1. MIMO-OFDM MIMO MIMO High diversity gain (space-time coding) High diversity gain (space-time coding) High multiplexing gain (BLAST) High multiplexing gain (BLAST) OFDM OFDM Bandwidth efficient Bandwidth efficient Robust to multipath fading thanks to cyclic prefix Robust to multipath fading thanks to cyclic prefix Easy to implement thanks to the IFFT/FFT Easy to implement thanks to the IFFT/FFT Flexible in resource allocation Flexible in resource allocation

2. Diversity & Coding Diversity in space, time and frequency Diversity in space, time and frequency Antenna diversity (space) Antenna diversity (space) Delay diversity (time) Delay diversity (time) Multipath diversity (frequency) Multipath diversity (frequency) Coding over space, time and frequency Coding over space, time and frequency Space-time (ST) coding Space-time (ST) coding Space-frequency (SF) coding Space-frequency (SF) coding Space-time-frequency (STF) coding Space-time-frequency (STF) coding

3. Coded MIMO-OFDM T: Number of OFDM symbols N: Number of subcarriers M t : Number of Tx M r : Number of Rx Coding f: S  C

4. Code Rate N s : The length of input data sequence S.  Uncoded single-antenna OFDM: R=1 (N s =N, T=1)  Alamouti Code: R=1 (N=1, N s =T=2)  Golden code: R=2 (N=1, N s =4, T=2) [Belfiore, 2005]  BLAST: R=M t (N=1, N s =Mt, T=1) [Foschini, 1996]

5. Diversity Gain vs. Coding Gain -- Coding gain -- Diversity gain

6. Optimal Coding 1. Should guarantee maximum diversity gain 2. Should achieve highest transmission rate 3. Should have lowest decoding complexity No coding scheme could achieve all! No coding scheme could achieve all! Code design is indeed to get a better tradeoff among 1- 3. Code design is indeed to get a better tradeoff among 1- 3.

7. ST Coded OFDM The conventional ST code is directly applied to MIMO- OFDM by viewing each subchannel as a virtual antenna. The conventional ST code is directly applied to MIMO- OFDM by viewing each subchannel as a virtual antenna. The ST coding for MIMO-OFDM is indeed coding across antennas and OFDM blocks on the same subchannel. The ST coding for MIMO-OFDM is indeed coding across antennas and OFDM blocks on the same subchannel. ST-OFDM cannot guarantee the exploitation of multipath diversity. ST-OFDM cannot guarantee the exploitation of multipath diversity. With a mapping structure, an ST code design is proposed to achieve full-diversity and admit simple ML decoding [Zhang, Xia, and Ching, ICASSP2006] With a mapping structure, an ST code design is proposed to achieve full-diversity and admit simple ML decoding [Zhang, Xia, and Ching, ICASSP2006] W. Zhang, X.-G. Xia, and P. C. Ching, IEEE Trans. Wireless Commun., May 2007

8. Full-diversity SF coding via repetition mapping, Su et al 2003 2-Tx W. Su, et. al., IEEE Trans. Signal Processing, Nov. 2003. OFDM subchannel OFDM block k  Antenna 1  l OFDM subchannel OFDM block k  Antenna 2  l j m j m 2 -x n  1 x * n  x 1 x 2 * x 1 x 2 * 2 1 x *

9. Example of full-diversity SF coding 2-Tx R=1 W. Su, et. al., IEEE Trans. Inf. Theory, Jan. 2005.  is rotation matrix to generate signal space diversity.

10. Example of full-diversity SF coding 2-Tx R=2 W. Zhang, X.-G. Xia, and P. C. Ching, IEEE Trans. Commun., Jan. 2007.  is a rotation matrix to generate signal space diversity.

11. STF Coded OFDM

12. Example of full-diversity STF coding W. Zhang, X.-G. Xia, and P. C. Ching, IEEE Trans. Commun., Jan. 2007.  is a rotation matrix to generate signal space diversity. Tx-1 Tx-2 OFDM block-1 OFDM block-2 2-Tx For any 4 subcarriers R=2

13. Performance Comparison 2x2 MIMO-OFDM (64-pt FFT) system at 4 bps/Hz in block fading channels. STF coding achieves a higher diversity gain than SF coding.

14. Performance Comparison

15. Some Papers to Read W. Zhang, X.-G. Xia, and K. B. Letaief, Space-Time/Frequency Coding for MIMO-OFDM in Next Generation Broadband Wireless Systems, IEEE Wireless Communications, Special Issue on Next Generation CDMA vs. OFDMA for 4G Wireless Applications, vol. 14, no. 3, 2007. This is a tutorial paper. H. Bolcskei and A. Paulraj, “Space-frequency codes for broadband fading channels,” in Proc. IEEE Int. Symp. Inf. Theory, Washington, DC, June 24-29, 2001, p. 219. W. Su, Z. Safar, M. Olfat, and K. J. R. Liu, “Obtaining full-diversity space-frequency codes from space-time codes via mapping,” IEEE Trans. Signal Processing, vol. 51, pp. 2905– 2916, Nov. 2003. W. Zhang, X.-G. Xia, and P. C. Ching, “High-rate full-diversity space-time-frequency codes for broadband MIMO block fading channels,” IEEE Trans. Commun., vol. 55, pp. 25-34, Jan. 2007. W. Zhang, X.-G. Xia, and P. C. Ching, Full-diversity and fast ML decoding properties of general orthogonal space-time block codes for MIMO-OFDM systems, IEEE Trans. on Wireless Communications, May 2007. Zhefeng Li and X.-G. Xia, PAPR Reduction for Repetition Space-Time-Frequency Coded MIMO-OFDM Systems Using Chu Sequences, IEEE Trans. on Wireless Communications, April 2008. Zhefeng Li and X.-G. Xia, Single-Symbol ML Decoding for Orthogonal and Quasi- Orthogonal STBC in Clipped MIMO-OFDM Systems Using A Clipping Noise Model, IEEE Trans. on Communications, July 2008.