  This is the second part of a two-part series of papers, where the error
performance of multidimensional lattice constellations with signal space
diversity (SSD) is investigated. In Part I, following a novel combinatorial
geometrical approach which is based on parallelotope geometry, we have
presented an exact analytical expression and two closed-form bounds for the
symbol error probability (SEP) in Additive White Gaussian Noise (AWGN). In the
present Part II, we extend the analysis and present a novel analytical
expression for the Frame Error Probability (FEP) of multidimensional lattice
constellations over Nakagami-m fading channels. As the FEP of infinite lattice
constellations is lower bounded by the Sphere Lower Bound (SLB), we propose the
Sphere Upper Bound (SUB) for block fading channels. Furthermore, two novel
bounds for the FEP of multidimensional lattice constellations over block fading
channels, named Multiple Sphere Lower Bound (MSLB) and Multiple Sphere Upper
Bound (MSUB), are presented. The expressions for the SLB and SUB are given in
closed form, while the corresponding ones for MSLB and MSUB are given in closed
form for unitary block length. Numerical and simulation results illustrate the
tightness of the proposed bounds and demonstrate that they can be efficiently
used to set the performance limits on the FEP of lattice constellations of
arbitrary structure, dimension and rank.
