Probability of symbol error of OFDM system with 3-Dimensional signal constellations

In this paper, symbol error probabilities of orthogonal frequency division multiplexing (OFDM) with 3-dimensional (3-D) signal constellations over additive white Gaussian noise is computed and analyzed. We present the exact closed-form expressions of the symbol error probabilities of the OFDM system with 3-D 8-ary and 32-ary constellations. In the case of 16-ary constellation, an approximation symbol error probability is computed. The higher level 3-D constellations can be built by extension of a basic structure consisting of the regular hexahedron. Simulation result verifies that the theoretical error performance found in this paper matches well with the experimental values. It is also noted that the OFDM systems with 3-D constellation have much lower symbol error probability than general OFDM systems.