Hawkynt

Alamouti Space-Time Block Code

First space-time block code for 2 transmit antennas. Achieves full transmit diversity with simple linear decoding. Used in 3G, 4G LTE, WiFi 802.11n. Orthogonal design: [s1 s2; -s2* s1*]. Rate 1, no bandwidth expansion. Maximum likelihood decoding with simple combining.

Properties

Property	Value
Category	Error Correction
Sub-category	Space-Time Code
Security status	🎓 Educational Only
Complexity	Intermediate
Inventor	Siavash Alamouti
Year	1998
Origin	🇺🇸 United States
Source	algorithms/ecc/alamouti-code.js

Security

Status: 🎓 Educational Only

Known vulnerabilities

Issue	Description	Mitigation
Requires 2 Transmit Antennas	Alamouti code is specifically designed for 2 transmit antennas. Extensions to more antennas require different STBC designs.	—
Channel Estimation Accuracy	Performance depends critically on accurate channel state information at the receiver. Channel estimation errors degrade diversity gain.	—
Frequency-Selective Fading	Original design assumes flat fading. OFDM is typically used to convert frequency-selective channels to multiple flat-fading subcarriers.	—

Documentation

• Alamouti’s Original Paper
• Wikipedia - Alamouti Code
• MIMO-OFDM Wireless Textbook
• IEEE 802.11n Standard
• 3GPP LTE Specifications

References

• A Simple Transmit Diversity Technique for Wireless Communications
• Space-Time Block Codes from Orthogonal Designs
• IEEE Trans. on Communications, Vol. 46, No. 10, Oct 1998

Test vectors

8 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — Alamouti encoding: [1, 0] -> [1, 0; 0, 1]

Field	Value
input	0100
expected	01000001

Vector 2 — Alamouti encoding: [0, 1] -> [0, 1; -1, 0]

Field	Value
input	0001
expected	[0,1,-1,0]

Vector 3 — Alamouti encoding: [1, 1] -> [1, 1; -1, 1]

Field	Value
input	0101
expected	[1,1,-1,1]

Vector 4 — Alamouti encoding: [-1, 1] -> [-1, 1; -1, -1]

Field	Value
input	[-1,1]
expected	[-1,1,-1,-1]

Vector 5 — Alamouti encoding: [2, -2] -> [2, -2; 2, 2]

Field	Value
input	[2,-2]
expected	[2,-2,2,2]

Vector 6 — Alamouti encoding: [0, 0] -> [0, 0; 0, 0]

Field	Value
input	0000
expected	00000000

Vector 7 — IEEE 802.11n pattern: [3, 4]

Field	Value
input	0304
expected	[3,4,-4,3]

Vector 8 — 3GPP LTE pattern: [-2, 3]

Field	Value
input	[-2,3]
expected	[-2,3,-3,-2]

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