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It has been proven<ref name="COD">{{cite journal|author=Xue-Bin Liang|title=Orthogonal Designs With Maximum Rates|journal=IEEE Transactions on Information Theory|pages=2468–2503|volume=49|issue=10|month=October | year=2003|doi=10.1109/TIT.2003.817426}}</ref> that the highest rate any <math>n_T</math>-antenna code can achieve is
: <math>r_
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|author=Kejie Lu, Shengli Fu, and Xiang-Gen Xia|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|month=December | year=2005|doi=10.1109/TIT.2005.858943}}</ref>
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