Transform order division multiplexing

Multiplexing in the fractional Fourier domain (FRFD) only transmits the signals in a single direction in the time-frequency plane and the transform order of the fractional Fourier transform (FRFT) is not used sufficiently. In this paper, we apply the perfect reconstruction transmultiplexer in the FRFD to develop the transform order division multiplexing (TODM), which transmits the original information in the multidirections in the time-frequency plane simultaneously. The proposed TODM systems can be divided into two types. One needs the multitransmission of the original information while the other needs the modifications of the original information by the interpolation and the inverse discrete FRFT. The performance analysis of the TODM systems is also presented, including the system capacity, the reconstruction accuracy, the security, and the limitation. Compared with the multiplexing in the FRFD, the TODM is more flexible and the security of the system is highly strengthened. Finally, simulation results confirm the obtained analytical results.