A review of the Wigner distribution function approach to analyse electromagnetic field

Wigner distribution function approach to analyze MIMO communication within a waveguide

“…The starting point for our discussion is to construct a channel matrix for a MIMO setup within an enclosure, where the antennas are mounted on plane surfaces, such as with patch antennas. The channel matrix is expressed in terms of a transfer operator which in turn is used to construct a Hermitian kernel, the Hermitian kernel is a propagated correlation function [9] from the source. The next logical step would be to exploit the relationship between the CF and the WDF.…”

“…The Eq. (7) is a model obtained in [9] which gives us a propagator rule that helps us analyse wave propagation in free space. The Eq.…”

“…5 and Fig. 6 can be obtained by performing a simple coordinate rotation [9] and then performing a Fourier transform with respect to the displacement variable as in Eq. (22) .…”

“…In the paper we see that the source function in the transmitting domain and the resulting wave in the receiving domain are expanded using complete sets of basis functions which we have adopted for surfaces in this paper. However, we do not address the issue of channel capacity maximization here as we mainly focus on modelling of wave propagation within an enclosure by a statistical model which is an extension of our previous work on wave propagation in freespace [5] , [6] , [7] , [8] , [9] .…”

“…The propagation of correlation functions (CFs) and the use of Wigner distribution function (WDF) allows us to transform CFs of currents or emitted fields into functions of phase space co-ordinates as seen in [9] . We have also seen that the CF-based approach has proved an effective tool to predict radiation from printed circuit boards (PCBs) in [5] .…”