A Computer Signal Processing Approach for the Shapiro Fourth Test of the General Theory of Relativity

摘要

I. I. Shapiro has proposed a new test of the general theory of relativity. The test involves the measurement of a discrepancy (of about 30 km) in the measured range of Mercury or Venus as the direct path from the earth to the planet passes through the strong gravitational field of the sun. Such measurements are now made possible by means of modern high-power radars as the Haystack Experimental Facility. Still the signal-to-noise ratios available at superior conjunction preclude sufficiently accurate range measurements by the ranging techniques used to date in radar astronomy. The primary difficulties arise from the doppler spreading due to planetary rotation and range spreading due to the radar depth of a rough planet. R. Price suggested using measurements made of the planetary range-doppler profile for comparison in a two-dimensional cross correlation. He showed that such a procedure yields for the power levels available at Haystack, an overall ranging accuracy of better than 1.5 km (9 Msec in round trip travel time), as opposed to a value of 6 km obtainable with an optimum choice of transmitter pulse length and a matched filter receiver. The Fourier analyses required for obtaining a detailed range-doppler profile require a tremendous amount of computation time. This report describes a table look-up approach that effects a Fourier transform without the use of multiplication. A time saving of at least 10:1 is achieved over a straightforward Fourier analysis. It is thus possible to perform the Fourier analysis and other functions such as pulse compression analysis (also described in detail) in real time on the computer facilies available on site. (Author)