《OFDM技术开发系列》（英文版） sem04 06 01 King Lee[1]

Georgialnstitute of Technology CSIP Center for Sigmal Image pnocessing Space-Time and Space-Frequency Coded Orthogonal Frequency Division Multiplexing Transmitter Diversity Techniques King f. Lee

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

Georgia Institute of Technology Center for Signal and Image Processing 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

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 (OF DM) 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

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

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 ffT. x1-x2 Antenna#2:yt Georgia Institute of Technology Center for Signal and Image Processing

Georgia Institute of Technology Center for Signal and Image Processing 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: Space-Time Block Code - I * 1 2 x x − * 2 1 x x 1 2 2 * * 2 1 x x x x   =     − G

Space-Time Block Code -l The received signals are y=a,x+a2* 2+n y2==01X2+c2x1+n2 Calculate the decision variables as 米=a+2=(1P+1)x++n Vi-aly (a2+1)-h+an 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

Georgia Institute of Technology Center for Signal and Image Processing • 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. Space-Time Block Code - II ( ) ( ) 2 2 * * * 1 1 1 2 2 1 2 1 1 1 2 2 2 2 * * * 2 2 1 1 2 1 2 2 1 2 2 1 ˆ . ˆ x y y x x y y x                   = + = + + + = − = + − + 1 1 1 2 2 1 * * 2 1 2 2 1 2 . y x x y x x       = + + = − + +

OFDM Conventional orthogonal frequency division multiplexing(OFDM) system X(m)- serial to idFT h(n) Parallel X(n) Cyclic Prefix Prefix X(m) Parallel to serial qualizer( +Y(n) detector Removal det ann mator Georgia Institute of Technology Center for Signal and Image Processing

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

OFDM- 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

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)

OFDM- Assuming the channel response remains constant and G2L, the demodulated signal is given by Y(n)=A(n)X(n)+z(n),where A(n) is diagonal, or, equivalently, as Y(n,k)=a(n,)X(n,k)+Z(mn,k),0≤k≤K 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) OF DM with a cyclic prefix transforms a frequency selective fading channel into K decoupled and perfectly flat fading subchannels Georgia Institute of Technology Center for Signal and Image Processing

Georgia Institute of Technology Center for Signal and Image Processing OFDM - III • Assuming the channel response remains constant and G  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! Y(n n n n n ) = + Λ X Z Λ ( ) ( ) ( ) , where is diagonal, ( ) Y n k n k X n k Z n k k K ( , , , , , 0 1. ) = +   −  ( ) ( ) ( )

Space- Time Block-Coded OFDM- Space-time coding on two adjacent blocks of data symbols, i.e., X(n)and X(n+1) idFt h() Cycl Prefix Serial to X(m) Parallel idft h2 (n+1) Cyclic Prefix Parallel Combiner Pref to Serial&Detector (n+1) Removal det Channel Estimato Georgia Institute of Technology Center for Signal and Image Processing

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

Space-Time Block-Coded OFDM-ll 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 X(n+) Antenna#2: X(n+1) X(n) Georgia Institute of Technology Center for Signal and Image Processing

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 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)