This article deals with synchronization in the Envelope Elimination and Restoration (EER) type of transmitter architecture. To illustrate the performances of such solution, we choose to apply this architecture to a 64 carriers 16QAM modulated OFDM. We first introduce the problematic of the realisation of a highly linear transmitter.We then present the Envelope Elimination and Restoration solution and draw attention to its major weakness: a high sensitivity to desynchronization between the phase and envelope signal paths. To address this issue, we propose an adaptive synchronization algorithm relying on a feedback loop, a LeastMean Square formulation and involving an interpolation step. It enables the correction of delay mismatches and tracking of possible variations. We demonstrate that the quality of the interpolator has a direct impact on Error Vector Magnitude (EVM) value and output spectrum. Implementation details are provided along with an analysis of the behaviour and performances of the method. We present HPADS and Matlab simulation results and then focus on the enhancement of the transmitter performances using the proposed algorithm.