A method for correcting the aim of a beam-waveguide microwave antenna compensates for the beam aberration that occurs during radio tracking of a target that has a component of velocity transverse to the line of sight from the tracking station. The method was devised primarily for use in tracking of distant target spacecraft by large terrestrial beam-waveguide antennas of NASA's Deep Space Network (DSN). The method should also be adaptable to tracking, by other beam-waveguide antennas, of targets that move with large transverse velocities at large distances from the antennas.

The aberration effect arises whenever a spacecraft is not moving along the line of sight as seen from an antenna on Earth. In such a case, the spacecraft has a cross-velocity component, which is normal to the line-of-sight direction. In order to obtain optimum two-way communication, the uplink and downlink beams must be pointed differently for simultaneous uplink and downlink communications. At any instant of time, the downlink (or receive, R_{x}) beam must be pointed at a position where the spacecraft was 1/2-round-trip light time (RTLT) ago, and the uplink (or transmit, T_{x}) beam must be pointed where the spacecraft will be in 1/2 RTLT (see figure). In the case of a high-gain, narrow-beam antenna such as is used in the DSN, aiming the antenna in other than the correct transmitting or receiving direction, or aiming at a compromise direction between the correct transmitting and receiving directions, can give rise to several dB of pointing loss.

In the present method, the antenna is aimed directly at the apparent position of the target, so that no directional correction is necessary for reception of the signal from the target. Hence, the effort at correction is concentrated entirely on the transmitted beam. In physical terms, the correction is implemented by moving the transmitting feed along a small displacement vector chosen so that the direction of the transmitted beam is altered by the small amount needed to make the beam point to the anticipated position of the target at the anticipated time of arrival of the transmitted signal at the target.

The angular and linear coordinates mentioned in the following sentences are defined in the figure. The angular separation between the transmitting and receiving beams is described in terms of the separation angle a and the clock angle b. The transmitting feed is mounted on an X-Y translation table. The problem is to compute the polar coordinates r and f of the amount by which the transmitting feed must be displaced in the X-Y plane to move the direction transmitting beam, away from the direction of the receiving beam, by the amounts of the required angular separation. The problem becomes one of computing the r and f needed to obtain the required a and b. (Then the required X and Y are calculated from r and f by simple trigonometry.)

The algorithm used to control the X-Y table implements a closed-form representation of the coordinates r and f as functions of the coordinates a and b. This representation can be obtained by experimentation and/or physical-optics-based, computational-simulation studies of electromagnetic scattering by the pertinent antenna optics configuration for various combinations of r and f. The representation is of the general form

r = c_{1}a + c_{2}a^{2} and

f = f_{F} - b + q_{EL} - q_{AZ}- *n*Π/2 radians,

where c_{1} and c_{2} are coefficients determined by the computational study; f_{F} is related to the feed position on the floor; q_{EL }and q_{AZ} are the elevation and azimuth angles, respectively; and *n*is one of the integers between -1 and +2, determined through measurements of beam offsets obtained at known feed offsets.

*This work was done by Manuel Franco, Stephen Slobin, and Watt Veruttipong of Caltech for *NASA's Jet Propulsion Laboratory*. For further information, access the Technical Support Package (TSP) *free on-line at www.techbriefs.com/tsp* under the Computers/Electronics category.*

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