Estimation of the orbital angular momentum order using a vector antenna in the presence of noise

The use of the orbital angular momentum (OAM) may be of interest in the radio-frequency spectrum notably to multiple the number of communication channels. Another way to use this property is to transmit data through the OAM state (Q-bit) of the transmitted wave. In a noiseless environment, the local estimation of the OAM order can be realized by means of a vector antenna that measures the 6 components of the electromagnetic field. In this article, we study the sensitivity to noise of this estimation. The OAM wave is generated via Laguerre-Gauss beams. For several mode orders, signal-to-noise ratio and distances to the transmitter, we perform a statistical analysis from which we obtain a probability of error in the order estimation. We demonstrate that the local estimation of the OAM order is very sensitive to noise, especially in the far-field zone.