STBC BASED STTC CODES OPTIMIZED DESIGNS FOR THREE TRANSMIT ANTENNA SYSTEMS CANCES Jean-Pierre XLIM - Dépt. C 2 S 2 UMR CNRS 6172 ENSIL Parc ESTER - BP LIMOGES Cedex

- Introduction - Set Partitioning criteria and SOSTTC Construction - Three transmit antenna case - Simulation Results - Conclusion Presentation Summary

Scope of the study : - Improving the performances of STTC codes by using STBC based STTC codes - For two transmit antennas, Alamouti’s scheme exhibits the maximum diversity gain - Different Alamouti’s scheme are available without constellation expansion  Building trellis with STBC component codes enables to obtain STTC design with higher diversity gain Necessity to define construction criteria to define the states of these particular STTC codes => set partitioning using the determinant criterion  SOSTTC codes Introduction

Scope of the study : - Different kinds of Alamouti’s scheme with two transmit antennas -  belongs to the transmit constellation alphabet if we don’t want to expand the transmit constellation, - L = 4 for QPSK transmit constellation => 4 possible STBC matrix construction with  = 0,  and 3.  /2

1. STBC design criteria : - Let denote the STBC transmission matrix as G and the difference of the transmission matrices for codewords c 1 and c 2 as D(c 1, c 2 ). - The code is full diversity when D(c 1, c 2 ) is full rank for every pair of distinct codewords c 1 and c 2 - Miminum of det A(c 1, c 2 ) with corresponds to the coding gain => Coding Gain Distance between c 1 and c 2 Set Partitioning

2. Application to Alamouti’s scheme : Using we obtain : with Set Partitioning

2. Application to Alamouti’s scheme : This yields to : - Maximization of this determinant is equivalent of optimizing the coding gain within each coset. Using this criterion, we obtain a powerful tool for set partitioning

3. Set Partitioning examples : Set Partitioning Set partitioning for a) BPSK, b) QPSK and c) 8-PSK

Set Partitioning 4. Three Transmit Antenna case : We use the following basic STBC structure : Angles  and  are necessary to optimize the minCGD value within each coset. For example, when second symbols are equal, we obtain :

Set Partitioning 4. Three Transmit Antenna case : - Optimizing the CGD within each coset yields to the following set partitioning

Set Partitioning 4. Three Transmit Antenna case (QPSK):

Set Partitioning 4. Three Transmit Antenna case (8-PSK):

SOSTTC Construction 1. Several degrees of freedom are available (2 Tx antennas): - Different rotation angles can be affected to each subset. - It is possible to connect similar subsets to each other provided that there is a sufficient number of available angles to be affected to each state

SOSTTC Construction 2. SOSTTC Construction Examples (2 Tx): - minCGD = 16 - minCGD = 64

3. Three transmit antenna case : To obtain a full diversity code it is necessary to separate the cosets by the use of unitary transform matrices of the following form : We affect a different unitary transform matrix to each coset SOSTTC Construction

3. Three transmit antenna case : example of a 16 state trellis with QPSK

Decoding Quasi-Orthogonal STBC based STTC codes 1. Decoding : - Assuming quasi-static flat Rayleigh fading channels between each pair of transmit-receive antenna. h 1 h 2 h 3 : three complex Gaussian random variables with zero mean and variance 0.5 per complex dimension

1. Decoding : We form the auxiliary quantities : Then we use MRC technique : Decoding Quasi-Orthogonal STBC based STTC codes

1. Decoding : Summing equations 2 and 3 yields to : Decoding Quasi-Orthogonal STBC based STTC codes

1.Decoding : Detection rule => Minimization of (Branch metric computation in the Viterbi algorithm) Suboptimum metric : Decoding Quasi-Orthogonal STBC based STTC codes

Simulation Results - Three transmit antenna case (quasi-orthogonal design) 3 Tx 1 Rx, FER Performance Comparison with optimized STTC QPSK mod.

Simulation Results - Three transmit antenna case (quasi-orthogonal design) 3 Tx 2 Rx, FER Performance Comparison with optimized STTC QPSK mod.

Simulation Results - Three transmit antenna case (quasi-orthogonal design) 3 Tx 1 Rx, FER Performance Comparison with optimized STTC 8-PSK mod.

Simulation Results - Three transmit antenna case (quasi-orthogonal design) 3 Tx 2 Rx, FER Performance Comparison with optimized STTC 8-PSK mod.

Conclusion - Construction of STBC based STTC codes based on the optimization of the determinant criterion - Slight but real improvement when we compare their FER performances with the best known STTC. (Better CGD values)