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

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. Tx h (n) IDFT & Serial to X X(m) (n) Cyclic Parallel Prefix Rx Prefix Parallel Equalizer Y X(m) (n) Removal to Serial & Detector & DFT Channel Estimator 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. Tx1 h1(n) IDFT & Cyclic Prefix * - X(n+1) X(n) Rx Serial to Parallel Tx2 X(m) h2(n) IDFT & Cyclic Prefix * X(n) X(n+1) Prefix Removal & DFT Parallel to Serial Combiner & Detector Y(n+1) Y(n) X(m) Channel Estimator Space-Time Block-Coded OFDM - I • Space-time coding on two adjacent blocks of data symbols, i.e., X(n) and X(n+1).

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(n+1) and transmits Antenna #1: X(n)-X*(n+1) Antenna #2: X(n+1)X*(n)

11. Space-Time Block-Coded OFDM - III • Denote X(n) as Xe and X(n+1) as Xo, and Y(n) as Ye and Y(n+1) as Yo. Assuming L1 and L2 remain constant, the demodulated vectors are • Calculate which yields

12. f =10Hz; K=256 D 0 0 10 10 -2 -2 10 10 -4 -4 Average Bit Error Rate 10 10 -6 -6 10 10 Single OFDM transmitter (simulated) STBC-OFDM transmitter diversity (simulated) Two-branch transmitter diversity (ideal) -8 -8 10 10 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Average Received SNR (dB) STBC-OFDM Simulation Results • STBC-OFDM achieves near optimal diversity gain in slow fading. • Still outperforms non-diversity OFDM system at fD=100Hz. f =20 and 100Hz; K=256 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)

13. Tx1 h1(n) IDFT & Cyclic Prefix X1(n) Rx Space-Freq Encoder Serial to Parallel Tx2 X(m) h2(n) IDFT & Cyclic Prefix X2(n) Prefix Removal & DFT Parallel to Serial Space-Freq Decoder Y(n) X(m) Channel Estimator 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 15~20% 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.