The particular technology that I am interested mostly is in the Unitary Space-Time Codes (UST). In this technology, the information is encoded in blocks spanning space and time. In the simplest case, we could think of N antennas with a sequence of N pulses, so that the information block can be represented as an NxN complex matrix. It is mathematically convenient to use unitary matrices, so the name UST is justified in this case.
Inside the UST field I am paying attention to the Cayley encoding [1,2,3] because it seems to be elegant, simple and easy to understand.
- Cayley Differential Unitary Space-Time Codes by B. Hochwald, B. Hassibi
- Unitary space-time modulation via Cayley transform by Y Jing, B Hassibi
- Yindi Jing Thesis
- Representation Theory for High-Rate Multiple-Antenna Code Design by B. Hassibi, B. Hochwald, A. Shokrollahi, W. Sweldens
- Differential Unitary Space-Time Modulation by B. Hochwald, W. Sweldens
- Random Matrices for Wireless Communications
A. Tulino, S. Verdu (at Princeton)
- Circuits for Wireless Communications: Selected Readingsby Banlue Srisuchinwong (Editor), Wanlop Surakampontorn (Editor), Sawasd Tantaratana (Editor)
- Space-time coding for broadband wireless communications by By Georgios B. Giannakis, Zhiqiang Liu
- Random Matrices For Wireless Communications I
- Random Matrices For Wireless Communications II
More applications of group theory in engineering can be found at