It is now widely recognized that multiple antennas will figure prominently in future wireless communications systems, since they can significantly boost the channel capacity, as well as lower the probability of error, of a wireless communications link. However, before the above promise can be realized in a practical communications system, there are several key research challenges that must be addressed. This research studies several of the information-theoretic, coding-theoretic, and signal processing challenges encountered, as well as the impact of integrating their solutions into a multi-user wireless network. A common thread encountered throughout is that the tools developed, as well as the results obtained, have implications well beyond multi-antenna communications--both in terms of the introduction of new mathematical methods, as well as in terms of their applicability to more general communication problems. The first research challenge addressed is information-theoretic: the actual channel capacity of a multi-antenna wireless link is known only under certain idealized conditions. For most realistic conditions, the channel capacity is unknown and it is not clear how it depends on the speed of the fading, the number of antennas, and the SNR. Nor is it clear what the optimal transmission strategies should be and what the performance of training-based schemes are. This research will focus on these problems for continuously- and block-fading channels, where the analysis appears to be tractable and where the theory of random matrices plays a major role. The second challenge is that of designing space-time codes that deliver on the high data rates promised by theory, have good error performance, and that lend themselves to efficient encoding and decoding. Compared to conventional codes, the added spatial dimension adds a whole new twist to the code design problem, and a variety of information-theoretic, linear-algebraic, and group-theoretic ideas play a prominent role. The signal processing research challenge is to devise algorithms that are efficient, so that all the processing can be done in real time. Recent work by the researcher has analytically demonstrated that, for a wide range of rates and SNRs, polynomial-time maximum-likelihood decoding of several classes of space-time codes is possible. This research will fully pursue the implications of this result, both in terms of the design of new algorithms and codes, as well as in terms of understanding the tradeoffs between maximum-likelihood performance and computational complexity.
This project was originally funded as a CAREER award, and was converted to a Presidential Early Career Award for Engineers and Scientists (PECASE) award in May 2004.