V-OFDM: On Performance Limits over Multi-Path Rayleigh Fading Channels

As a bridge of connecting orthogonal frequency division multiplexing (OFDM) with single-carrier frequency domain equalization (SC-FDE) techniques, Vector OFDM (V-OFDM) provides significant flexibility in system design. This paper presents an analytical study of V-OFDM over multi-path fading channels. Our goal is to investigate the diversity gain and coding gain of each vector block (VB) in V-OFDM so as to ultimately reveal its performance limits over fading channel. By using algebraic number theory tools, we rigorously prove for the first time that a majority of VBs in V-OFDM can surely realize the diversity gain of min {M,G} , where M is the length of each VB, and G is the total number of channel taps. Furthermore, some specific VBs, whose length equals the total number of channel taps, can not only harvest the maximum diversity gain but also achieve the maximum coding gain. It is further demonstrated that, even though VBs fail to benefit from additional diversity gain when M exceeds G, they can enjoy significantly increased coding gains. Our analysis concludes that it is preferable to choose the length of VBs to be equal to the number of channel taps in consideration of both overall system performance and computational complexity.

[1]  Georgios B. Giannakis,et al.  Complex-field coding for OFDM over fading wireless channels , 2003, IEEE Trans. Inf. Theory.

[2]  David J. Goodman,et al.  Peak-To-Average Power Ratio of Single Carrier FDMA Signals with Pulse Shaping , 2006, 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications.

[3]  David Falconer,et al.  Frequency domain equalization for single-carrier broadband wireless systems , 2002, IEEE Commun. Mag..

[4]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5]  Genyuan Wang,et al.  On optimal multilayer cyclotomic space-time code designs , 2005, IEEE Transactions on Information Theory.

[6]  Xiang-Gen Xia.  Precoded OFDM systems robust to spectral null channels and vector OFDM systems with reduced cyclic prefix length , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[7]  B. R. Saltzberg.  Comparison of single-carrier and multitone digital modulation for ADSL applications , 1998 .

[8]  K. J. Ray Liu,et al.  Full-rate full-diversity space-frequency codes with optimum coding advantage , 2005, IEEE Transactions on Information Theory.

[9]  J.A.C. Bingham,et al.  Multicarrier modulation for data transmission: an idea whose time has come , 1990, IEEE Communications Magazine.

[10]  Jean-Claude Belfiore,et al.  Algebraic tools to build modulation schemes for fading channels , 1997, IEEE Trans. Inf. Theory.

[11]  Stefan Parkvall,et al.  LTE: the evolution of mobile broadband , 2009, IEEE Communications Magazine.

[12]  Georgios B. Giannakis,et al.  Space-time diversity systems based on linear constellation precoding , 2003, IEEE Trans. Wirel. Commun..

[13]  R. Kalbasi,et al.  Single-carrier frequency domain equalization , 2008, IEEE Signal Processing Magazine.

[14]  Ying Chen,et al.  Asymmetric OFDM Systems Based on Layered FFT Structure , 2007, IEEE Signal Processing Letters.

[15]  Takeshi Hashimoto,et al.  Constellation-rotated vector OFDM and its performance analysis over rayleigh fading channels , 2010, IEEE Transactions on Communications.

[16]  Geoffrey Ye Li,et al.  OFDM and Its Wireless Applications: A Survey , 2009, IEEE Transactions on Vehicular Technology.

[17]  Xiang-Gen Xia,et al.  Systematic and optimal cyclotomic lattices and diagonal space-time block code designs , 2004, IEEE Transactions on Information Theory.

[18]  Liara Aparecida dos Santos Leal,et al.  Diagonalization and spectral decomposition of factor block circulant matrices , 1988 .

[19]  Xiang-Gen Xia.  Precoded and vector OFDM robust to channel spectral nulls and with reduced cyclic prefix length in single transmit antenna systems , 2001, IEEE Trans. Commun..

[20]  L.J. Cimini,et al.  Synchronization techniques and guard-band-configuration scheme for single-antenna vector-OFDM systems , 2005, IEEE Transactions on Wireless Communications.

[21]  A. Robert Calderbank,et al.  Space-Time Codes for High Data Rate Wireless Communications : Performance criterion and Code Construction , 1998, IEEE Trans. Inf. Theory.

[22]  Georgios B. Giannakis,et al.  Linear constellation-precoding for OFDM with maximum multipath diversity and coding gains , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[23]  Seung Hee Han,et al.  An overview of peak-to-average power ratio reduction techniques for multicarrier transmission , 2005, IEEE Wireless Communications.

[24]  Emanuele Viterbo,et al.  Signal Space Diversity: A Power- and Bandwidth-Efficient Diversity Technique for the Rayleigh Fading Channel , 1998, IEEE Trans. Inf. Theory.

[25]  Xiang-Gen Xia,et al.  Precoded OFDM with Adaptive Vector Channel Allocation for Scalable Video Transmission over Frequency-Selective Fading Channels , 2002, IEEE Trans. Mob. Comput..

[26]  Björn E. Ottersten,et al.  On the complexity of sphere decoding in digital communications , 2005, IEEE Transactions on Signal Processing.

[27]  Marc Moeneclaey,et al.  BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise , 1995, IEEE Trans. Commun..

[28]  S. Lang.  Algebraic Number Theory , 1971 .

[29]  Xiang-Gen Xia,et al.  Iterative decoding and demodulation for single-antenna vector OFDM systems , 2006, IEEE Transactions on Vehicular Technology.