Open-Loop Analysis of a Nonlinearly Modified Gardner Synchronizer

Recovery of the symbol timing with Gardner synchronizers is frequently suggested in the open literature, not only because of its simplicity from the computational point of view, but also because knowledge about carrier and data is not needed. However, the Gardner detector suffers from the drawback that its slope vanishes more and more, if waveforms with little or no excess bandwidth have to be processed. In this letter, it is shown that a simple squaring unit ahead of the Gardner detector makes the tracking loop work under highly bandwidth-efficient conditions. To this end, the detector characteristic (S-curve) is derived in closed form such that the linearized recovery loop can be designed appropriately. In particular with respect to PSK schemes, it is demonstrated that the modified Gardner synchronizer is a serious candidate for systems, where bandwidth efficiency is a major figure of merit.