Application of student´s t and behrens-fisher distributions to the analysis of enhanced noise after zero-forcing frequency domain equalisation

Since many years the Gaussian or normal distribution has been a useful tool to model data observations in fields as physics or astronomy. In communication systems, for instance, this distribution is widely used to model thermal noise. However, there exist many natural physical phenomena that exhibit tails decay following a power law that cannot be modelled by the classical Gaussian distribution. In many of these cases, Student´s t distributions can be useful for modelling these kind of data because they allow heavy tails which are more realistic. This study provides a brief introduction to those distributions and their convolutions, which are distributed according to the Behrens-Fisher distributions. The goal is to highlight the potential application of non-Gaussian distributions to the analysis of communication systems. With this purpose, the authors present their work applying those distributions to describe the enhanced noise when zero-forcing (ZF) equalisation is used to compensate the effects of a selective fading Rayleigh channel. Obtained results allows the analysis of enhanced noise in three different scenarios: an orthogonal frequency division multiplexing (OFDM) transmission, an OFDM-based relay network and a single carrier frequency division multiple access (SC-FDMA) transmission.