False lock performance of Shuttle Costas loop receivers

Abstract

The false (sideband) lock problem in Shuttle Costas loop receivers, in the presence of noise, is assessed. False lock margin is defined depending on symbol signal-to-noise ratio rather than in the absence of noise. Closed-form results are given for the case where the arm filters of the Costas loop are one-pole Butterworth filters as used in the Shuttle receivers. However, the approach taken is also general enough to cover filters of arbitrary characteristics. As part of the development of the false lock margin, it is shown that the false lock phenomenon of the squaring loop is identical to that of the Costas loop.