SpaceTime and SpaceFrequency Coded Orthogonal Frequency Division Multiplexing

Space-Time and Space-Frequency Coded Orthogonal Frequency Division Multiplexing Transmitter Diversity Techniques King F. Lee

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. Georgia Institute of Technology Center for Signal and Image Processing

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 Georgia Institute of Technology Center for Signal and Image Processing

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: Georgia Institute of Technology Antenna #2: Center for Signal and Image Processing

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. Georgia Institute of Technology Center for Signal and Image Processing

OFDM - I • Conventional orthogonal frequency division multiplexing (OFDM) system. Tx X(m) Serial to Parallel to Serial X(n) Equalizer & Detector h (n) IDFT & Cyclic Prefix Rx Y(n) Prefix Removal & DFT Channel Estimator Georgia Institute of Technology Center for Signal and Image Processing

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). Georgia Institute of Technology Center for Signal and Image Processing

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 frequencyselective fading channel into K decoupled and perfectly flat fading subchannels! Georgia Institute of Technology Center for Signal and Image Processing

Space-Time Block-Coded OFDM - I • Space-time coding on two adjacent blocks of data symbols, i. e. , X(n) and X(n+1). Tx 1 * - X(n+1) X(m) Serial to Parallel to Serial * X(n) Combiner & Detector X(n) X(n+1) Y(n) IDFT & Cyclic Prefix Y(n+1) h 1(n) Rx Tx 2 h 2(n) Prefix Removal & DFT Channel Estimator Georgia Institute of Technology Center for Signal and Image Processing

Space-Time Block-Coded OFDM - II • Combine space-time block code with OFDM to achieve spatial diversity gain over frequencyselective 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) Georgia Institute of Technology Center for Signal and Image Processing

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 L 1 and L 2 remain constant, the demodulated vectors are • Calculate which yields Georgia Institute of Technology Center for Signal and Image Processing

STBC-OFDM Simulation Results f =10 Hz; K=256 Average Bit Error Rate 10 10 f =20 and 100 Hz; K=256 D 0 10 -2 10 Average Bit Error Rate 10 -4 -6 10 10 Single OFDM transmitter (simulated) STBC-OFDM transmitter diversity (simulated) Two-branch transmitter diversity (ideal) -8 0 5 10 15 20 25 30 Average Received SNR (d. B) 35 40 10 D 0 -2 -4 -6 Single OFDM Transmitter; f =20 Hz D Single OFDM Transmitter; f =100 Hz D Two OFDM Transmitters; f =20 Hz D Two OFDM Transmitters; f =100 Hz D -8 0 5 10 15 20 25 30 Average Received SNR (d. B) 35 40 • STBC-OFDM achieves near optimal diversity gain in slow fading. • Still outperforms non-diversity OFDM system at f. D=100 Hz. Georgia Institute of Technology Center for Signal and Image Processing

Space-Frequency Block-Coded OFDM - I • Coding on adjacent DFT frequency bins of each block of X(n). Tx 1 X 1(n) X(m) Serial to Parallel to Serial Space-Freq Encoder Space-Freq Decoder IDFT & Cyclic Prefix X 2(n) IDFT & Cyclic Prefix Y(n) Prefix Removal & DFT h 1(n) Rx Tx 2 h 2(n) Channel Estimator Georgia Institute of Technology Center for Signal and Image Processing

Space-Frequency Block-Coded OFDM - II • Space-frequency encoder codes each data vector X(n), into two vectors X 1(n) and X 2(n) as or in terms of the even and odd polyphase vectors as Georgia Institute of Technology Center for Signal and Image Processing

Space-Frequency Block-Coded OFDM - III • The demodulated vector is or, equivalently, as • Calculate • Assuming yields Georgia Institute of Technology Center for Signal and Image Processing

SFBC-OFDM Simulation Results - I • SFBC-OFDM achieves similar diversity gain as STBC-OFDM in slow fading. • SFBC-OFDM performs better in fast fading. Georgia Institute of Technology Center for Signal and Image Processing

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. Georgia Institute of Technology Center for Signal and Image Processing

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 spacefrequency 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. Georgia Institute of Technology Center for Signal and Image Processing

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. Georgia Institute of Technology Center for Signal and Image Processing