Improved performance of four dimensional 8-PSK-TCM using fractional Fourier transform

Abstract

We introduce and evaluate the performance of reliable fractional Fourier transform (FRFT) blocks both in the emitter and the receiver side for the four-dimensional 8-PSK-TCM previously designed for the NASA CCSDS standard. This new FRFT block makes use of weak inter correlation observed between signal and Gaussian noise in a particular FRFT plane and consequently allows near-optimal MMSE filtering. In addition, four orthogonal FRFT planes are also wisely chosen for attenuating the inter-symbols interference and create effective spatial multidimensionality instead of simple symbol concatenation used in conventional multi-dimensional TCM. Complex impulse shape functions are no longer needed since simple rectangle function can supply for the need of band limited spectral density. Simulation result shows 8 dB coding gain for BER= 10-4 by comparison to the standard four-dimensional 8-PSK-TCM. In addition, the method is as complex as the well known FFT.