# The application of orthogonal designs to wireless communication

Conference Paper

We introduce space-block codzng, a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signal perturbed by noise. Decoding is achieved in a simple way using the orthogonal structure of tlie space-block code and maximum likelihood decoding algorithm is totally based on linear processing at the receiver. Space-black codes are designed to achieve the maximum diversity gain of transmit and receive antennas with the constraint of having a simple decoding algorithm. It is shown that the classical mathematical framework of orthogonal designs can be applied to construct cliannel codes which have a simple decoding algorithm, while providing tlie full spatial diversity order. Space-block codes constructed in this way only exist for few sporadic values of n and therefore there is a need for a new mathematical theory. In this light, we introduce the theory of Generalzzed Deszgns which provides codes for both real and complex constellations for any number of transmit antennas. Using this theory, we construct space-block codes that achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For any arbitrary complex constellation such as PSK and QAM, we construct space-block codes that achieve half of the maximum possible transmission rate for any number of transmit antennas. For tlie specific cases of two, three and four transmit antennas, we provide space-block codes that achieve respectively the whole, 3/4 and 3/4 of maximum possible transmission rate using arbitrary complex constellations. The best trade-off between tlie decoding delay and the number of transmit antennas is also computed and it is shown that the designed codes are optimal in this sense as well. Various fundamental problems are posed which are both inatliematically appealing and have immediate application to the design of a physical layer for wireless communication systems.

### Full Text

### Duke Authors

### Cited Authors

- Tarokh, V; Jafarkhani, H; Calderbank, AR

### Published Date

- January 1, 1998

### Published In

- 1998 Information Theory Workshop, Itw 1998

### Start / End Page

- 46 - 47

### International Standard Book Number 10 (ISBN-10)

- 0780344081

### International Standard Book Number 13 (ISBN-13)

- 9780780344082

### Digital Object Identifier (DOI)

- 10.1109/ITW.1998.706408

### Citation Source

- Scopus