doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 1 Rotated and Scaled Alamouti Coding Date: Authors: Notice: This document has been prepared to assist IEEE It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) 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 and Procedures: The contributor is familiar with the IEEE 802 Patent Policy and Procedures, including the statement "IEEE standards may include the known use of patent(s), including patent applications, provided the IEEE receives assurance from the patent holder or applicant with respect to patents essential for compliance with both mandatory and optional portions of the standard." Early disclosure to the Working Group of patent information that might be relevant to the standard is essential to reduce the possibility for delays in the development process and increase the likelihood that the draft publication will be approved for publication. Please notify the Chair as early as possible, in written or electronic form, if patented technology (or technology under patent application) might be incorporated into a draft standard being developed within the IEEE Working Group. If you have questions, contact the IEEE Patent Committee Administrator at.

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 2 Abstract This presentation introduces a new space-time coding scheme for 2 transmit antenna systems to the community. Alamouti-coding [1998] used in 11n for 2x2 MIMO systems is based on repetition- retransmission. Shown to be suboptimum for multiple receive antennas (Diversity-Multiplexing Tradeoff) [Tse-2004] We propose to use instead of ordinary repetition so-called "scaled repetition" together with rotation. It is demonstrated that the rotated and scaled Alamouti code has a hard-decision performance which is only slightly worse than that of the Golden code [Belfiore- 2005], the best known 2x2 space-time code. Decoding the Golden code requires an exhaustive search over all codewords, while our rotated and scaled Alamouti code can be decoded with an acceptable complexity.

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 3 Motivation STBCs are attractive to increase the reliability of the wireless transmissions –Effective but simple schemes are needed! –Alamouti coding Effective Low decoding complexity Optimum ? –Yes, for 1 receive antenna –No, for multiple receive antennas  in 11n at least 2 receive antennas is mandatory! –Is there any better space-time block code for 2x2 MIMO systems? Golden codes [Belfiore-2005] Tilted QAM [Wornell-2003] –What about decoding complexity? Exhaustive ML search –Is there any better space-time block code for 2x2 MIMO systems with low decoding complexity?

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 4 Space-Time Block Codes and Retransmission Schemes Coding in both space and time Space-time block codes can be viewed as a re-transmission scheme where at each time interval, you repeat the same information content by sending a different spatially formatted version The methodologies used in re-transmission schemes can be used for designing new space-time block codes. Time Space RX Transmission 1Transmission 2

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 5 Simplest Re-transmission: Ordinary Repetition is bad! When we retransmit (repeat) codewords, each symbol x k from such a codeword (x 1, x 2, …, x K ) is actually transmitted and received twice, i.e., Simple optimal receiver structure The ordinary repetition capacity for a single repetition is Ordinary repetition is not the best way to retransmit!

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 6 Scaled Repetition

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 7 Name and Capacity Comparison Name is Scaled Repetition since we scale a symbol by a factor (2 here) and then compensate (add D 2 (α)= +5 or -5) to obtain a symbol from A 4-PAM

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 8 Results for Re-transmission Schemes Scaled repetition is definitively superior to ordinary repetition if the SNR is not very small. The "capacity" for scaled repetition is only slightly smaller than the basic capacity. The difference comes from the fact that uniform inputs are used instead of Gaussians.

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 9 Alamouti Coding Two complex symbols s 1 and s 2 are transmitted in transmission 1, and in transmission 2 these symbols are more or less repeated. Advantages: –Orthogonal structure  Low complexity decoding –Full diversity Disadvantage –The symbols transmitted in the second transmission are ordinary repetitions of the symbols in the first transmission.

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide QAM Scaled and Rotated Alamouti Coding Use Scaled Repetition to improve upon the Alamouti scheme. With we transmit the signals The rotation angle  adds an additional degree of freedom in the code design

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 11 Best Rotation A good value for the rotation angle can be found using the Determinant Criterion [Tarokh et.al.-1998] The maximum value of the minimum determinant occurs at  =1.028 (for 16-QAM).

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 12 Hard Decision Performance We have compared the Message-Error-Rate Pr(Ĉ≠C) for several R=4 space-time codes. For each "test" we generate a message (8-bit) and 2x2 MIMO channel matrix with i.i.d. complex Gaussian entries. The decoder performs ML-decoding (exhaustive search, 256 alternatives). We have considered: –Spatial Multiplexing –Alamouti Coding [1998] –Tilted QAM [Wornell et al.-2003] –Rotated and Scaled Alamouti –Golden Code [Belfiore et al.-2005] –Telatar (Pr(Capacity(H)<4))

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 13 Performance Comparison The Golden code wins. Rotated and Scaled Alamouti is only slightly worse. Alamouti coding is roughly 2 dB worse.

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 14 Conclusions & Remarks ROTATED and SCALED ALAMOUTI CODING PROVIDES –Better Message-Error-Rate performance than the ALAMOUTI CODE for systems with multiple receive antennas. –Good Message-Error-Rate performance close to the GOLDEN CODE. REMARKS: –Single receive-antenna behavior: as good as Alamouti! –Receiver schemes with low decoding complexity and providing practically no loss w.r.t. ML decoding exist!

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 15 References S. M. Alamouti, A simple transmit diversity technique for wireless communications, IEEE Journal on Selected Areas in Communications, Vol. 16(8), Oct. 1998, pp.1451 – L. Zheng and D. N. C. Tse, Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels, IEEE Transactions on Information Theory,Vol. 49(5), May 2003 pp.1073 – J. C. Belfiore, G. Rekaya and E. Viterbo, The golden code: a 2x2 full- rate space-time code with nonvanishing determinants, IEEE Transactions on Information Theory, Vol. 51(4), April 2005, pp.1432 – H. Yao and G. W. Wornell, Achieving the Full MIMO Diversity- Multiplexing Frontier with Rotation-Based Space-Time Codes, in Proc. Allerton Conf. Comm., Contr., and Computing, (Illinois), Oct

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 16 Single Receive Antenna Performance

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 17 Low Complexity Decoding Two ways of decoding the scaled and rotated Alamouti coding!  Choose the best way depending on the channel realization

doc.: IEEE /2114r0 Submission July 2007 Semih Serbetli, PhilipsSlide 18 Low Complexity Decoder Performance Alamouti: Double slicing operation Golden, tilted QAM : 256 symbol combinations for exhaustive search Rotated and Scaled Alamouti Coding: suboptimum 16 double slicing (due to the structure of the new code) suboptimum smart slicing (method1, method 2)