Modified Shannon’s Capacity for Wireless Communication [Speaker's Corner

Abstract

In 1948, Claude Shannon published "A Mathematical Theory of Communication", which laid the foundation of modern digital communications, where the maximum channel capacity is given by the famous Shannon’s equation: C = B x log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (1+P/N) where B is the channel bandwidth, P is the signal power transmitted, and N is the noise floor of the system (or channel). Normally, P/N is also defined as the signal-to-noise ratio (SNR). This equation is known as the Shannon limit. If the conducting losses are ignored for wired communication, then all of the power from the sender will be received by the receiver. Thus, the transmitter and the corresponding receiver will both have the same maximum channel capacity, as given above. Although the equation was given for pointto-point wired communication, this equation has been widely adopted in the literature for modern wireless and mobile communication, including the coming 5G and beyond. Now 6G is under discussion worldwide, and the equation is still being applied in the literature as the golden rule to determine the maximum channel capacity for 5G and beyond. The equation can be modified to show the maximum channel capacity for wireless communications It is argued that instead of using the normal noise floor N in Shannon's equation, received power strength P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> and the minimum detectable power level of a receiver P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> are used, which allows the inclusion of both the path-loss effect and the hardware requirements, which makes it more practical. Thus, the new definition of the channel capacity is linked with the system parameters so that the entire wireless system can be optimized from the hardware point of view. With a given required minimum SNR and the maximum power ceiling, the channel capacity can be determined. In addition, the modified Shannon's equation shows that higher-order modulations result in lower capacity if the maximum transmitting power is fixed.