Randomized Isometric Linear-Dispersion Space-Time Block Coding for the DF Relay Channel

This article presents a randomized linear-dispersion space-time block code for decode-andforward synchronous relays. The coding matrices are obtained as a set of columns (or rows) of randomly-generated Haar-distributed unitary matrices. With respect to i.i.d.-generated codes, this particular isometric structure reduces the intersymbol interference generated within each relay. The gain over i.i.d. codes in terms of spectral efficiency is analyzed for both the LMMSE and the ML receivers under the assumption of frequency-flat quasi-static fading. In this setting, the spectral efficiency is a random quantity, since it depends on the random coding matrices. However, it is proven that the spectral efficiency converges in probability to a deterministic quantity when the dimensions of the matrices tend to infinity while keeping constant their ratio, i.e. the coding rate α. Consequently, when the random coding matrices are large enough, the presented system behaves as a deterministic one...

• Type: Journal
• Year: 2012
• Where: TSP
• Authors: David Gregoratti, Walid Hachem, Xavier Mestre
• Keywords: Artificial Intelligence, Free Probability Theory, Rectangular Matrices, TSP 2012, Unitary Matrices