The need to transmit at high data rates with better performance has recently motivated research on signal processing and coding for multiple-input multiple-output (MIMO) channels. As multiple antenna systems have large capacity, design criteria have been set up for space-time signals used in these systems through minimizing the pairwise word error probability [11][19]. Orthogonal and algebraic designs allowed to achieve very high data rates with full diversity and very good performance in uncoded systems and quasi-static fading environments [8][17][2].
Precoding signals for fading channels, which is well known in single antenna transmissions, has been rediscovered for multiple antenna channels. Battail was the first to suggest rotations to combat channel fluctuations [1]. The pioneering work on multi-dimensional rotated modulations achieved in the nineties, such as [3][7][4], opened the way for the study of multi-dimensional rotations (i.e. linear unitary precoders) in MIMO channels.
Rotations in single antenna systems have been designed by classical algebraic criteria, except for orthogonal transforms proposed by Rainish which are based on the minimization of the cut-off rate [16]. Also, it has been shown in [15] that random rotations perform as good as algebraic rotations in a high-diversity high-dimensional environment. In [13], the authors proposed an information theoretical tool to design space-time codes. They designed codes that maximize the ergodic capacity of the channel, but such space-time codes perform poorly on a non-ergodic block fading channel. Furthermore, space-time signal modulations must be combined to error-correcting codes in order to achieve optimal performance in the information theoretical sense.
In [5][10], the authors considered bit-interleaved coded modulations [6] for space-time coding (ST-BICM). They showed that quasi-optimal global ML performance of the coded modulation is achieved by imposing specific constraints (called genie conditions) on the structure of the space-time precoder. The ML performance is attained in practice after some iterations in a joint detection/decoding process at a high signal-to-noise ratio.
We propose in this article full-rate rotations that minimize the outage probability of a MIMO system in block fading environments. The paper is organized as follows: section II presents the system model and notations, section III describes different design techniques for space-time codes, including the outage minimization criterion. Computer simulation results and conclusions are drawn in the last section.

Joseph Jean Boutros 2005-05-07