SuperOrthogonal Space Time BPSK Trellis Code Design for

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 1

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

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

Diversity Techniques n 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? n n n Frequency Diversity Time Diversity Space Diversity 4

Why Transmit Diversity? n 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 ¨ n Put additional processing and complexity at the base station => Transmit Diversity 5

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

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

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

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

Design Criteria Quasi-Static Fading Fast Fading Diversity Gain Rank Criteria Effective Code Length Coding Gain Determinant Criteria Sum-Product Distance 10

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

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

Super-Orthogonal ST Trellis Codes n 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. 13

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

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

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

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

Code Design n i {0, } , i=1, 2, 3. n 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 n n ¨ 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 18

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

Simulation Results n 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 20

Simulation Results n n 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 quasistatic fading channel criteria for four transmit antennas n Reference Code 2 ¨ 4 -state BPSK SOSTTC designed for two transmit antennas regarding fast fading channel criteria 21

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

Conclusion n n n 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 > 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. 23

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