Physical modeling of communication systems in information theory

It is common in information theoretic channel models to rely on the average squared Euclidean norm of the channel input as being proportional to transmit power. Likewise, it is common to assume noise that is additive, Gaussian, and white. It is a legitimate question to ask, whether such a modeling approach has enough degrees of freedom to capture the physical constraints that are imposed on implementations of a communication system. In this paper, we show that in many, though not all, situations it is indeed possible to obtain a complete physical model, while nevertheless sticking with average squared Euclidean norm as power, and white Gaussian noise. Our systematic approach works in two steps. First, all channel inputs and outputs are replaced by ports, which are defined by two conjugated variables (like voltage and current). By this multi-port modeling approach, we can obtain a complete physical model. Secondly, we introduce linear transformations between the inputs and outputs of the information theoretic channel model on the one hand, and the physical inputs and physical outputs of the communication system, on the other. This approach gives us enough degrees of freedom to obtain a complete information theoretic model, which correctly reflects the physical constraints that are imposed upon the communication system by its environment. We apply the proposed approach to a multi-antenna communication system, and show that it is indeed possible that the channel capacity of multi-antenna systems can grow super-linearly with the number of antennas for large signal to noise ratios.