doc.: ieee 802.11-07/2114r0 submission july 2007 semih serbetli, philipsslide 1 rotated and scaled...
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July 2007
Semih Serbetli, Philips
Slide 1
doc.: IEEE 802.11-07/2114r0
Submission
Rotated and Scaled Alamouti CodingDate: 2007-07-17
Name Affiliations Address Phone email Semih Serbetli Philips High Tech Campus
WY5.017 Eindhoven, The Netherlands
+314027449755 [email protected]
Frans Willems Philips, Tech. Univ. of Eindhoven
High Tech Campus WY5.017A Eindhoven, The Netherlands
+314027449766 [email protected]
Authors:
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July 2007
Semih Serbetli, Philips
Slide 2
doc.: IEEE 802.11-07/2114r0
Submission
Abstract• This presentation introduces a new space-time coding scheme for 2 transmit antenna
systems to the 802.11 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.
July 2007
Semih Serbetli, Philips
Slide 3
doc.: IEEE 802.11-07/2114r0
Submission
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?
July 2007
Semih Serbetli, Philips
Slide 4
doc.: IEEE 802.11-07/2114r0
Submission
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.
TimeSpace
*
12
*
21
21 xx
xxxx
RX
Transmission 1 Transmission 2
July 2007
Semih Serbetli, Philips
Slide 5
doc.: IEEE 802.11-07/2114r0
Submission
Simplest Re-transmission: Ordinary Repetition is bad!
• When we retransmit (repeat) codewords, each symbol xk from such a codeword (x1, x2 , …, xK) 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!
July 2007
Semih Serbetli, Philips
Slide 6
doc.: IEEE 802.11-07/2114r0
Submission
Scaled Repetition
July 2007
Semih Serbetli, Philips
Slide 7
doc.: IEEE 802.11-07/2114r0
Submission
Name and Capacity Comparison
• Name is Scaled Repetition since we scale a symbol by a factor (2 here) and then compensate (add D2(α)= +5 or -5) to obtain a symbol from A4-PAM
July 2007
Semih Serbetli, Philips
Slide 8
doc.: IEEE 802.11-07/2114r0
Submission
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.
July 2007
Semih Serbetli, Philips
Slide 9
doc.: IEEE 802.11-07/2114r0
Submission
Alamouti Coding• Two complex symbols s1 and s2 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.
July 2007
Semih Serbetli, Philips
Slide 10
doc.: IEEE 802.11-07/2114r0
Submission
16-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
July 2007
Semih Serbetli, Philips
Slide 11
doc.: IEEE 802.11-07/2114r0
Submission
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).
July 2007
Semih Serbetli, Philips
Slide 12
doc.: IEEE 802.11-07/2114r0
Submission
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))
July 2007
Semih Serbetli, Philips
Slide 13
doc.: IEEE 802.11-07/2114r0
Submission
Performance Comparison
The Golden code wins. Rotated and Scaled Alamouti is only slightly worse. Alamouti coding is roughly 2 dB worse.
July 2007
Semih Serbetli, Philips
Slide 14
doc.: IEEE 802.11-07/2114r0
Submission
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!
July 2007
Semih Serbetli, Philips
Slide 15
doc.: IEEE 802.11-07/2114r0
Submission
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 – 1458.
• 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 – 1096.
• 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 – 1436.
• 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. 2003.
July 2007
Semih Serbetli, Philips
Slide 16
doc.: IEEE 802.11-07/2114r0
Submission
Single Receive Antenna Performance
July 2007
Semih Serbetli, Philips
Slide 17
doc.: IEEE 802.11-07/2114r0
Submission
Low Complexity Decoding
Two ways of decoding the scaled and rotated Alamouti coding! Choose the best way depending on the channel realization
July 2007
Semih Serbetli, Philips
Slide 18
doc.: IEEE 802.11-07/2114r0
Submission
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)