  We give a new definition of a L\'{e}vy driven CARMA random field, defining it
as a generalized solution of a stochastic partial differential equation (SPDE).
Furthermore, we give sufficient conditions for the existence of a mild solution
of our SPDE. Our model finds a connection between all known definitions of
CARMA random fields, and especially for dimension 1 we obtain the classical
CARMA process.
