A Look at the Concept of Channel Capacity from a Maxwellian Viewpoint

Wireless communication is an active area of current research in communication technology. To assess the performance of a wireless system, one needs to quantify its ability to handle information. Typically, the performance of such systems is characterized in terms of the channel capacity. In this article, we look at the various mathematical representations of the channel capacity, and trace how they have evolved from the initial concept of entropy. Two popular mathematical representations of channel capacity involve the power and the voltage related to the incident field at the receiver. If one uses similar values for the background noise power in the two formalisms, and ensures that the transmitting and receiving antennas are matched, then the two formulas may yield similar results, even though they are functionally different. The essential point to be made here is that the channel capacity, like entropy, is an abstract mathematical number that has little connection to the electromagnetic properties of the system. However, introducing Maxwellian physics can help one interpret the channel-capacity formulas in a physically realistic way by using the vector electromagnetic equations. In electromagnetics, power is carried by the fields, and that is why the fields are fundamental in nature. In this case, a Maxwellian approach to wireless technology is not only relevant, but also vitally important. Such a formalism will correct the variety of deficiencies in the current wireless-communication literature. The primary objective of this paper is to apply the various formulas for channel capacity in a physically proper way. First, the channel capacity of any system needs to be characterized under the same input-power constraints, while simultaneously accounting for the radiation efficiency of the transmitting and receiving antennas. Second, the voltage form of the channel capacity is more useful for wireless systems than the power form, since the sensitivities of the receivers are generally characterized in terms of the received electric fields. In addition, the received power is at least two orders of magnitude larger than the background noise. Third, in a near-field scenario, it is not clear how to evaluate the power in a simple way. Consequently, we will show that the voltage form of the channel capacity, which depends only on the electric field, is always applicable to both the near and far fields. In contrast, the power form depends on the electric and magnetic fields (unless the antennas are conjugately matched). The solution of the vector electromagnetic problem also illustrates that deploying antennas near the ground yields a higher capacity than placing them on top of a high tower, away from the Earth. In addition, electrical tuning of the antennas further increases the capacity. These subtle points are generally missed by a statistical formulation. In addition, the practice of unrealistically representing antennas by point sources is devoid of any near-field effects, which require both the electric and the magnetic fields to compute the power. Examples are presented for single-input-single-output situations to illustrate the subtleties of the vector nature of the problem, which is missing in current formulations. In particular, the results of simulations of a dielectric box surrounding a receiving antenna suggest that the box enhances signals in some cases, instead of impeding line-of-sight propagation.