Space-Time and Space-Frequency Coded Orthogonal Frequency Division Multiplexing Transmitter...

Space-Time and Space-Frequency Coded

Orthogonal Frequency Division Multiplexing

Transmitter Diversity Techniques

King F. Lee

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 (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


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 2x x *

2 1x x

1 22 * *

2 1

x x

x x

G


• 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


• 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 - 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 - 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!

, where is diagonal,n n n n n Y Λ X Z Λ

, , , , , 0 1.Y n k n k X n k Z n k k K


• 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


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)


Tx2

h2(n)

- X(n+1)

X(n)

*

*


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)


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 1 and 2 remain constant, the demodulated vectors are

• Calculate

which yields

1 2* *

1 2

.e e o e

o o e o

Y Λ X Λ X Z

Y Λ X Λ X Z

* *1 2

* *2 1

ˆ,

ˆe e o

o e o

X Λ Y Λ Y

X Λ Y Λ Y

2 2

1 2 1 2

2 2

1 2 2 1

ˆ

.ˆ

e e e o

o o e o

X Λ Λ X Λ Z Λ Z

X Λ Λ X Λ Z Λ Z


STBC-OFDM Simulation Results

• STBC-OFDM achieves near optimal diversity gain in slow fading.

• Still outperforms non-diversity OFDM system at fD=100Hz.

0 5 10 15 20 25 30 35 4010

-8

10-6

10-4

10-2

100

Average Received SNR (dB)

Ave

rag

e B

it E

rro

r R

ate

fD

=10Hz; K=256

Single OFDM transmitter (simulated) STBC-OFDM transmitter diversity (simulated)Two-branch transmitter diversity (ideal)

0 5 10 15 20 25 30 35 4010

-8

10-6

10-4

10-2

100


Ave

rag

e B

it E

rro

r R

ate

fD

=20 and 100Hz; K=256

Single OFDM Transmitter; fD

=20Hz

Single OFDM Transmitter; fD

=100Hz

Two OFDM Transmitters; fD

=20Hz

Two OFDM Transmitters; fD

=100Hz


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

Space-Frequency Block-Coded OFDM - I

Serial to Parallel


Prefix Removal & DFT

X(m)

X1(n)

Space-Freq Decoder

X(m)

Channel Estimator

Tx1

Rx

h1(n)

Parallel to Serial Y(n)


Tx2

h2(n)

Space-Freq Encoder

X2(n)


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

1

2

,0 ,1 , 2 , 1,

,1 ,0 , 1 , 2

T

T

n X n X n X n K X n K

n X n X n X n K X n K

X

X

1, 1,

2, 2,

,.

,

e e o o

e o o e

n n n n

n n n n

X X X X

X X X X

,,0 ,1 , 2 , 1T

n X n X n X n K X n K X


Space-Frequency Block-Coded OFDM - III• The demodulated vector is

or, equivalently, as

• Calculate

• Assuming

yields

1 1 2 2 ,n n n n n n Y Λ X Λ X Z

*

1, 2,

*

2, 1,

ˆ.

ˆe e e o o

o e e o o

n n n n n

n n n n n

X Λ Y Λ Y

X Λ Y Λ Y

2 2

1, 2, 1, 2,

2 2

1, 2, 2, 1,

ˆ

.ˆ

e e e e e e o o

o o o o e e o o

X Λ Λ X Λ Z Λ Z

X Λ Λ X Λ Z Λ Z

1, 1, 2, 2,and ,e o e on n n n Λ Λ Λ Λ

1, 1, 2, 2,

1, 1, 2, 2,

.e e e e e e

o o o o o o

n n n n n n

n n n n n n

Y Λ X Λ X Z

Y Λ X Λ X Z


SFBC-OFDM Simulation Results - I

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

• SFBC-OFDM performs better in fast fading.

0 5 10 15 20 25 30 35 4010

-8

10-6

10-4

10-2

100


Ave

rag

e B

it E

rro

r R

ate

fD

=10Hz; K=512

Single OFDM transmitter (simulated) STBC-OFDM transmitter diversity (simulated)SFBC-OFDM transmitter diversity (simulated)Two-branch transmitter diversity (ideal)

0 5 10 15 20 25 30 35 4010

-8

10-6

10-4

10-2

100


Ave

rag

e B

it E

rro

r R

ate

fD

=100Hz; K=512

Single OFDM transmitter (simulated) STBC-OFDM transmitter diversity (simulated)SFBC-OFDM transmitter diversity (simulated)Two-branch transmitter diversity (ideal)


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.

102

103

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Me

an

Su

bca

rrie

r G

ain

Va

ria

tion

Block Size (K)

TUBU

0 5 10 15 20 25 30 35 4010

-8

10-6

10-4

10-2

100


Ave

rag

e B

it E

rro

r R

ate

fD

=10Hz; K=64

Single OFDM transmitter (simulated) SFBC-OFDM transmitter diversity (simulated)Two-branch transmitter diversity (ideal)


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.


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.

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