# Orthogonal Spacetime Block Code (OSTBC)[1]

## Description

The codewords are \(T\times n\) matrices as defined for spacetime codes, with the additional condition that columns of the coding matrix are orthogonal. The parameter \(n\) is the number of channels, and \(T\) is the number of time slots.

## Protection

If the matrix \(C-C'\), where \(C\) and \(C'\) are distinct codewords, has minimum rank \(b\), the code has diversity order \(bn_R\) [2; Sec. 28.2.1], where \(n_R\) is the number of receivers. The maximum possible diversity order is \(nn_R\).

## Rate

The greatest rate which can be achieved is \(\frac{n_0+1}{2n_0}\), where either \(n=2n_0\) or \(n=2n_0-1\) [3].

## Decoding

Maximum-likelihood decoding can be achieved with only linear processing [4].

## Parent

- Spacetime block code (STBC) — The same construction without the constraint that the codeword matrices are orthogonal.

## Child

## References

- [1]
- S. M. Alamouti, “A simple transmit diversity technique for wireless communications”, IEEE Journal on Selected Areas in Communications 16, 1451 (1998) DOI
- [2]
- F. Oggier, "Spacetime Coding." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
- [3]
- Xue-Bin Liang, “Orthogonal designs with maximal rates”, IEEE Transactions on Information Theory 49, 2468 (2003) DOI
- [4]
- V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block coding for wireless communications: performance results”, IEEE Journal on Selected Areas in Communications 17, 451 (1999) DOI

## Page edit log

- Victor V. Albert (2022-04-21) — most recent
- Richard Barney (2022-04-05)

## Cite as:

“Orthogonal Spacetime Block Code (OSTBC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/orth_spacetime_block