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Alamouti code[1]

Description

The simplest OSTBC, with \(n=2\) transmitting antennas, \(m=1\) receiving antennas, and \(t=2\) uses.

The unitary coding matrix is \begin{align} \begin{pmatrix}c_{1} & c_{2}\\ -c_{2}^{\star} & c_{1}^{\star} \end{pmatrix}~, \tag*{(1)}\end{align} where \(c_i\) are complex numbers, and where \(\star\) denotes complex conjugation.

Rate

The only OSTBC with full rate, \(k = mt = 2\).

Realizations

Wireless standards since: 3G, LTE, LTE-Advanced, and 5G.Wireless communication: IEEE 802.11n, IEEE 802.11ad, IEEE 802.11ay, etc.

Member of code lists

Primary Hierarchy

Classical Domain
Matrix Kingdom
Matrix-based codeECC
Spacetime code (STC)
Spacetime block code (STBC)
Orthogonal Spacetime Block Code (OSTBC)
Parents
Orthogonal Spacetime Block Code (OSTBC)
Linear STCSTC ECC
Alamouti code

References

[1]
S. M. Alamouti, “A simple transmit diversity technique for wireless communications”, IEEE Journal on Selected Areas in Communications 16, 1451 (1998) DOI
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Zoo Code ID: alamouti

Cite as:
“Alamouti code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/alamouti
BibTeX:
@incollection{eczoo_alamouti, title={Alamouti code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/alamouti} }
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Permanent link:
https://errorcorrectionzoo.org/c/alamouti

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/matrices/spacetime/alamouti.yml.