Information lossless space-time coding for Rayleigh faded multiple access systems

In this paper we consider multiple access systems affected by flat Rayleigh fading, where users and access point are equipped with multiple antennas. The exploitation of some of the MIMO potentials relies necessarily on space-time coding. However, such a processing may induce severe losses in terms of achievable information rates. In this paper we prove necessary and sufficient conditions ensuring that the space-time coding is information lossless, in the sense that it achieves the ergodic capacity region of the multiple access system. In particular, the information lossless property is guaranteed if each user makes use of a full-rate Trace-Orthogonal Design, that is a linear space-time code whose encoding matrices are orthogonal with respect to the trace inner product. Noteworthy, different users can also adopt the same set of encoding matrices.