Waveform design for higher-level 3D constellation mappings and its construction based on regular tetrahedron cells

Abstract

In this paper, we propose a generalized method of high-level three dimensional (3D) signal constellation mapping based on the most basic 3D structure: regular tetrahedron cells. First, we redefined the waveform design, the normalized frequency and phase modulation for the geometric construction of tetrahedron cells. Then, the new topology of tetrahedron cells based on the traditional lattice 3D constellation were constructed. Especially, we focused on the two essential types, 8-ary and 16-ary based on tetrahedron cells on behalf of the odd and even carry bits, respectively. The available range and closed forms of the symbol error probability (SEP) were derived to increase the effectiveness and safety of wireless communication systems. Normalized minimum Euclidean distance and average number of neighbors were utilized to measure the performance against Gaussian noise. Simulation results showed that the proposed 8-ary and 16-ary 3D constellation mapping obtained 0.25 and 0.5 dB gain at the SEP of 10⁻⁶ and 10⁻⁴, respectively, over traditional 3D lattice structure in additive white Gaussian noise (AWGN) channel.

创新点

本文提出了基于正四面体空间结构的高阶三维星座图的一般调制方式。首先, 我们重新定义了正四面体星座图的波形结构为归一化的相频调制。基于传统的三维格式结构, 我们给出了一种正四面体的维度拓展方式。为了区分奇偶比特拓展特征, 本文重点研究了8点和16点的三维星座图, 并推导出误符号率的闭式解。我们利用归一化的最小欧氏距离和相邻星座点数衡量该星座图的抗噪声性能, 并通过仿真验证了代表奇偶比特调制的8点和16点三维星座图相对于传统的三维格式结构分别获得了0.25dB和0.5dB的误符号率增益。