Super-Orthogonal Space- Time BPSK Trellis Code Design for 4 Transmit Antennas in Fast Fading Channels Asli Birol Yildiz Technical University,Istanbul,Turkey Ümit Aygölü Istanbul Technical University, Istanbul,Turkey

2 Outline Introduction to Space-Time Codes Introduction to Space-Time Codes Design Criteria for Fast Fading Channels Design Criteria for Fast Fading Channels Super-Orthogonal Space-Time Trellis Codes Super-Orthogonal Space-Time Trellis Codes Code Design for Fast Fading Channel Code Design for Fast Fading Channel Simulation Results Simulation Results Conclusion 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 minimum sum-product distance  via computer program

10 Design Criteria Quasi-Static FadingFast Fading Diversity GainRank CriteriaEffective Code Length Coding GainDeterminant CriteriaSum-Product Distance

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 x 1 x 2 x 3 x 4 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 transmit antennas Reference Code 2  4-state BPSK SOSTTC designed for two transmit antennas regarding fast fading channel criteria

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…