Asli Birol Yildiz Technical University,Istanbul,Turkey Ümit Aygölü

1. Super-Orthogonal Space-Time BPSK Trellis CodeDesign for 4 Transmit Antennasin Fast Fading Channels Asli Birol Yildiz Technical University,Istanbul,Turkey Ümit Aygölü Istanbul Technical University, Istanbul,Turkey

2. Outline • Introduction to Space-Time Codes • Design Criteria for Fast Fading Channels • Super-Orthogonal Space-Time Trellis Codes • Code Design for Fast Fading Channel • Simulation Results • Conclusion

3. Wireless Communication • Recent trends in wireless communication • Rapid growth in the number of wireless subscribers • Increasing demand for multimedia applications • Wireless channel impairments • Fading • Limited Bandwidth • Dynamism (random access, mobility) • Limited power (at least on one end) • Interference

4. Diversity Techniques • Diversity: • Primary technique used to improve performance on a fading channel. • Main idea is to provide the receiver with multiple versions of the same transmit signal over independent channels. • How to create independent channels needed for diversity? • Frequency Diversity • Time Diversity • Space Diversity

5. Why Transmit Diversity? • In downlink, • Receive diversity is difficult to implement • Requires multiple antennas and additional processing at the mobile station • Not suitable due to size and battery power limitation at mobile • Put additional processing and complexity at the base station => Transmit Diversity

6. Transmit Diversity • Close loop transmit diversity • Requires feedback of channel from the receiver to the transmitter • Open loop transmit diversity • No need for feedback • ex: Delay diversity • an ancestor of space-time trellis codes. • Main idea:Transmission of same information from transmit antennas simultaneously with different delays

7. Space-Time Coding (STC) • Significance: First systematic treatment of coding for achieving (open-loop) transmit diversity • Objective: To achieve full M×N diversity without channel knowledge at transmitter and to maximize coding gain as a secondary criteria

8. Design Criteria for Fast Fading Channels • transmitted symbol sequence • erroneously decided symbol sequence • pairwise error probability (c,e) : the set of time instances that c and e differ l:number of elements in (c,e) :sum-product distance

9. Design Criteria for Fast Fading Channels • maximize the minimum l • parallel transitions between any state pair are avoided. • the shortest error event path will have two steps • maximize the minimumsum-product distance • via computer program

10. Design Criteria

11. Space Time Codes • ST Trellis Code: • Full diversity as well as coding gain. • No systematic code design method. • ST Block Code (OSTBC): • Full diversity, simple decoding. • No coding gain. • TCM + OSTBC • Rate loss • SOSTTC • Motivation : find a systematic design method for space time code to achieve full diversity, more coding gain, and no rate loss.

12. Super-Orthogonal ST Trellis Codes • OSTBC does not use all orthogonal matrice, use all of them to do TCM • Ex. 2 transmit antennas, BPSK

13. Super-Orthogonal ST Trellis Codes • A super-orthogonal code is defined as • an extension of orthogonal design code • does not extend the constellation alphabet of the transmitted signals • does expand the number of available orthogonal matrices.

14. Super-Orthogonal ST Trellis Codes • The coding procedure can be departed into 2 step: • set partitioning for super-orthogonal code • construct trellis code using the super-orthogonal code

15. Orthogonal Designs • Full-rate orthogonal designs with complex symbols are impossible for more than two transmit antennas. • Alamouti’s scheme • a full-rate N×N real orthogonal design only exists for N=2,4,8.

16. Orthogonal Designs • example of a 4×4 real orthogonal design :

17. Orthogonal Designs • To expand the number of orthogonal matrices phase rotations can be used as follows: • In general, for N transmit antennas, N-1rotations can be used.

18. Code Design • i {0, } , i=1,2,3. • Set partitioning based on sum-product distance. • Best result is obtained using (1,2,3)=(0,0,0) and (1,2,3)=(,,). • the orthogonal matrices are denoted by • i=1,2 represents (1,2,3) = (0,0,0) and (1,2,3) = (,,), respectively • j= 1,2,…,16 denotes all realizations of the binary codeword x1x2x3x4 as 0000, 1111, 0011, 1100, 0101, 1010, 0110, 1001, 0001, 1110, 0010, 1101, 0100,1011, 1111, 1000, respectively, which are mapped to the BPSK symbols by the rule 0-1, 11

19. 16-state BPSK SOSTTC • Space-time symbol wise Hamming distance =8 • Sum-product distance = 32

20. Simulation Results • Properties of the system considered • 4 transmit and 1 receive antenna • 130 symbol/frame from each transmit antenna • fast fading channel • the signals received from different transmit antennas experience independent fading

21. Simulation Results • For the case of 4 transmit antennas, any BPSK SOSTTC designed according to fast fading channel criteria is not available in the literature. • Reference Code 1 • 2-state BPSK SOSTTC designed according to quasi-static fading channel criteria for four transmitantennas • Reference Code 2 • 4-state BPSK SOSTTC designedfor two transmit antennas regarding fast fading channelcriteria

22. Simulation Results • performances of proposed 16-state BPSK SOSTTC and reference codes on Rayleigh fast fading channels

23. Conclusion • a new BPSK SOSTTC designed for four transmit antennas in fast fading channels is proposed. • The new code provides full rate, full diversity, and high coding gain. • Comparison of Coding gain : SOSTTC > STTC > STBC • Simulation results confirm that the proposed code offer a better performance compared to their counterparts given in the literature. • The research is restricted to BPSK scheme, since full-rate complex orthogonal designs for four transmit antennas does not exist. • Allowing a decrease in rate or using quasiorthogonal transmission matrices, the research can be expanded to complex constellation schemes.

24. Thank you for your attention… abirol@yildiz.edu.tr