Abstract
The theoretical limit given by the Shannon Capacity equation has been the origin of communications systems based on the interchange between bandwidth and power. This article explores the interchange between the power spectral density and the reflections that can be generated in a communications channel, with the ultimate aim of being able to decrease the power spectral density for the same capacity. The reflections can be expressed as a number of controlled reflections or by a reflection coefficient. The channels studied show that this exchange is possible. A new model based on feedback circuits was found to represent a transmission line, which was useful to study the MISO channel formed by several transmission lines of different length. A geometric elliptic dispersion model to represent a SISO channel was studied too.
Highlights
One of the great advances in communications theory introduced by Claude Shannon is the source coding
It is possible to apply an analytic focus for finding the relationship between useful bandwidth and the transmission distance in underwater channels (Stojanovic, 2007) or for changing the transfer functions of indoor power line channels (Cárdenas, 2014)
This paper explores a possible interchange between the reflections inside the channel with Power Spectral Density (PSD) for same capacity
Summary
One of the great advances in communications theory introduced by Claude Shannon is the source coding. This fact was the principle for the development of PCM (Pulse Code Modulation) and, more recently, it was useful in technologies based in spread spectrum. The success of PCM was based in the fact of a possible interchange between bandwidth and transmission power for a certain channel capacity. This fact became in a telecommunications principle (Oliver, Pierce, & Shannon, 1948), which has continued to be discussed in advanced books (Haykin, 2014). 2007; Patzold M., 2012; Patzold & Hogstad, 2006) and a new way of transmission line modeling has been developed
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