Electromagnetic Degrees of Freedom in 2-D Scattering Environments

The electromagnetic (EM) degrees of freedom (DOF) of a noise limited system in two dimensions with random multiple scattering is evaluated numerically following a rigorous DOF theory first developed by Miller and Piestun for optical systems. The received EM fields are efficiently calculated by fast multipole method (FMM), and the ensemble average of the DOF number is obtained through Monte Carlo simulation technique. The results show that the average EM DOF number is strongly dependent on the sizes of the transmit volume, the receive volume, and the scattering region. In particular, the average number of DOF generally increases with both the transmit and receive volumes. However this increase is a non-linear process and will not continue indefinitely. As the transmit volume or the receive volume expands, an upper-bound of the average DOF number is expected due to noise effects. Due to the lack of criteria for choosing a critical parameter involved in Miller and Piestun´s original DOF definition, a modified definition is also considered. Even though the modified definition is SNR dependent, it provides a clearer physical meaning of the DOF. In addition, the simulations also suggest that it might not be appropriate to ignore the influence of the SNR on the DOF number when the system concerned is of general form and relative small, where no critical point of the channel quality can be identified. A logarithmic dependence of the DOF number on the total source power is demonstrated for such systems