Scarce-resource capacity sharing in cognitive radio environments: a new game theoretical model

This paper proposes a novel model of the input impedance of a circular-loop antenna based on wave equations. A circular-loop antenna is equivalent to uniform parallel double wires with losses and a short circuit load. The characteristic impedance, the propagation coefficient and the inductance, capacitance and resistance per unit length of the uniform parallel double wires with losses can first be expressed as closed solutions, and the mathematical model of the input impedance of the circular-loop antenna can then be derived naturally from the wave equations. Comparison of the data curve from this model with curves from simulations and experiments show that they are similar; however, some discrepancies are observed, and are attributed to the estimation error of the radiation resistance of the circular-loop antenna. As long as the circular-loop antenna is made from an isotropic material and its size remains uniform, the equivalent method is valid electrically for both small- and large-sized circular-loop antennas.