Performance of a Conventional Costas Loop having a Phase Imbalance between In-phase and Quadrature Arms

Abstract

The present paper examines the effect of having a quadrature arm signal with relative phase—(90+α)° to the in-phase arm signal in a Costas loop. Here the additional phase shift a, is a nonzero, positive or negative quantity, arising due to the imperfect design of the phase shifter used in the practical system. First, the tracking response of such a non-ideal Costas loop is examined for a noise-free input. Next its acquisition behavior is studied in the delayed case. Lastly, performance of the loop is examined in the face of noisy inputs.