Standard form for balanced complex orthogonal design

Space-time block codes based on complex orthogonal design (COD) have been widely investigated for their attractive performance. Adams et al. constructed a class of balanced complex orthogonal designs (BCODs) which have rate 1/2 and decoding delay 2^m when n = 2m-1 or 2m. Comparing with the maximum rate CODs, the growth of decoding delay of BCODs is decreased from factorial order (2m:m+1) to exponential order 2^m, while the rate is decreased from (m+1)/2m to 1/2. In this paper, we focus on the study of the structure of BCODs. In order to keep the symmetric structure unchanged, we impose restrictions on the equivalence operations. Then by using the restricted narrow equivalence operations, we construct four submatrixes sequences for any BCOD, and then prove that all of these submatrixes have some symmetric characteristics in common. Based on those symmetric characteristics, we immediately define a standard form for BCODs. And finally we reach the conclusion that, for any BCOD, we can make it into another standard form BCOD under equivalence operations.