Error Performance of Multidimensional Lattice Constellations-Part II: Evaluation over Fading Channels

TL;DR

This paper extends the analysis of multidimensional lattice constellations' error performance to fading channels, deriving new bounds for frame error probability that aid in understanding their limits in practical wireless communication scenarios.

Contribution

It introduces novel analytical expressions and bounds for the frame error probability of lattice constellations over Nakagami-m and block fading channels, expanding previous AWGN-focused work.

Findings

Proposed Sphere Upper Bound (SUB) for fading channels.

Developed Multiple Sphere Bounds (MSLB and MSUB) for block fading.

Numerical results show bounds are tight and useful for performance assessment.

Abstract

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.