Extension to Shannon’s channel capacity —the theoretical proof

Shannon\´s channel capacity equation, a very important theory, defines the maximum transmission rate of communication systems. However, a new communication scheme, named ultra narrow band, is said to "break" Shannon\´s limit. During the research, a special kind of filters having different signal and noise bandwidth was found, therefore, the aim of our study was to extend Shannon\´s channel capacity formula in the case of different signal and noise bandwidth. Considering the conversion of time and space domain, a new capacity formula was deduced based on MIMO theory. Results indicated that extension equation is in good agreement with Shannon\´s channel capacity equation under the assumption of the same signal and noise bandwidth, but in different signal and noise bandwidth, capacity values calculated by this extension is larger than ones by Shannon\´s equation, which is the reason for "breaking" Shannon\´s capacity in ultra narrow band system.