Rose and Wright review energy-efficient methods by which an extraterrestrial civilization might communicate over interstellar distances (1). Overall energy expenditure may not be the proper figure of merit, however. Instead, one might consider methods according to the amount of energy demanded from the civilization.
For example, page 127 of Stephen Webb’s excellent book, “If the Universe is Teeming with Aliens… Where is Everybody?,” notes two communication methods that modulate the energy output of the civilization’s star. These would not be low-energy according to Rose and Wright, because a star expends prodigious energies. Nevertheless, they would be highly advantageous because they require very little energy investment from the civilization.
Frank Drake suggested that unusual chemical elements, e.g. praseodymium, could be launched into a star to change its spectrum, causing a signal, and
Philip Morrison suggested that matter be placed in orbit around the star so it periodically obscures the star’s light output.
Both methods would be detectable at long distances, and could be modulated to give clear evidence of life (e.g. modulating in a prime number pattern). Certainly, the success of the Kepler probe proves that Morrison modulation can be detected over interstellar distances.
The comparatively low signal-bandwidth of these methods need not be a hinderance. Once a civilization is detected by such a method, an investment in higher-energy, higher-bandwidth communication is easily justified.
Thus, the best approach to interstellar communication would seem to be modulation of stellar electromagnetic emissions. Realizing this, our civilization could launch a program called “Stellar Oscillations To Observe Sentience.”
(1) Rose C, Wright G. Nature. 2004 Sep 2;431(7004):47-49. Inscribed matter as an energy-efficient means of communication with an extraterrestrial civilization. PubMed 15343327