Degrees of freedom per communication node

The classical definition of degrees of freedom (DoF) deals with the degrees of a communication channel or multiple communication channels in the limit of high SNR. This can be interpreted as the number of independent streams that can be sent in each communication channel in the high SNR regime. We introduce the concept of DoF per communication node where at a transmitting node the DoF is the number of independent dimensions that can be used for transmission and at each receiver node the DoF is the number of independent dimensions that can be used for receiving data signals. In general the communication channels or links in a network can be divided into two sets: the interfering channels and the intended channels; hence, the network may be considered as an overlay of two networks, respectively: the interfering network and data-intended network. In the classical form, DoF is defined for channels in the data-intended network. We illustrate a new interpretation of DoF that depends only on the interfering network and can be formalized in full generality based on degrees of freedom per node in the network. While the classical DoF has been studied generally in the context of interference and X-channels, the per node DoF concept generalizes the idea to other possible networks. Using this generalized notion of DoF, this paper provides new results on DoF for different networks and also makes a connection to the classical definition of DoF defined in interference and X-channels.