Error probability on the orbital angular momentum detection

The orbital angular momentum (OAM) is a physical property of an electromagnetic (EM) radiation, distinct from polarization, carrying a mechanical moment. In radio frequency range, OAM can be viewed as a phase gradient on the wave front. In this paper, the problem of the detection of the orbital angular momentum (OAM) order (or topological charge) for electromagnetic (EM) radiation is addressed. The OAM order detection problem is first presented as a multiple hypothesis testing problem. The maximum likelihood test leading to the error probability on the OAM order detection in additive white Gaussian noise (AWGN) channel is derived when the transmitting and receiving arrays are perfectly aligned and misaligned. A simpler receiver based on fast fourier transform (FFT) is then presented. The performances of this receiver are then presented through extensive simulation runs for various degrees of misalignment between the transmitter and the receiver.