A combinatorial geometrical approach to the error performance of multidimensional finite lattice constellations

We present a novel combinatorial geometrical approach for evaluating the performance of multidimensional finite lattice constellations in Additive White Gaussian Noise (AWGN). More specifically, we present an analytical expression for the exact symbol error probability (SEP) of multidimensional signal sets, which is then used to derive a tight closed-form lower bound of the SEP, named Multiple Sphere Lower Bound (MLSB). Simulations are used to compare the proposed bound with the performance of various lattice constellations. It is clearly demonstrated that the MSLB can be efficiently used in finite lattice constellations, with arbitrary structure, dimension and rank. Furthermore, it can be easily extended to the case of fading channels, where multidimensional signal sets are commonly used to combat fading degradation.