Bounds on symbol error rate for additive isotropic generalised Gaussian noise channels

Novel lower and upper bounds on the symbol error rate of the minimum distance detector are derived for signal constellations impaired by additive isotropic (i.e. spherically symmetric) generalised Gaussian noise (GGN). The proposed bounds depend only on the constellation dimensionality, the shape parameter of the GGN distribution and the maximum and minimum distances between the constellation points. They are expressed in terms of the well-known Gamma and upper incomplete Gamma functions. An asymptotic analysis of the proposed bounds establishes the sphere hardening effect, which plays a prominent role in the design of high-performance modulation systems, in the case of additive isotropic GGN channels.