Closed-form expressions for the symbol error probability of 3-D OFDM

In this letter, closed-form expressions for the symbol error probability of 3-D orthogonal frequency division multiplexing in additive white Gaussian noise channel are derived. When a 3-D 4-ary constellation is used as signal mapper, we calculate the upper and the lower bound for the error probability, and also provide its approximation. Since decision boundaries of 8- ary constellation form an extended regular hexahedron, an exact symbol error probability can be computed. It is verified that the theoretical error probabilities are very close to or almost the same as simulation results.

I. Introduction

Both signal mapper and discrete Fourier transform (DFT) are the core elements of an orthogonal frequency division multiplexing (OFDM). In a general OFDM system, 2-D signal constellations such as multilevel phase-shift keying (MPSK) and quadrature amplitude modulation (QAM) are used as signal mapper. IDFT modulates a set of complex subchannel signals to produce an OFDM symbol in the time domain. To reduce computational complexity, a fast Fourier transform (FFT) algorithm is generally employed.