MIMO-OFDM

1
MIMO-OFDM

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

2
Diversity Coding

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

3
Coded MIMO-OFDM
T Number of OFDM symbols N Number of
subcarriers Mt Number of Tx Mr Number of Rx
Coding f S ? C
4
Code Rate
Ns The length of input data sequence S.

• Uncoded single-antenna OFDM R1 (NsN, T1)
• Alamouti Code R1 (N1, NsT2)
• Golden code R2 (N1, Ns4, T2) Belfiore,
  2005
• BLAST RMt (N1, NsMt , T1) Foschini, 1996

5
Diversity Gain vs. Coding Gain
-- Coding gain
-- Diversity gain
6
Optimal Coding

• Should guarantee maximum diversity gain
• Should achieve highest transmission rate
• Should have lowest decoding complexity
• No coding scheme could achieve all!
• 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 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.
• 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
OFDM subchannel

OFDM subchannel

2-Tx
j

j

k
k


l
l


m
m












OFDM block

OFDM block

Antenna 1

Antenna 2

W. Su, et. al., IEEE Trans. Signal Processing,
Nov. 2003.
9
Example of full-diversity SF coding
2-Tx R1
? is rotation matrix to generate signal space
diversity.
W. Su, et. al., IEEE Trans. Inf. Theory, Jan.
2005.
10
Example of full-diversity SF coding
2-Tx R2
? is a rotation matrix to generate signal space
diversity.
W. Zhang, X.-G. Xia, and P. C. Ching, IEEE Trans.
Commun., Jan. 2007.
11
STF Coded OFDM
12
Example of full-diversity STF coding
2-Tx For any 4 subcarriers R2
OFDM block-2
OFDM block-1
? is a rotation matrix to generate signal space
diversity.
Tx-2
Tx-1
W. Zhang, X.-G. Xia, and P. C. Ching, IEEE Trans.
Commun., Jan. 2007.
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. 29052916, 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.