Novel Modulation Recognition for WFRFT-Based System Using 4th-Order Cumulants

Abstract

We present a novel modulation recognition for weighted-type fractional Fourier transform (WFRFT)-based systems using the fourth-order cumulants. First, the constellation characteristics of the basic digital modulations ASK, PSK, and QAM are analyzed, and the corresponding relationships between the neighboring constellation points' distance and the constellation size are deduced. Second, the closed-form expressions of the fourth-order cumulants (C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">42</sub> ) for the WFRFT-based systems with ASK, PSK, and QAM are derived. Finally, through the first- and second-order derivatives of the C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">42</sub> , we prove that the optimal WFRFT order α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> can be obtained through the minimization of the C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">42</sub> . The simulation results show that the novel recognition for the WFRFT-based system is feasible and can reach an accuracy of almost 90% when energy per bit-to-noise power spectrum density ratio (E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) is greater than 6.