MIT Department of Electrical Engineering & Computer Science

Space-Time Block Codes

Dr. Vahid Tarokh
AT&T Labs

Thursday, March 30, 2000
2:45 PM (refreshments 2:30)
Grier Room, Room 34-401B
EECS Special Seminar

Abstract

Space-Time block coding is a new method for communication over wireless channels using multiple transmit antennas. It is now adapted for use in third generation wireless systems by WCDMA and CDMA 2000 standardization bodies. Not only these codes support an extremely simple maximum likelihood detection algorithm based only on linear processing at the receiver, but also they can be used for multiple transmit antenna differential detection.

We will first consider a multiple transmit/receive antenna wireless communication system. Data is encoded using a space-time 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. Maximum likelihood decoding is achieved in a simple way through de-coupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. Space-time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm.

The classical mathematical framework of orthogonal designs (Radon-Hurwitz Theory) will be applied to construct space-time block codes. It will be shown that space-time block codes constructed in this way only exist for few sporadic values of $n$. Subsequently, a generalization of orthogonal designs will be shown to provide space-time block codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For an arbitrary complex constellation such as PSK and QAM, space-time block codes are designed that achieve 1/2 of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three and four transmit antennas, space-time block codes are designed that achieve respectively all, 3/4 and 3/4 of maximum possible transmission rate using arbitrary complex constellations. The best trade-off between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well.

Finally, some simulation results demonstrating the performance of these codes will be presented.