# Spacetime block code (STBC)[1]

## Description

In a space-time block code, \(n\) spatially separated channels transmit symbols in \(T\) time slots. These symbols can be arranged in a \(T\times n\) matrix where the columns correspond to the channels, and the rows correspond to the time slots. The codewords \(\{X\}\) are \(T\times n\) matrices such that the codeword difference matrices have rank \(n\), and \(\min_{X\neq 0}\det(XX^*)\) is maximized.

## Protection

Provides protection against errors due to thermal noise and destructive interference arising from traversing an environment with scattering, reflection, and/or refraction.

## Realizations

## Parent

- Spacetime code (STC) — Spacetime codes also use spatial and temporal diversity, but do not necessarily use blocks as codewords.

## Child

- Orthogonal Spacetime Block Code (OSTBC) — The same construction without the constraint that the codeword matrices are orthogonal.

## Zoo code information

## 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]
- R. Vidhya Lavanya and M. Madheswaran, “Wimax (IEEE 802.16 m) system based on space time block code and discrete multiwavelet transform and implementation in FPGA”, Telecommunication Systems 56, 327 (2013). DOI
- [3]
- S. P. Alex and L. M. A. Jalloul, “Performance Evaluation of MIMO in IEEE802.16e/WiMAX”, IEEE Journal of Selected Topics in Signal Processing 2, 181 (2008). DOI

## Cite as:

“Spacetime block code (STBC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spacetime_block