency Selective Fading Wireless Channels,” IEEE Transactions on Signal Processing, Vol. 48, No. 8, August 2000, pp. 2353-2365. doi:10.1109/78. 852 016
[14]	X. Wu and G. Kang, “Pilot Sequence Design Scheme for MIMO OFDM Systems under Time-Varying Channels,” IEEE Wireless Communication Conference, Singapore, May 2008, pp. 777-781.
[15]	X. Dai, “Optimal Training Design for Linearly Time- Varying MIMO/OFDM Channels Modeled by a Complex Exponential Basis Expansion,” IET Communications, Vol. 1, No. 5, 2007, pp. 945-953. doi:10.1049/iet-com:200453 01
[16]	T. Wang, C. Li and H. Chen, “Basis Expansion Model and Doppler Diversity Techniques for Frequency Domain Channel Estimation and Equalization in DS-CDMA Systems,” Proceedings of ICC’07, 2007, pp. 4907-4912.
[17]	A. Gorokhov and J. P. Linnartz, “Robust OFDM Receivers for Dispersive Time-Varying Channels: Equalization and Channel Acquisition,” IEEE Transactions on Communications, Vol. 52, No. 4, 2004, pp. 572-583. doi:10. 1109/TCOMM.2004.826354
[18]	W. Hou and B. Chen, “ICI Cancellation for OFDM Communication Systems in Time-Varying Multipath Fading Channels,” IEEE Transactions on Wireless Communications, Vol. 4, No. 5, 2005, pp. 2100-2110. doi:10.1109/ TWC.2005.853837
[19]	I. Cosovic and G. Auer, “Capacity Achieving Pilot Design for MIMO-OFDM over Time-Varying Frequency- Selective Channels,” Proceedings of ICC’07, 2007, pp. 779-784.
[20]	J. K. Tugnait and W. Luo, “Linear Prediction Error Method for Blind Denti?cation of Periodically Time- Varying Channels,” IEEE Transactions on Signal Processing, Vol. 50, No. 12, 2002, pp. 3070-3082. doi:10. 1109/TSP.2002.805493
[21]	D. K. Borah and B. D. Hart, “Frequency-Selective Fading Channel Estimation with a Polynomial Time-Varying Channel Model,” IEEE Transactions on Communications, Vol. 47, No. 6, 1999, pp. 862-873. doi:10.1109/26.771 34 3
[22]	X. Ma, G. B. Giannakis and B. Lu, “Block Differential Encoding for Rapidly Fading Channels,” IEEE Transac- tions on Communications, Vol. 52, No. 3, 2004, pp. 416- 425. doi:10.1109/TCOMM.2004.823604
[23]	S. Song and A. Singer, “Pilot-Aided OFDM Channel Estimation in the Presence of the Guard Band,” IEEE Transactions on Communications, Vol. 55, No. 8, August 2007, pp. 1459-1465. doi:10.1109/TCOMM.2007.902526
[24]	S. M. Kay, “Fundamentals of Statistical Signal Processing: Estimation Theory,” Prentice Hall PTR, Upper Saddle River, 1993.