Space Time Block Codes

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. Alamouti’s Scheme 1. Encoding : For two branch transmission scheme 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 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. 1998. [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. 2000. [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 COMMUNLETTERS, 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 ?