This paper deals with the performance of the fractional delay estimator in the joint complex amplitude / delay estimation algorithm dedicated to digital Tx leakage compensation in FDD transceivers. Such transceivers are affected from transmitter-receiver signal leakage. Combined with non linearity of components in the received path, it leads to a pollution in the baseband signal. The baseband polluting term depends on the equivalent Tx leakage channel, modeling leakages and the received path. We have proposed in [7, 8] a joint estimation of the complex gain and the fractional delay and derived asymptotic performance of the complex gain estimator, that showed the necessity of the fractional delay estimation. In this paper, we propose a comprehensive study of the fractional delay estimation algorithm and its analytic performance. The study is based on the analysis of the S-curve and loop noise variance of the timing error detector, from which an approximation of the asymptotic performance of the joint estimation algorithm is derived.