The Reduction of Energy Consumption in Deep Space Communications Through Transmitter Programming

An analytic and quantitative study is performed of the programming of transmitter power output to minimize the energy consumption required to maintain a specified minimal information rate from an astronautical vehicle to a terrestrial receiving system over the trajectory of the vehicle. The representative trajectories used as a basis of discussion include an idealized, rectilinear trajectory, deep-space probe with variable terminal ranges, and solar circular orbits at variable radii in the plane of the ecliptic. For the first, consideration of the integral of the admissible lower bound to the radiated power shows that the minimal energy consumption is five eights of that resulting from a constant power output program. An optimal two-stage program is shown to be an efficient approximation to the idealized one of continuous power variation. The transmitter-receiver relative range at transfer from low to high power output and the resultant energy consumption are each seen to be approximately 0.7 of their respective maxima. For the orbital case, the economies resulting from an optimal program are seen to be moderately functionally dependent upon the orbital radius, but independent of the sense of motion of the vehicle within its orbit. As before, a satisfactory two-stage fixed transmitter program may be defined, in which the optimal time of transition between stages is independent of the orbital radius and sense of rotation. In passage from inferior to superior conjunction, the optimal transition between the two stages is at CT and, in passage from superior to inferior conjunction, at (1-C)T, where C = 0.42 and T denotes the time interval involved in the change from inferior to superior conjunction, and conversely. Variational methods are used to determine a lower bound to the energy consumption if the totality of information output is specified and the system is assumed to be operating at the maximum channel capacity corresponding to the instantaneous power radiation level. It is shown that if the mission duration and the totality of information communicated are both large, independently of the trajectory the resultant minimal energy consumption corresponds to the difference of that of a constant power output system and one programmed to yield a fixed signal power density at the receiver. Lastly, generally applicable contours are provided which display the relative energy consumptions involved in the optimal and approximating power radiation programs, and the transmitter-receiver separations at the time that switching of the transmitter power level is to be accomplished for both categories of trajectories.