SpaceTime and SpaceFrequency Coded Orthogonal Frequency Division Multiplexing Transmitter Diversity

1
Space-Time and Space-Frequency Coded Orthogonal
Frequency Division Multiplexing Transmitter
Diversity Techniques

• King F. Lee

2
Introduction

• Frequency-selective fading is a dominant
  impairment in mobile communications.
• Fading reduces receive signal-to-noise ratio and
  degrades the bit-error-rate (BER).
• Frequency selectivity of the channel, i.e., delay
  spread, induces inter-symbol interference (ISI).
• To combat frequency-selective fading, diversity
  techniques must be resilient to ISI.
• Transmitter diversity techniques are attractive,
  especially for portable receivers where current
  drain and physical size are important constraints.

3
Background

• Space-time block coding has emerged as an
  efficient means of achieving near optimal
  transmitter diversity gain Alamouti 98,Tarokh
  99.
• Existing implementations are sensitive to delay
  spreads and, therefore, are limited to flat
  fading environments, such as indoor wireless
  networks.
• Orthogonal frequency division multiplexing (OFDM)
  with a sufficiently long cyclic prefix can
  convert frequency-selective fading channels into
  multiple flat fading subchannels.
• Combine space-time block code and OFDM

4
Space-Time Block Code - I

• Example
• Assume two transmit antennas and one receive
  antenna.
• The space-time block code transmission matrix is
• For each pair of symbols transmit
• Antenna 1 Antenna 2

5
Space-Time Block Code - II

• The received signals are
• Calculate the decision variables as
• Similar to that of a two-branch maximal ratio
  combining receiver diversity system!
• Unfortunately, the technique is sensitive to
  delays.

6
OFDM - I

• Conventional orthogonal frequency division
  multiplexing (OFDM) system.

7
OFDM - II

• Serial to parallel converter collects K serial
  data symbols X(m) into a data block or vector
  X(n).
• X(n) is modulated by an IDFT into OFDM symbol
  vector x(n).
• A length G cyclic prefix is added to x(n) and
  transmitted through a frequency-selective channel
  h(n) of order L.
• At the receiver, the cyclic prefix is removed
  from the received signal and the remaining signal
  is demodulated by an DFT into Y(n).

8
OFDM - III

• Assuming the channel response remains constant
  and G ³ L, the demodulated signal is given by
• or, equivalently, as
• Besides the noise component, the demodulated
  symbol Y(n,k) is just the product of the complex
  gain and the corresponding data symbol X(n,k).
• OFDM with a cyclic prefix transforms a
  frequency-selective fading channel into K
  decoupled and perfectly flat fading subchannels!

9
Space-Time Block-Coded OFDM - I

• Space-time coding on two adjacent blocks of data
  symbols, i.e., X(n) and X(n1).

10
Space-Time Block-Coded OFDM - II

• Combine space-time block code with OFDM to
  achieve spatial diversity gain over
  frequency-selective fading channels.
• In effect, apply space-time coding on blocks of
  data symbols instead of individual symbols.
• Space-time encoder takes two data vectors X(n)
  and X(n1) and transmits
• Antenna 1 X(n) -X(n1)
• Antenna 2 X(n1) X(n)

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Space-Time Block-Coded OFDM - III

• Denote X(n) as Xe and X(n1) as Xo, and Y(n) as
  Ye and Y(n1) as Yo. Assuming L1 and L2 remain
  constant, the demodulated vectors are
• Calculate
• which yields

12
STBC-OFDM Simulation Results
f
20 and 100Hz K256
D
Average Bit Error Rate
Single OFDM Transmitter f
20Hz
D
Single OFDM Transmitter f
100Hz
D
Two OFDM Transmitters f
20Hz
D
Two OFDM Transmitters f
100Hz
D
Average Received SNR (dB)

• STBC-OFDM achieves near optimal diversity gain in
  slow fading.
• Still outperforms non-diversity OFDM system at
  fD100Hz.

13
Space-Frequency Block-Coded OFDM - I

• Coding on adjacent DFT frequency bins of each
  block of X(n).

14
Space-Frequency Block-Coded OFDM - II

• Space-frequency encoder codes each data vector
  X(n),
• into two vectors X1(n) and X2(n) as
• or in terms of the even and odd polyphase
  vectors as

15
Space-Frequency Block-Coded OFDM - III

• The demodulated vector is
• or, equivalently, as
• Calculate
• Assuming
• yields

16
SFBC-OFDM Simulation Results - I

• SFBC-OFDM achieves similar diversity gain as
  STBC-OFDM in slow fading.
• SFBC-OFDM performs better in fast fading.

17
SFBC-OFDM Simulation Results - II

• STBC-OFDM is more sensitive to channel gain
  variation over time.
• SFBC-OFDM is more sensitive to channel gain
  variation over frequency.

18
Future Work

• The cyclic prefix for OFDM can require up to
  1520 bandwidth overhead. It is desirable to
  develop techniques that eliminate or reduce the
  cyclic prefix.
• Channel estimation techniques for space-time and
  space-frequency coded OFDM systems.
• Consider combining space-time codes with other
  transforms to achieve other desirable
  characteristics such as better performance in
  fast fading environments.
• Investigate optimum combination of
  error-correction code with STBC-OFDM and
  SFBC-OFDM systems.
• Study the co-channel interference performance of
  STBC and SFBC-OFDM systems.

19
References

• S. M. Alamouti, A simple transmitter diversity
  scheme for wireless communications, IEEE J.
  Select. Areas Commun., vol. 16, no. 8, pp.
  1451-1458, Oct. 1998.
• V. Tarokh, H. Jafarkhani, and A. R. Calderbank,
  Space-time block coding for wireless
  communications performance results, IEEE J.
  Select. Areas Commun., vol. 17, no. 3, pp.
  451-460, March 1999.
• K. F. Lee and D. B. Williams, A space-time coded
  transmitter diversity technique for frequency
  selective fading channels, in Proc. IEEE Sensor
  Array and Multichannel Signal Processing
  Workshop, Cambridge, MA, March 2000, pp. 149-152.
• K. F. Lee and D. B. Williams, A Space-Frequency
  Transmitter Diversity Technique for OFDM
  Systems, in Proc. IEEE GLOBECOM, San Francisco,
  CA, November 2000, pp. 1473-1477.
• K. F. Lee and D. B. Williams, A Multirate
  Pilot-Symbol-Assisted Channel Estimator for OFDM
  Transmitter Diversity Systems, in Proc. IEEE
  ICASSP, Salt Lake City, UT, May 2001.