Matrix-D 2x2 Space Time Code Document Number: IEEE S802.16m-08/330 Date Submitted: May 5, 2008 Source: S. Sezginer, H. Sari, B.Muquet, F. Buda, S. Labonte,

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Matrix-D 2x2 Space Time Code Document Number: IEEE S802.16m-08/330 Date Submitted: May 5, 2008 Source: S. Sezginer, H. Sari, B.Muquet, F. Buda, S. Labonte, J. Gosteau Sequans 19 Le Parvis de la Defense Paris La Defense CEDEX France Venue: Session #55, Macao Base Contribution: 16m SDD Purpose: Discuss and adopt for 16m. Notice: This document does not represent the agreed views of the IEEE Working Group or any of its subgroups. It represents only the views of the participants listed in the “Source(s)” field above. It is offered as a basis for discussion. It is not binding on the contributor(s), who reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor grants a free, irrevocable license to the IEEE to incorporate material contained in this contribution, and any modifications thereof, in the creation of an IEEE Standards publication; to copyright in the IEEE’s name any IEEE Standards publication even though it may include portions of this contribution; and at the IEEE’s sole discretion to permit others to reproduce in whole or in part the resulting IEEE Standards publication. The contributor also acknowledges and accepts that this contribution may be made public by IEEE Patent Policy: The contributor is familiar with the IEEE-SA Patent Policy and Procedures: and. Further information is located at and.

Matrix-D Full-rate, full-diversity 2x2 STC with low decoder complexity for 16m Serdar Sezginer et al. The authors acknowledge the funding provided by the European Commission for this work, performed in the framework of the FP7 WiMAGIC project.

2x2 MIMO Schemes M : Constellation size We propose “Matrix-D” –Essentially achieves the performance of Matrix-C in any channel –With a much lower optimum receiver complexity Achieves the diversity-multiplexing tradeoff frontier (constant coding gain) Transmission of symbols with the same average power at each channel use The single Matrix-D provides the robustness of Matrix A on degraded channels, and the capacity of Matrix-B on favorable channels Matrix-D eliminates the need for MIMO feedback MatrixRateTx DiversityOptimum Rx Complexity A12Lowest B2-Low C22high (M 4 ) D (new)22Medium (M 2 )

Matrix-D Matrix-D coding matrix: ( s 1, s 2, s 3, s 4 ) are the data symbols. a, b, c, d are complex-valued design parameters to be determined for best performance We can show (see contribution) that the following parameter set yields –optimum ML detection with reduced complexity, –equal power at each transmitted symbol, –maximum diversity gain and –maximized coding gain

Matrix-D Receiver Matrix D is an ingenious superposition of two A Matrices! –For given ( s 3, s 4 ) symbols ( s 1, s 2 ) are orthogonal –For given ( s 1, s 2 ) symbols ( s 3, s 4 ) are orthogonal –This property allows reducing the minimum distance calculation of optimum ML detection from M 4 to M 2. Two stage optimum ML receiver: –First, detect ( s 1, s 2 ) for all combinations of symbol pair ( s 3, s 4 ) –From the resulting symbol sets, find the symbol set ( s 1, s 2, s 3, s 4 ) minimizing the distance over the M 2 alternatives. Similar complexity reduction in any ML-like suboptimal detector –Decreases the search from 4 symbols to 2 symbols

Recommendation We recommend that Matrix-D be adopted in 16m because it offers the best achievable performance (that of Matrix C) with affordable receive complexity.