Space–time block code: Difference between revisions

Revision as of 21:10, 29 January 2023

Revision as of 15:47, 5 February 2023

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: <math>r_\max = \frac{n_0 + 1}{2n_0},</math>

where <math>n_T = 2n_0</math> or <math>n_T = 2n_0 - 1</math>, if no linear processing is allowed in the code matrix (the above maximal rate proved in<ref name="COD"/> only applies to the original definition of orthogonal designs, i.e., any entry in the matrix is <math>0, c_i, -c_i, c_i^*,</math>, or <math>-c_i^*</math>, which forces that any variable <math>c_i</math> can not be repeated in any column of the matrix). This rate limit is conjectured to hold for any complex orthogonal space-time block codes even when any linear processing is allowed among the complex variables.<ref name="bounds" /> Closed-form recursive designs have been found.<ref>{{cite journal|author1=Kejie Lu |author2=Shengli Fu |author3=Xiang-Gen Xia |name-list-style=amp |title=Closed-Form Designs of Complex Orthogonal Space-Time Block Codes of Rates (k+1)/(2k) for 2k-1 or 2k Transmit Antennas|journal=IEEE Transactions on Information Theory|pages=4340–4347|volume=51|issue=12|date=December 2005|doi=10.1109/TIT.2005.858943|doi-access=free}}</ref>

==Quasi-orthogonal STBCs==

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The orthogonality criterion only holds for columns (1 and 2), (1 and 3), (2 and 4) and (3 and 4). Crucially, however, the code is full-rate and still only requires linear processing at the receiver, although decoding is slightly more complex than for orthogonal STBCs. Results show that this Q-STBC outperforms (in a bit-error rate sense) the fully orthogonal 4-antenna STBC over a good range of [[signal-to-noise ratio]]s (SNRs). At high SNRs, though (above about 22&nbsp;dB in this particular case), the increased diversity offered by orthogonal STBCs yields a better BER. Beyond this point, the relative merits of the schemes have to be considered in terms of useful data throughput.

Q-STBCs have also been developed considerably from the basic example shown.

Q-STBCs have also been developed considerably from the basic example shown. With some algebraic manipulation, it can be shown that the MIMO detection problem using <math>C_{4,1}</math> decomposes into a [[multiuser detection]] problem consisting of two virtual users using the Alamouti code, <math>C_2</math>, which permits the development of adaptive technique like [[code diversity]] that uses feedback to improve the performance of open-loop transmit diversity scheme.<ref>{{Cite journal|author1=C. W. Tan |author2=A. Robert Calderbank |name-list-style=amp |title=Multiuser Detection of Alamouti Signals|journal= IEEE Transactions on Communications|volume= 57|issue= 7|pages= 2080–2089|date=Jul 2009|doi= 10.1109/TCOMM.2009.07.070592 }}</ref>

==See also==