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

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.