1. Space Time Block Codes
Poornima Nookala

2. Outline Motivation Revisit MRRC Two transmit and one Receiver scheme
Two Transmit and Two receiver scheme
Performance of Alamouti’s Scheme
Basics of STBC
Design of codes
Capacity of STBC
Outage Capacity
Applications
Performance of STBC in Powerline and satellite Communication
Advantages
Implementation Issues

3. MOTIVATION
Mobile units are small, hence not optimal for receiver diversity
Decoding complexity limited by the Processor
Need for efficient open loop system
Simple encoding and decoding algorithms
Limited Power
Need for transmit diversity at base station

4. Revisit- MRRC
Received Signal:
Combiner:
Si will be selected iff:
[1]

5. Alamouti’s Scheme Three functions:
The encoding and transmission sequence
Combining sequence
Maximum likelihood decision region
[1]

6. 1. Encoding : For two branch transmission scheme
Alamouti’s Scheme
1. Encoding : For two branch transmission scheme
Time
Antenna 0
Antenna 1 t S0 S1
t+T
-S1*
S0*
Assume fading is constant for two consecutive symbol periods
Received signal is given by
[1]

7. Alamouti’s Scheme – Combining Sequence & Maximum likelihood Detection
2. Combining Sequences
(a)
Solving
(b)
3. Maximum likelihood detection is used to find the most probable symbols
[1]

8. Alamouti’s scheme- 2Tx & 2 Rx
Received signals
Combiner
Solving
[1]

9. Alamouti’s scheme- Performance
BER comparison of coherent BPSK with MRRC and STBC In Rayleigh fading
[1]

10. STBC
STBC is the generalized scheme developed by Alamouti to an arbitrary number of tx antennas
Encoding is represented by matrix
is linear combination of symbols
(repetition code)
Code Rate – If the block encodes k symbols, code rate = k/T
The decoding is same as Alamouti’s scheme

11. STBC
No coding scheme included here, contrary to Space time trellis code (STTCs) which provides both coding as well as diversity gain.
Orthogonal designs are used to construct STBC satisfying:
AiTAk+ AkTAi = [0],
AiTAi = I

12. Properties of Orthogonal Designs
There are two attractions in providing transmit diversity via orthogonal designs:
There is no loss in bandwidth, in the sense that orthogonal designs provide maximum possible transmission rate at full diversity
There is an extremely simple maximum- likelihood decoding algorithm which uses linear combination at the receiver.
[2]

13. Higher Order STBC for complex Constellations
Three Transmit antennas ,
Four Transmit antennas
[2]

14. Higher order STBC
Its proved that no code for more than 2 transmit antennas can achieve full rate.
For more than two antennas the maximum rate that can be achieved is ¾
Alamouti’s scheme is a special form of STBC which provides full diversity and rate
Quasi – Orthogonal codes – rate 1, but not orthogonal

15. Performance of STBC
Bit error probability versus SNR for space–time block codes at 3 bits/s/Hz; one receive antenna.

16. Capacity of STBC The block capacity for the channel is given by
The STBC capacity in bits per channel is
The difference in the capacity (ie) capacity loss:
Where P is the SNR
[2]

17. Capacity
Space time block codes are optimal with respect to capacity when:
Code rate is one
Channel rank is one
[2]

18. Capacity difference increases in SNR and number of antennas [2]

19. Outage Capacity
5%-outage capacity as a function of the average SNR at the receiver
(before decoding) for some uncorrelated MIMO ricean fading channels with
different number of antennas, code rates (R) and ricean-K factors (K).
[4]

20. Some Potential Applications
802.11n(hybrid scheme – STBC/SMX)
UTRA (Alamouti’s scheme)
Powerline Communication(PLC)
Satellite communication

21. Performance of STBC in PLC
Channel is assumed to be frequency selective, multipath fading with AWCN
BER performance of PLC using BPSK

22. Performance of STBC in Satellite Communication
Satellite channel for urban channel is modeled as combination Rayleigh and log normal process in presence of AWGN
BER performance of satellite channel using BPSK modulation

23. Advantages of STBC
Can achieve full diversity with linear processing at the receiver.
Open loop transmit diversity technique
Simple encoding and decoding
No bandwidth expansion

24. Issues Sensitivity to channel estimation error Delay Effects
Antenna Configurations
Soft failures
[1]

25. References
[1] S. M. Alamouti, “A simple transmitter diversity scheme for wireless communications,” IEEE J. Select. Areas Commun., vol. 16, pp. 1451–1458, Oct
[2] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Trans. Inform. Theory, vol. 45, pp. 1456–1467, July 1999.
[3] S. Sandhu and A. Paulraj, “Space-time block codes: A capacity perspective,” IEEE Commun. Lett., vol. 4, pp. 384–386, Dec
[4] Jes´us P´erez, Jes´us Ib´a˜nez, Luis Vielva, and Ignacio Santamar´ıa, “Closed-form Approximation for the Outage Capacity of Orthogonal STBC”, IEEE COMMUN LETTERS, VOL. 9, NO. 11, NOVEMBER 2005
[5] Anna Papaioannou, George D. Papadopoulos, and Fotini-NioviPavlidou, “Performance of Space-Time Block Coding in Powerline and Satellite Communications”, IEEE JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005

26. Questions ?