Prove the Minimal Delay of Complex Orthogonal Space-Time Block Code by Hadamard Matrix

The complex orthogonal designs with maximal rates and minimal delays is an open problem for space-time block code. Maximal rate can effectively transmit symbols to the lonest distance in the space dimension; and minimal delay is the least decoding delay in the time dimension. Many authors have observed that regarding the complex orthogonal designs for space-time block codes with the antennas n = 4k (k ∈ N), its minimal delay is the same as that for n = 4k - 1. However none was able to prove it. In this paper, we use the characteristics of Hadamard matrix to prove this property to fulfill this vacancy.