Receiving multiport antennas using regression analysis: A Case study for physical limits of linear modelling in EM sensing

Open-circuit voltage estimation of a receiving Multiport Antenna (MPA) is potentially possible if and only if incident electric field intensity on it comes in a number, by one direction, greater than one under the constraints in regression analysis. This is occurring because one direction will cause a projection matrix that cannot be determined. Linearity comes as a limit at two electric field intensities and proved as inherent in the case of greater than two in number electric field intensities. The afore-mentioned is stated using the proper regression model concluding to the following facts: a) the residual for an MPA with greater than two incident electric intensities on them and b) zero theoretical residual for 2 incident electric field intensities on MPA as expected. These findings are forming a general proof for the limits of linearity since the procedure behind them is possible to apply to other equations that describe physical phenomena.