Derivation of Gardner's Timing-Error Detector from the Maximum Likelihood Principle

Abstract

In a recent paper [1], Gardner described a new timing-error detector for sampled receivers. The detector derives timing information without decision direction from a BPSK or QPSK signal sampled at rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2/T</tex> (symbol interval <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> ). We will show how this detector can be derived from the maximum likelihood principle, and thus give insight into the nature of the algorithm.