A general deterministic spacetime system theory of antennas suitable for the analysis and design of wireless communication links is rigorously developed using the recently introduced antenna current Green's function formalism. We provide the first complete derivation of the antenna spatio-temporal response to a delta source using only electromagnetic Green's functions, effectively eliminating all field and current distributions in the final expressions. While the theory works well in both space and time, it puts into sharper focus how the spatio-temporal structure of electromagnetic processes imposes restrictions on the signal processing capabilities of antenna systems by constraining the allowable mathematical form of the effective impulse response of the global wireless communication link. It is shown that the antenna current Green's functions of both the receive and transmit terminals, plus the propagation environment Green's functions, are the only quantities needed to obtain the single input-single output link response function in closed form. One of the results deduced from the theory is that an exact impulse response cannot be ascribed to an arbitrary antenna in general, but may be approximated for many applications. The theory can be deployed for future antenna systems research to boost up spectral efficiency (without increasing physical bandwidth) by directly incorporating electromagnetic knowledge into the design of the communication system's signal processing functions.royalsocietypublishing.org/journal/rspa Proc. R. Soc. A 475: 20180699 treated in parallel [1][2][3][4][5][6][7]. For example, some recent book-length treatments of such interdisciplinary topic appear to address issues pertinent to a unified electromagnetic/communicationtheoretic formalism [5][6][7]. Several research articles have also been published in this domain, e.g. see [2,3] (a non-exhaustive list; however, see [5] for an extensive literature on electromagnetic information theory). Owing to the increasing complexity of 5G and other future communication systems, it is no longer possible to separate the study of the physical layer to purely signal processing and purely electromagnetic parts. Indeed, each process is now expected to feed on the other, and for that reason, there is a need to reexamine the subject at the broadest and most comprehensive theoretical level possible, especially in light of some recent advances in fundamental research. As a step toward this goal, the antenna current Green's function (ACGF) [7] was recently introduced as a frequency-domain spatial transfer function method capable of providing an alternative approach to applied electromagnetics more in line with signal processing and communication theory [8,9]. The ACGF formalism is a complete exact electromagnetic generalization of the idea of the 'impulse response' of antenna systems. It was formulated recently in [7-25] using a hybrid approach incorporating functional analysis, distribution theory, differential geometry into electromagnetic theory. Although t...