This paper did a survey in the area of degrees of freedom (DoF) in wireless network. We give the definitions of degrees of freedom in different areas first. Then we introduce some methods used to determine the degrees of freedom in different scenario. In section IV, we discuss the applications of the degrees of freedom. We state some interesting open questions in the end of this survey.

We explore the available degrees of freedom for various multiuser MIMO communication scenarios such as the multiple access, broadcast, interference, relay, X and Z channels. For the two user MIMO interference channel, we find a general inner bound and a genie-aided outer bound that give us the exact number of degrees of freedom in many cases. We also study a share-and-transmit scheme for transm...

Low order Whitney elements are widely used for electromagnetic field problems. Higher order approximations are receiving increasing interest but their definition remains unduly complex. In this paper we propose a new simple construction for Whitney p-elements of polynomial degree higher than one that use only degrees of freedom associated to p-chains. We provide a basis for these elements on si...

When using smoothing splines to estimate a function, the user faces the problem of choosing the smoothing parameter. Several techniques are available for selecting this parameter according to certain optimality criteria. Here, we take a different point of view and we propose a technique for choosing between two alternatives, for example allowing for two different levels of degrees of freedom. T...

We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix X. Like the well-known result of Zou et al. (2007), which gives the degrees of freedom of the lasso fit when X has full column rank, we express our result in terms of the active set of a lasso solution. We extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitr...